diff options
| author |  A. Unique TensorFlower <gardener@tensorflow.org> | 2017-01-30 15:04:21 -0800 |
|---|---|---|
| committer | TensorFlower Gardener <gardener@tensorflow.org> | 2017-01-30 15:27:27 -0800 |
| commit | e2108bc52d8ad2819a99fd5eeebce19165499f73 (patch) | |
| tree | 876fc06bafe540428fa0aed157020ec80032b390 /tensorflow/g3doc | |
| parent | d0897c6eacb70bd676b637be977b221a133b932f (diff) | |
Update generated Python Op docs.
Change: 146044756
Diffstat (limited to 'tensorflow/g3doc')
9 files changed, 482 insertions, 386 deletions
diff --git a/tensorflow/g3doc/api_docs/python/contrib.distributions.md b/tensorflow/g3doc/api_docs/python/contrib.distributions.md index 12465088d4..a560fd8b93 100644 --- a/tensorflow/g3doc/api_docs/python/contrib.distributions.md +++ b/tensorflow/g3doc/api_docs/python/contrib.distributions.md @@ -10780,16 +10780,30 @@ than returning `NaN`. ### `class tf.contrib.distributions.Laplace` {#Laplace} -The Laplace distribution with location and scale > 0 parameters. +The Laplace distribution with location `loc` and `scale` parameters. #### Mathematical details -The PDF of this distribution is: +The probability density function (pdf) of this distribution is, + +```none +pdf(x; mu, sigma) = exp(-|x - mu| / sigma) / Z +Z = 2 sigma +``` -```f(x | mu, b, b > 0) = 0.5 / b exp(-|x - mu| / b)``` +where `loc = mu`, `scale = sigma`, and `Z` is the normalization constant. Note that the Laplace distribution can be thought of two exponential distributions spliced together "back-to-back." + +The Lpalce distribution is a member of the [location-scale family]( +https://en.wikipedia.org/wiki/Location-scale_family), i.e., it can be +constructed as, + +```none +X ~ Laplace(loc=0, scale=1) +Y = loc + scale * X +``` - - - #### `tf.contrib.distributions.Laplace.__init__(loc, scale, validate_args=False, allow_nan_stats=True, name='Laplace')` {#Laplace.__init__} @@ -10806,14 +10820,15 @@ broadcasting (e.g., `loc / scale` is a valid operation). of the distribution. * <b>`scale`</b>: Positive floating point tensor which characterizes the spread of the distribution. -* <b>`validate_args`</b>: `Boolean`, default `False`. Whether to validate input - with asserts. If `validate_args` is `False`, and the inputs are - invalid, correct behavior is not guaranteed. -* <b>`allow_nan_stats`</b>: `Boolean`, default `True`. If `False`, raise an - exception if a statistic (e.g. mean/mode/etc...) is undefined for any - batch member. If `True`, batch members with valid parameters leading to - undefined statistics will return NaN for this statistic. -* <b>`name`</b>: The name to give Ops created by the initializer. +* <b>`validate_args`</b>: Python `Boolean`, default `False`. When `True` distribution + parameters are checked for validity despite possibly degrading runtime + performance. When `False` invalid inputs may silently render incorrect + outputs. +* <b>`allow_nan_stats`</b>: Python `Boolean`, default `True`. When `True`, + statistics (e.g., mean, mode, variance) use the value "`NaN`" to + indicate the result is undefined. When `False`, an exception is raised + if one or more of the statistic's batch members are undefined. +* <b>`name`</b>: `String` name prefixed to Ops created by this class. ##### Raises: @@ -12129,13 +12144,28 @@ denotes expectation, and `Var.shape = batch_shape + event_shape`. ### `class tf.contrib.distributions.Normal` {#Normal} -The scalar Normal distribution with mean and stddev parameters mu, sigma. +The Normal distribution with location `loc` and `scale` parameters. #### Mathematical details -The PDF of this distribution is: +The probability density function (pdf) is, -```f(x) = sqrt(1/(2*pi*sigma^2)) exp(-(x-mu)^2/(2*sigma^2))``` +```none +pdf(x; mu, sigma) = exp(-0.5 (x - mu)**2 / sigma**2) / Z +Z = (2 pi sigma**2)**0.5 +``` + +where `loc = mu` is the mean, `scale = sigma` is the std. deviation, and, `Z` +is the normalization constant. + +The Normal distribution is a member of the [location-scale family]( +https://en.wikipedia.org/wiki/Location-scale_family), i.e., it can be +constructed as, + +```none +X ~ Normal(loc=0, scale=1) +Y = loc + scale * X +``` #### Examples @@ -12143,14 +12173,14 @@ Examples of initialization of one or a batch of distributions. ```python # Define a single scalar Normal distribution. -dist = tf.contrib.distributions.Normal(mu=0., sigma=3.) +dist = tf.contrib.distributions.Normal(loc=0., scale=3.) # Evaluate the cdf at 1, returning a scalar. dist.cdf(1.) # Define a batch of two scalar valued Normals. # The first has mean 1 and standard deviation 11, the second 2 and 22. -dist = tf.contrib.distributions.Normal(mu=[1, 2.], sigma=[11, 22.]) +dist = tf.contrib.distributions.Normal(loc=[1, 2.], scale=[11, 22.]) # Evaluate the pdf of the first distribution on 0, and the second on 1.5, # returning a length two tensor. @@ -12165,7 +12195,7 @@ Arguments are broadcast when possible. ```python # Define a batch of two scalar valued Normals. # Both have mean 1, but different standard deviations. -dist = tf.contrib.distributions.Normal(mu=1., sigma=[11, 22.]) +dist = tf.contrib.distributions.Normal(loc=1., scale=[11, 22.]) # Evaluate the pdf of both distributions on the same point, 3.0, # returning a length 2 tensor. @@ -12173,32 +12203,33 @@ dist.pdf(3.0) ``` - - - -#### `tf.contrib.distributions.Normal.__init__(mu, sigma, validate_args=False, allow_nan_stats=True, name='Normal')` {#Normal.__init__} +#### `tf.contrib.distributions.Normal.__init__(loc, scale, validate_args=False, allow_nan_stats=True, name='Normal')` {#Normal.__init__} -Construct Normal distributions with mean and stddev `mu` and `sigma`. +Construct Normal distributions with mean and stddev `loc` and `scale`. -The parameters `mu` and `sigma` must be shaped in a way that supports -broadcasting (e.g. `mu + sigma` is a valid operation). +The parameters `loc` and `scale` must be shaped in a way that supports +broadcasting (e.g. `loc + scale` is a valid operation). ##### Args: -* <b>`mu`</b>: Floating point tensor, the means of the distribution(s). -* <b>`sigma`</b>: Floating point tensor, the stddevs of the distribution(s). - sigma must contain only positive values. -* <b>`validate_args`</b>: `Boolean`, default `False`. Whether to assert that - `sigma > 0`. If `validate_args` is `False`, correct output is not - guaranteed when input is invalid. -* <b>`allow_nan_stats`</b>: `Boolean`, default `True`. If `False`, raise an - exception if a statistic (e.g. mean/mode/etc...) is undefined for any - batch member. If `True`, batch members with valid parameters leading to - undefined statistics will return NaN for this statistic. -* <b>`name`</b>: The name to give Ops created by the initializer. +* <b>`loc`</b>: Floating point tensor; the means of the distribution(s). +* <b>`scale`</b>: Floating point tensor; the stddevs of the distribution(s). + Must contain only positive values. +* <b>`validate_args`</b>: Python `Boolean`, default `False`. When `True` distribution + parameters are checked for validity despite possibly degrading runtime + performance. When `False` invalid inputs may silently render incorrect + outputs. +* <b>`allow_nan_stats`</b>: Python `Boolean`, default `True`. When `True`, + statistics (e.g., mean, mode, variance) use the value "`NaN`" to + indicate the result is undefined. When `False`, an exception is raised + if one or more of the statistic's batch members are undefined. +* <b>`name`</b>: `String` name prefixed to Ops created by this class. ##### Raises: -* <b>`TypeError`</b>: if mu and sigma are different dtypes. +* <b>`TypeError`</b>: if `loc` and `scale` have different `dtype`. - - - @@ -12436,6 +12467,13 @@ Indicates that `event_shape == []`. - - - +#### `tf.contrib.distributions.Normal.loc` {#Normal.loc} + +Distribution parameter for the mean. + + +- - - + #### `tf.contrib.distributions.Normal.log_cdf(value, name='log_cdf')` {#Normal.log_cdf} Log cumulative distribution function. @@ -12575,13 +12613,6 @@ Mode. - - - -#### `tf.contrib.distributions.Normal.mu` {#Normal.mu} - -Distribution parameter for the mean. - - -- - - - #### `tf.contrib.distributions.Normal.name` {#Normal.name} Name prepended to all ops created by this `Distribution`. @@ -12754,7 +12785,7 @@ sample. - - - -#### `tf.contrib.distributions.Normal.sigma` {#Normal.sigma} +#### `tf.contrib.distributions.Normal.scale` {#Normal.scale} Distribution parameter for standard deviation. @@ -12849,19 +12880,19 @@ denotes expectation, and `Var.shape = batch_shape + event_shape`. - - - -### `class tf.contrib.distributions.NormalWithSoftplusSigma` {#NormalWithSoftplusSigma} +### `class tf.contrib.distributions.NormalWithSoftplusScale` {#NormalWithSoftplusScale} -Normal with softplus applied to `sigma`. +Normal with softplus applied to `scale`. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.__init__(mu, sigma, validate_args=False, allow_nan_stats=True, name='NormalWithSoftplusSigma')` {#NormalWithSoftplusSigma.__init__} +#### `tf.contrib.distributions.NormalWithSoftplusScale.__init__(loc, scale, validate_args=False, allow_nan_stats=True, name='NormalWithSoftplusScale')` {#NormalWithSoftplusScale.__init__} - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.allow_nan_stats` {#NormalWithSoftplusSigma.allow_nan_stats} +#### `tf.contrib.distributions.NormalWithSoftplusScale.allow_nan_stats` {#NormalWithSoftplusScale.allow_nan_stats} Python boolean describing behavior when a stat is undefined. @@ -12882,7 +12913,7 @@ undefined. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.batch_shape(name='batch_shape')` {#NormalWithSoftplusSigma.batch_shape} +#### `tf.contrib.distributions.NormalWithSoftplusScale.batch_shape(name='batch_shape')` {#NormalWithSoftplusScale.batch_shape} Shape of a single sample from a single event index as a 1-D `Tensor`. @@ -12902,7 +12933,7 @@ independent distributions of this kind the instance represents. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.cdf(value, name='cdf')` {#NormalWithSoftplusSigma.cdf} +#### `tf.contrib.distributions.NormalWithSoftplusScale.cdf(value, name='cdf')` {#NormalWithSoftplusScale.cdf} Cumulative distribution function. @@ -12927,7 +12958,7 @@ cdf(x) := P[X <= x] - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.copy(**override_parameters_kwargs)` {#NormalWithSoftplusSigma.copy} +#### `tf.contrib.distributions.NormalWithSoftplusScale.copy(**override_parameters_kwargs)` {#NormalWithSoftplusScale.copy} Creates a deep copy of the distribution. @@ -12950,7 +12981,7 @@ intialization arguments. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.covariance(name='covariance')` {#NormalWithSoftplusSigma.covariance} +#### `tf.contrib.distributions.NormalWithSoftplusScale.covariance(name='covariance')` {#NormalWithSoftplusScale.covariance} Covariance. @@ -12994,21 +13025,21 @@ length-`k'` vector. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.dtype` {#NormalWithSoftplusSigma.dtype} +#### `tf.contrib.distributions.NormalWithSoftplusScale.dtype` {#NormalWithSoftplusScale.dtype} The `DType` of `Tensor`s handled by this `Distribution`. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.entropy(name='entropy')` {#NormalWithSoftplusSigma.entropy} +#### `tf.contrib.distributions.NormalWithSoftplusScale.entropy(name='entropy')` {#NormalWithSoftplusScale.entropy} Shannon entropy in nats. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.event_shape(name='event_shape')` {#NormalWithSoftplusSigma.event_shape} +#### `tf.contrib.distributions.NormalWithSoftplusScale.event_shape(name='event_shape')` {#NormalWithSoftplusScale.event_shape} Shape of a single sample from a single batch as a 1-D int32 `Tensor`. @@ -13025,7 +13056,7 @@ Shape of a single sample from a single batch as a 1-D int32 `Tensor`. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.get_batch_shape()` {#NormalWithSoftplusSigma.get_batch_shape} +#### `tf.contrib.distributions.NormalWithSoftplusScale.get_batch_shape()` {#NormalWithSoftplusScale.get_batch_shape} Shape of a single sample from a single event index as a `TensorShape`. @@ -13039,7 +13070,7 @@ Same meaning as `batch_shape`. May be only partially defined. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.get_event_shape()` {#NormalWithSoftplusSigma.get_event_shape} +#### `tf.contrib.distributions.NormalWithSoftplusScale.get_event_shape()` {#NormalWithSoftplusScale.get_event_shape} Shape of a single sample from a single batch as a `TensorShape`. @@ -13053,14 +13084,14 @@ Same meaning as `event_shape`. May be only partially defined. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.is_continuous` {#NormalWithSoftplusSigma.is_continuous} +#### `tf.contrib.distributions.NormalWithSoftplusScale.is_continuous` {#NormalWithSoftplusScale.is_continuous} - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.is_scalar_batch(name='is_scalar_batch')` {#NormalWithSoftplusSigma.is_scalar_batch} +#### `tf.contrib.distributions.NormalWithSoftplusScale.is_scalar_batch(name='is_scalar_batch')` {#NormalWithSoftplusScale.is_scalar_batch} Indicates that `batch_shape == []`. @@ -13077,7 +13108,7 @@ Indicates that `batch_shape == []`. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.is_scalar_event(name='is_scalar_event')` {#NormalWithSoftplusSigma.is_scalar_event} +#### `tf.contrib.distributions.NormalWithSoftplusScale.is_scalar_event(name='is_scalar_event')` {#NormalWithSoftplusScale.is_scalar_event} Indicates that `event_shape == []`. @@ -13094,7 +13125,14 @@ Indicates that `event_shape == []`. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.log_cdf(value, name='log_cdf')` {#NormalWithSoftplusSigma.log_cdf} +#### `tf.contrib.distributions.NormalWithSoftplusScale.loc` {#NormalWithSoftplusScale.loc} + +Distribution parameter for the mean. + + +- - - + +#### `tf.contrib.distributions.NormalWithSoftplusScale.log_cdf(value, name='log_cdf')` {#NormalWithSoftplusScale.log_cdf} Log cumulative distribution function. @@ -13123,7 +13161,7 @@ a more accurate answer than simply taking the logarithm of the `cdf` when - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.log_pdf(value, name='log_pdf')` {#NormalWithSoftplusSigma.log_pdf} +#### `tf.contrib.distributions.NormalWithSoftplusScale.log_pdf(value, name='log_pdf')` {#NormalWithSoftplusScale.log_pdf} Log probability density function. @@ -13147,7 +13185,7 @@ Log probability density function. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.log_pmf(value, name='log_pmf')` {#NormalWithSoftplusSigma.log_pmf} +#### `tf.contrib.distributions.NormalWithSoftplusScale.log_pmf(value, name='log_pmf')` {#NormalWithSoftplusScale.log_pmf} Log probability mass function. @@ -13171,7 +13209,7 @@ Log probability mass function. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.log_prob(value, name='log_prob')` {#NormalWithSoftplusSigma.log_prob} +#### `tf.contrib.distributions.NormalWithSoftplusScale.log_prob(value, name='log_prob')` {#NormalWithSoftplusScale.log_prob} Log probability density/mass function (depending on `is_continuous`). @@ -13190,7 +13228,7 @@ Log probability density/mass function (depending on `is_continuous`). - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.log_survival_function(value, name='log_survival_function')` {#NormalWithSoftplusSigma.log_survival_function} +#### `tf.contrib.distributions.NormalWithSoftplusScale.log_survival_function(value, name='log_survival_function')` {#NormalWithSoftplusScale.log_survival_function} Log survival function. @@ -13219,35 +13257,28 @@ survival function, which are more accurate than `1 - cdf(x)` when `x >> 1`. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.mean(name='mean')` {#NormalWithSoftplusSigma.mean} +#### `tf.contrib.distributions.NormalWithSoftplusScale.mean(name='mean')` {#NormalWithSoftplusScale.mean} Mean. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.mode(name='mode')` {#NormalWithSoftplusSigma.mode} +#### `tf.contrib.distributions.NormalWithSoftplusScale.mode(name='mode')` {#NormalWithSoftplusScale.mode} Mode. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.mu` {#NormalWithSoftplusSigma.mu} - -Distribution parameter for the mean. - - -- - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.name` {#NormalWithSoftplusSigma.name} +#### `tf.contrib.distributions.NormalWithSoftplusScale.name` {#NormalWithSoftplusScale.name} Name prepended to all ops created by this `Distribution`. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.param_shapes(cls, sample_shape, name='DistributionParamShapes')` {#NormalWithSoftplusSigma.param_shapes} +#### `tf.contrib.distributions.NormalWithSoftplusScale.param_shapes(cls, sample_shape, name='DistributionParamShapes')` {#NormalWithSoftplusScale.param_shapes} Shapes of parameters given the desired shape of a call to `sample()`. @@ -13271,7 +13302,7 @@ Subclasses should override class method `_param_shapes`. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.param_static_shapes(cls, sample_shape)` {#NormalWithSoftplusSigma.param_static_shapes} +#### `tf.contrib.distributions.NormalWithSoftplusScale.param_static_shapes(cls, sample_shape)` {#NormalWithSoftplusScale.param_static_shapes} param_shapes with static (i.e. `TensorShape`) shapes. @@ -13301,14 +13332,14 @@ constant-valued tensors when constant values are fed. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.parameters` {#NormalWithSoftplusSigma.parameters} +#### `tf.contrib.distributions.NormalWithSoftplusScale.parameters` {#NormalWithSoftplusScale.parameters} Dictionary of parameters used to instantiate this `Distribution`. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.pdf(value, name='pdf')` {#NormalWithSoftplusSigma.pdf} +#### `tf.contrib.distributions.NormalWithSoftplusScale.pdf(value, name='pdf')` {#NormalWithSoftplusScale.pdf} Probability density function. @@ -13332,7 +13363,7 @@ Probability density function. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.pmf(value, name='pmf')` {#NormalWithSoftplusSigma.pmf} +#### `tf.contrib.distributions.NormalWithSoftplusScale.pmf(value, name='pmf')` {#NormalWithSoftplusScale.pmf} Probability mass function. @@ -13356,7 +13387,7 @@ Probability mass function. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.prob(value, name='prob')` {#NormalWithSoftplusSigma.prob} +#### `tf.contrib.distributions.NormalWithSoftplusScale.prob(value, name='prob')` {#NormalWithSoftplusScale.prob} Probability density/mass function (depending on `is_continuous`). @@ -13375,7 +13406,7 @@ Probability density/mass function (depending on `is_continuous`). - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.reparameterization_type` {#NormalWithSoftplusSigma.reparameterization_type} +#### `tf.contrib.distributions.NormalWithSoftplusScale.reparameterization_type` {#NormalWithSoftplusScale.reparameterization_type} Describes how samples from the distribution are reparameterized. @@ -13390,7 +13421,7 @@ or `distributions.NOT_REPARAMETERIZED`. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.sample(sample_shape=(), seed=None, name='sample')` {#NormalWithSoftplusSigma.sample} +#### `tf.contrib.distributions.NormalWithSoftplusScale.sample(sample_shape=(), seed=None, name='sample')` {#NormalWithSoftplusScale.sample} Generate samples of the specified shape. @@ -13412,14 +13443,14 @@ sample. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.sigma` {#NormalWithSoftplusSigma.sigma} +#### `tf.contrib.distributions.NormalWithSoftplusScale.scale` {#NormalWithSoftplusScale.scale} Distribution parameter for standard deviation. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.stddev(name='stddev')` {#NormalWithSoftplusSigma.stddev} +#### `tf.contrib.distributions.NormalWithSoftplusScale.stddev(name='stddev')` {#NormalWithSoftplusScale.stddev} Standard deviation. @@ -13446,7 +13477,7 @@ denotes expectation, and `stddev.shape = batch_shape + event_shape`. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.survival_function(value, name='survival_function')` {#NormalWithSoftplusSigma.survival_function} +#### `tf.contrib.distributions.NormalWithSoftplusScale.survival_function(value, name='survival_function')` {#NormalWithSoftplusScale.survival_function} Survival function. @@ -13472,14 +13503,14 @@ survival_function(x) = P[X > x] - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.validate_args` {#NormalWithSoftplusSigma.validate_args} +#### `tf.contrib.distributions.NormalWithSoftplusScale.validate_args` {#NormalWithSoftplusScale.validate_args} Python boolean indicated possibly expensive checks are enabled. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.variance(name='variance')` {#NormalWithSoftplusSigma.variance} +#### `tf.contrib.distributions.NormalWithSoftplusScale.variance(name='variance')` {#NormalWithSoftplusScale.variance} Variance. @@ -14204,23 +14235,38 @@ denotes expectation, and `Var.shape = batch_shape + event_shape`. ### `class tf.contrib.distributions.StudentT` {#StudentT} -Student's t distribution with degree-of-freedom parameter df. +Student's t-distribution with degree of freedom `df`, location `loc`, and `scale` parameters. #### Mathematical details -Write `sigma` for the scale and `mu` for the mean (both are scalars). The PDF -of this distribution is: +The probability density function (pdf) is, ```none -f(x) = (1 + y**2 / df)**(-0.5 (df + 1)) / Z +pdf(x; df, mu, sigma) = (1 + y**2 / df)**(-0.5 (df + 1)) / Z where, -y(x) = (x - mu) / sigma -Z = abs(sigma) sqrt(df pi) Gamma(0.5 df) / Gamma(0.5 (df + 1)) +y = (x - mu) / sigma +Z = abs(sigma) sqrt(df pi) Gamma(0.5 df) / Gamma(0.5 (df + 1)) ``` -Notice that `sigma` has semantics more similar to standard deviation than -variance. (Recall that the variance of the Student's t-distribution is -`sigma**2 df / (df - 2)` when `df > 2`.) +where: +* `loc = mu`, +* `scale = sigma`, and, +* `Z` is the normalization constant, and, +* `Gamma` is the [gamma function]( + https://en.wikipedia.org/wiki/Gamma_function). + +The StudentT distribution is a member of the [location-scale family]( +https://en.wikipedia.org/wiki/Location-scale_family), i.e., it can be +constructed as, + +```none +X ~ StudentT(df, loc=0, scale=1) +Y = loc + scale * X +``` + +Notice that `scale` has semantics more similar to standard deviation than +variance. However it is not actually the std. deviation; the Student's +t-distribution std. dev. is `scale sqrt(df / (df - 2))` when `df > 2`. #### Examples @@ -14237,8 +14283,8 @@ single_dist.pdf(1.) # The first has degrees of freedom 2, mean 1, and scale 11. # The second 3, 2 and 22. multi_dist = tf.contrib.distributions.StudentT(df=[2, 3], - mu=[1, 2.], - sigma=[11, 22.]) + loc=[1, 2.], + scale=[11, 22.]) # Evaluate the pdf of the first distribution on 0, and the second on 1.5, # returning a length two tensor. @@ -14253,7 +14299,7 @@ Arguments are broadcast when possible. ```python # Define a batch of two Student's t distributions. # Both have df 2 and mean 1, but different scales. -dist = tf.contrib.distributions.StudentT(df=2, mu=1, sigma=[11, 22.]) +dist = tf.contrib.distributions.StudentT(df=2, loc=1, scale=[11, 22.]) # Evaluate the pdf of both distributions on the same point, 3.0, # returning a length 2 tensor. @@ -14261,38 +14307,40 @@ dist.pdf(3.0) ``` - - - -#### `tf.contrib.distributions.StudentT.__init__(df, mu, sigma, validate_args=False, allow_nan_stats=True, name='StudentT')` {#StudentT.__init__} +#### `tf.contrib.distributions.StudentT.__init__(df, loc, scale, validate_args=False, allow_nan_stats=True, name='StudentT')` {#StudentT.__init__} Construct Student's t distributions. -The distributions have degree of freedom `df`, mean `mu`, and scale `sigma`. +The distributions have degree of freedom `df`, mean `loc`, and scale +`scale`. -The parameters `df`, `mu`, and `sigma` must be shaped in a way that supports -broadcasting (e.g. `df + mu + sigma` is a valid operation). +The parameters `df`, `loc`, and `scale` must be shaped in a way that +supports broadcasting (e.g. `df + loc + scale` is a valid operation). ##### Args: * <b>`df`</b>: Numeric `Tensor`. The degrees of freedom of the distribution(s). `df` must contain only positive values. -* <b>`mu`</b>: Numeric `Tensor`. The mean(s) of the distribution(s). -* <b>`sigma`</b>: Numeric `Tensor`. The scaling factor(s) for the distribution(s). - Note that `sigma` is not technically the standard deviation of this +* <b>`loc`</b>: Numeric `Tensor`. The mean(s) of the distribution(s). +* <b>`scale`</b>: Numeric `Tensor`. The scaling factor(s) for the distribution(s). + Note that `scale` is not technically the standard deviation of this distribution but has semantics more similar to standard deviation than variance. -* <b>`validate_args`</b>: `Boolean`, default `False`. Whether to assert that - `df > 0` and `sigma > 0`. If `validate_args` is `False` and inputs are - invalid, correct behavior is not guaranteed. -* <b>`allow_nan_stats`</b>: `Boolean`, default `True`. If `False`, raise an - exception if a statistic (e.g. mean/mode/etc...) is undefined for any - batch member. If `True`, batch members with valid parameters leading to - undefined statistics will return NaN for this statistic. -* <b>`name`</b>: The name to give Ops created by the initializer. +* <b>`validate_args`</b>: Python `Boolean`, default `False`. When `True` distribution + parameters are checked for validity despite possibly degrading runtime + performance. When `False` invalid inputs may silently render incorrect + outputs. +* <b>`allow_nan_stats`</b>: Python `Boolean`, default `True`. When `True`, + statistics (e.g., mean, mode, variance) use the value "`NaN`" to + indicate the result is undefined. When `False`, an exception is raised + if one or more of the statistic's batch members are undefined. +* <b>`name`</b>: `String` name prefixed to Ops created by this class. ##### Raises: -* <b>`TypeError`</b>: if mu and sigma are different dtypes. +* <b>`TypeError`</b>: if loc and scale are different dtypes. - - - @@ -14537,6 +14585,13 @@ Indicates that `event_shape == []`. - - - +#### `tf.contrib.distributions.StudentT.loc` {#StudentT.loc} + +Locations of these Student's t distribution(s). + + +- - - + #### `tf.contrib.distributions.StudentT.log_cdf(value, name='log_cdf')` {#StudentT.log_cdf} Log cumulative distribution function. @@ -14668,9 +14723,9 @@ Mean. Additional documentation from `StudentT`: -The mean of Student's T equals `mu` if `df > 1`, otherwise it is `NaN`. -If `self.allow_nan_stats=True`, then an exception will be raised rather -than returning `NaN`. +The mean of Student's T equals `loc` if `df > 1`, otherwise it is +`NaN`. If `self.allow_nan_stats=True`, then an exception will be raised +rather than returning `NaN`. - - - @@ -14682,13 +14737,6 @@ Mode. - - - -#### `tf.contrib.distributions.StudentT.mu` {#StudentT.mu} - -Locations of these Student's t distribution(s). - - -- - - - #### `tf.contrib.distributions.StudentT.name` {#StudentT.name} Name prepended to all ops created by this `Distribution`. @@ -14861,7 +14909,7 @@ sample. - - - -#### `tf.contrib.distributions.StudentT.sigma` {#StudentT.sigma} +#### `tf.contrib.distributions.StudentT.scale` {#StudentT.scale} Scaling factors of these Student's t distribution(s). @@ -14967,19 +15015,19 @@ NaN, when df <= 1 - - - -### `class tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma` {#StudentTWithAbsDfSoftplusSigma} +### `class tf.contrib.distributions.StudentTWithAbsDfSoftplusScale` {#StudentTWithAbsDfSoftplusScale} -StudentT with `df = floor(abs(df))` and `sigma = softplus(sigma)`. +StudentT with `df = floor(abs(df))` and `scale = softplus(scale)`. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.__init__(df, mu, sigma, validate_args=False, allow_nan_stats=True, name='StudentTWithAbsDfSoftplusSigma')` {#StudentTWithAbsDfSoftplusSigma.__init__} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.__init__(df, loc, scale, validate_args=False, allow_nan_stats=True, name='StudentTWithAbsDfSoftplusScale')` {#StudentTWithAbsDfSoftplusScale.__init__} - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.allow_nan_stats` {#StudentTWithAbsDfSoftplusSigma.allow_nan_stats} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.allow_nan_stats` {#StudentTWithAbsDfSoftplusScale.allow_nan_stats} Python boolean describing behavior when a stat is undefined. @@ -15000,7 +15048,7 @@ undefined. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.batch_shape(name='batch_shape')` {#StudentTWithAbsDfSoftplusSigma.batch_shape} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.batch_shape(name='batch_shape')` {#StudentTWithAbsDfSoftplusScale.batch_shape} Shape of a single sample from a single event index as a 1-D `Tensor`. @@ -15020,7 +15068,7 @@ independent distributions of this kind the instance represents. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.cdf(value, name='cdf')` {#StudentTWithAbsDfSoftplusSigma.cdf} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.cdf(value, name='cdf')` {#StudentTWithAbsDfSoftplusScale.cdf} Cumulative distribution function. @@ -15045,7 +15093,7 @@ cdf(x) := P[X <= x] - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.copy(**override_parameters_kwargs)` {#StudentTWithAbsDfSoftplusSigma.copy} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.copy(**override_parameters_kwargs)` {#StudentTWithAbsDfSoftplusScale.copy} Creates a deep copy of the distribution. @@ -15068,7 +15116,7 @@ intialization arguments. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.covariance(name='covariance')` {#StudentTWithAbsDfSoftplusSigma.covariance} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.covariance(name='covariance')` {#StudentTWithAbsDfSoftplusScale.covariance} Covariance. @@ -15112,28 +15160,28 @@ length-`k'` vector. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.df` {#StudentTWithAbsDfSoftplusSigma.df} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.df` {#StudentTWithAbsDfSoftplusScale.df} Degrees of freedom in these Student's t distribution(s). - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.dtype` {#StudentTWithAbsDfSoftplusSigma.dtype} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.dtype` {#StudentTWithAbsDfSoftplusScale.dtype} The `DType` of `Tensor`s handled by this `Distribution`. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.entropy(name='entropy')` {#StudentTWithAbsDfSoftplusSigma.entropy} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.entropy(name='entropy')` {#StudentTWithAbsDfSoftplusScale.entropy} Shannon entropy in nats. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.event_shape(name='event_shape')` {#StudentTWithAbsDfSoftplusSigma.event_shape} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.event_shape(name='event_shape')` {#StudentTWithAbsDfSoftplusScale.event_shape} Shape of a single sample from a single batch as a 1-D int32 `Tensor`. @@ -15150,7 +15198,7 @@ Shape of a single sample from a single batch as a 1-D int32 `Tensor`. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.get_batch_shape()` {#StudentTWithAbsDfSoftplusSigma.get_batch_shape} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.get_batch_shape()` {#StudentTWithAbsDfSoftplusScale.get_batch_shape} Shape of a single sample from a single event index as a `TensorShape`. @@ -15164,7 +15212,7 @@ Same meaning as `batch_shape`. May be only partially defined. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.get_event_shape()` {#StudentTWithAbsDfSoftplusSigma.get_event_shape} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.get_event_shape()` {#StudentTWithAbsDfSoftplusScale.get_event_shape} Shape of a single sample from a single batch as a `TensorShape`. @@ -15178,14 +15226,14 @@ Same meaning as `event_shape`. May be only partially defined. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.is_continuous` {#StudentTWithAbsDfSoftplusSigma.is_continuous} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.is_continuous` {#StudentTWithAbsDfSoftplusScale.is_continuous} - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.is_scalar_batch(name='is_scalar_batch')` {#StudentTWithAbsDfSoftplusSigma.is_scalar_batch} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.is_scalar_batch(name='is_scalar_batch')` {#StudentTWithAbsDfSoftplusScale.is_scalar_batch} Indicates that `batch_shape == []`. @@ -15202,7 +15250,7 @@ Indicates that `batch_shape == []`. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.is_scalar_event(name='is_scalar_event')` {#StudentTWithAbsDfSoftplusSigma.is_scalar_event} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.is_scalar_event(name='is_scalar_event')` {#StudentTWithAbsDfSoftplusScale.is_scalar_event} Indicates that `event_shape == []`. @@ -15219,7 +15267,14 @@ Indicates that `event_shape == []`. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.log_cdf(value, name='log_cdf')` {#StudentTWithAbsDfSoftplusSigma.log_cdf} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.loc` {#StudentTWithAbsDfSoftplusScale.loc} + +Locations of these Student's t distribution(s). + + +- - - + +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.log_cdf(value, name='log_cdf')` {#StudentTWithAbsDfSoftplusScale.log_cdf} Log cumulative distribution function. @@ -15248,7 +15303,7 @@ a more accurate answer than simply taking the logarithm of the `cdf` when - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.log_pdf(value, name='log_pdf')` {#StudentTWithAbsDfSoftplusSigma.log_pdf} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.log_pdf(value, name='log_pdf')` {#StudentTWithAbsDfSoftplusScale.log_pdf} Log probability density function. @@ -15272,7 +15327,7 @@ Log probability density function. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.log_pmf(value, name='log_pmf')` {#StudentTWithAbsDfSoftplusSigma.log_pmf} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.log_pmf(value, name='log_pmf')` {#StudentTWithAbsDfSoftplusScale.log_pmf} Log probability mass function. @@ -15296,7 +15351,7 @@ Log probability mass function. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.log_prob(value, name='log_prob')` {#StudentTWithAbsDfSoftplusSigma.log_prob} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.log_prob(value, name='log_prob')` {#StudentTWithAbsDfSoftplusScale.log_prob} Log probability density/mass function (depending on `is_continuous`). @@ -15315,7 +15370,7 @@ Log probability density/mass function (depending on `is_continuous`). - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.log_survival_function(value, name='log_survival_function')` {#StudentTWithAbsDfSoftplusSigma.log_survival_function} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.log_survival_function(value, name='log_survival_function')` {#StudentTWithAbsDfSoftplusScale.log_survival_function} Log survival function. @@ -15344,41 +15399,34 @@ survival function, which are more accurate than `1 - cdf(x)` when `x >> 1`. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.mean(name='mean')` {#StudentTWithAbsDfSoftplusSigma.mean} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.mean(name='mean')` {#StudentTWithAbsDfSoftplusScale.mean} Mean. Additional documentation from `StudentT`: -The mean of Student's T equals `mu` if `df > 1`, otherwise it is `NaN`. -If `self.allow_nan_stats=True`, then an exception will be raised rather -than returning `NaN`. +The mean of Student's T equals `loc` if `df > 1`, otherwise it is +`NaN`. If `self.allow_nan_stats=True`, then an exception will be raised +rather than returning `NaN`. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.mode(name='mode')` {#StudentTWithAbsDfSoftplusSigma.mode} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.mode(name='mode')` {#StudentTWithAbsDfSoftplusScale.mode} Mode. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.mu` {#StudentTWithAbsDfSoftplusSigma.mu} - -Locations of these Student's t distribution(s). - - -- - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.name` {#StudentTWithAbsDfSoftplusSigma.name} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.name` {#StudentTWithAbsDfSoftplusScale.name} Name prepended to all ops created by this `Distribution`. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.param_shapes(cls, sample_shape, name='DistributionParamShapes')` {#StudentTWithAbsDfSoftplusSigma.param_shapes} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.param_shapes(cls, sample_shape, name='DistributionParamShapes')` {#StudentTWithAbsDfSoftplusScale.param_shapes} Shapes of parameters given the desired shape of a call to `sample()`. @@ -15402,7 +15450,7 @@ Subclasses should override class method `_param_shapes`. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.param_static_shapes(cls, sample_shape)` {#StudentTWithAbsDfSoftplusSigma.param_static_shapes} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.param_static_shapes(cls, sample_shape)` {#StudentTWithAbsDfSoftplusScale.param_static_shapes} param_shapes with static (i.e. `TensorShape`) shapes. @@ -15432,14 +15480,14 @@ constant-valued tensors when constant values are fed. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.parameters` {#StudentTWithAbsDfSoftplusSigma.parameters} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.parameters` {#StudentTWithAbsDfSoftplusScale.parameters} Dictionary of parameters used to instantiate this `Distribution`. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.pdf(value, name='pdf')` {#StudentTWithAbsDfSoftplusSigma.pdf} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.pdf(value, name='pdf')` {#StudentTWithAbsDfSoftplusScale.pdf} Probability density function. @@ -15463,7 +15511,7 @@ Probability density function. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.pmf(value, name='pmf')` {#StudentTWithAbsDfSoftplusSigma.pmf} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.pmf(value, name='pmf')` {#StudentTWithAbsDfSoftplusScale.pmf} Probability mass function. @@ -15487,7 +15535,7 @@ Probability mass function. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.prob(value, name='prob')` {#StudentTWithAbsDfSoftplusSigma.prob} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.prob(value, name='prob')` {#StudentTWithAbsDfSoftplusScale.prob} Probability density/mass function (depending on `is_continuous`). @@ -15506,7 +15554,7 @@ Probability density/mass function (depending on `is_continuous`). - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.reparameterization_type` {#StudentTWithAbsDfSoftplusSigma.reparameterization_type} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.reparameterization_type` {#StudentTWithAbsDfSoftplusScale.reparameterization_type} Describes how samples from the distribution are reparameterized. @@ -15521,7 +15569,7 @@ or `distributions.NOT_REPARAMETERIZED`. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.sample(sample_shape=(), seed=None, name='sample')` {#StudentTWithAbsDfSoftplusSigma.sample} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.sample(sample_shape=(), seed=None, name='sample')` {#StudentTWithAbsDfSoftplusScale.sample} Generate samples of the specified shape. @@ -15543,14 +15591,14 @@ sample. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.sigma` {#StudentTWithAbsDfSoftplusSigma.sigma} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.scale` {#StudentTWithAbsDfSoftplusScale.scale} Scaling factors of these Student's t distribution(s). - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.stddev(name='stddev')` {#StudentTWithAbsDfSoftplusSigma.stddev} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.stddev(name='stddev')` {#StudentTWithAbsDfSoftplusScale.stddev} Standard deviation. @@ -15577,7 +15625,7 @@ denotes expectation, and `stddev.shape = batch_shape + event_shape`. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.survival_function(value, name='survival_function')` {#StudentTWithAbsDfSoftplusSigma.survival_function} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.survival_function(value, name='survival_function')` {#StudentTWithAbsDfSoftplusScale.survival_function} Survival function. @@ -15603,14 +15651,14 @@ survival_function(x) = P[X > x] - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.validate_args` {#StudentTWithAbsDfSoftplusSigma.validate_args} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.validate_args` {#StudentTWithAbsDfSoftplusScale.validate_args} Python boolean indicated possibly expensive checks are enabled. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.variance(name='variance')` {#StudentTWithAbsDfSoftplusSigma.variance} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.variance(name='variance')` {#StudentTWithAbsDfSoftplusScale.variance} Variance. @@ -26593,23 +26641,23 @@ representing the posterior or posterior predictive. - - - -### `tf.contrib.distributions.normal_conjugates_known_sigma_posterior(prior, sigma, s, n)` {#normal_conjugates_known_sigma_posterior} +### `tf.contrib.distributions.normal_conjugates_known_scale_posterior(prior, scale, s, n)` {#normal_conjugates_known_scale_posterior} Posterior Normal distribution with conjugate prior on the mean. This model assumes that `n` observations (with sum `s`) come from a -Normal with unknown mean `mu` (described by the Normal `prior`) -and known variance `sigma^2`. The "known sigma posterior" is -the distribution of the unknown `mu`. +Normal with unknown mean `loc` (described by the Normal `prior`) +and known variance `scale^2`. The "known scale posterior" is +the distribution of the unknown `loc`. Accepts a prior Normal distribution object, having parameters -`mu0` and `sigma0`, as well as known `sigma` values of the predictive +`loc0` and `scale0`, as well as known `scale` values of the predictive distribution(s) (also assumed Normal), and statistical estimates `s` (the sum(s) of the observations) and `n` (the number(s) of observations). Returns a posterior (also Normal) distribution object, with parameters -`(mu', sigma'^2)`, where: +`(loc', scale'^2)`, where: ``` mu ~ N(mu', sigma'^2) @@ -26617,15 +26665,15 @@ sigma'^2 = 1/(1/sigma0^2 + n/sigma^2), mu' = (mu0/sigma0^2 + s/sigma^2) * sigma'^2. ``` -Distribution parameters from `prior`, as well as `sigma`, `s`, and `n`. +Distribution parameters from `prior`, as well as `scale`, `s`, and `n`. will broadcast in the case of multidimensional sets of parameters. ##### Args: * <b>`prior`</b>: `Normal` object of type `dtype`: - the prior distribution having parameters `(mu0, sigma0)`. -* <b>`sigma`</b>: tensor of type `dtype`, taking values `sigma > 0`. + the prior distribution having parameters `(loc0, scale0)`. +* <b>`scale`</b>: tensor of type `dtype`, taking values `scale > 0`. The known stddev parameter(s). * <b>`s`</b>: Tensor of type `dtype`. The sum(s) of observations. * <b>`n`</b>: Tensor of type `int`. The number(s) of observations. @@ -26633,7 +26681,7 @@ will broadcast in the case of multidimensional sets of parameters. ##### Returns: A new Normal posterior distribution object for the unknown observation - mean `mu`. + mean `loc`. ##### Raises: @@ -26644,18 +26692,18 @@ will broadcast in the case of multidimensional sets of parameters. - - - -### `tf.contrib.distributions.normal_conjugates_known_sigma_predictive(prior, sigma, s, n)` {#normal_conjugates_known_sigma_predictive} +### `tf.contrib.distributions.normal_conjugates_known_scale_predictive(prior, scale, s, n)` {#normal_conjugates_known_scale_predictive} Posterior predictive Normal distribution w. conjugate prior on the mean. This model assumes that `n` observations (with sum `s`) come from a -Normal with unknown mean `mu` (described by the Normal `prior`) -and known variance `sigma^2`. The "known sigma predictive" +Normal with unknown mean `loc` (described by the Normal `prior`) +and known variance `scale^2`. The "known scale predictive" is the distribution of new observations, conditioned on the existing observations and our prior. Accepts a prior Normal distribution object, having parameters -`mu0` and `sigma0`, as well as known `sigma` values of the predictive +`loc0` and `scale0`, as well as known `scale` values of the predictive distribution(s) (also assumed Normal), and statistical estimates `s` (the sum(s) of the observations) and `n` (the number(s) of observations). @@ -26663,12 +26711,12 @@ and statistical estimates `s` (the sum(s) of the observations) and Calculates the Normal distribution(s) `p(x | sigma^2)`: ``` - p(x | sigma^2) = int N(x | mu, sigma^2) N(mu | prior.mu, prior.sigma^2) dmu - = N(x | prior.mu, 1/(sigma^2 + prior.sigma^2)) +p(x | sigma^2) = int N(x | mu, sigma^2) N(mu | prior.loc, prior.scale**2) dmu + = N(x | prior.loc, 1/(sigma^2 + prior.scale**2)) ``` Returns the predictive posterior distribution object, with parameters -`(mu', sigma'^2)`, where: +`(loc', scale'^2)`, where: ``` sigma_n^2 = 1/(1/sigma0^2 + n/sigma^2), @@ -26676,15 +26724,15 @@ mu' = (mu0/sigma0^2 + s/sigma^2) * sigma_n^2. sigma'^2 = sigma_n^2 + sigma^2, ``` -Distribution parameters from `prior`, as well as `sigma`, `s`, and `n`. +Distribution parameters from `prior`, as well as `scale`, `s`, and `n`. will broadcast in the case of multidimensional sets of parameters. ##### Args: * <b>`prior`</b>: `Normal` object of type `dtype`: - the prior distribution having parameters `(mu0, sigma0)`. -* <b>`sigma`</b>: tensor of type `dtype`, taking values `sigma > 0`. + the prior distribution having parameters `(loc0, scale0)`. +* <b>`scale`</b>: tensor of type `dtype`, taking values `scale > 0`. The known stddev parameter(s). * <b>`s`</b>: Tensor of type `dtype`. The sum(s) of observations. * <b>`n`</b>: Tensor of type `int`. The number(s) of observations. diff --git a/tensorflow/g3doc/api_docs/python/functions_and_classes/shard1/tf.contrib.distributions.StudentT.md b/tensorflow/g3doc/api_docs/python/functions_and_classes/shard1/tf.contrib.distributions.StudentT.md index fe431bceb6..d239930923 100644 --- a/tensorflow/g3doc/api_docs/python/functions_and_classes/shard1/tf.contrib.distributions.StudentT.md +++ b/tensorflow/g3doc/api_docs/python/functions_and_classes/shard1/tf.contrib.distributions.StudentT.md @@ -1,20 +1,35 @@ -Student's t distribution with degree-of-freedom parameter df. +Student's t-distribution with degree of freedom `df`, location `loc`, and `scale` parameters. #### Mathematical details -Write `sigma` for the scale and `mu` for the mean (both are scalars). The PDF -of this distribution is: +The probability density function (pdf) is, ```none -f(x) = (1 + y**2 / df)**(-0.5 (df + 1)) / Z +pdf(x; df, mu, sigma) = (1 + y**2 / df)**(-0.5 (df + 1)) / Z where, -y(x) = (x - mu) / sigma -Z = abs(sigma) sqrt(df pi) Gamma(0.5 df) / Gamma(0.5 (df + 1)) +y = (x - mu) / sigma +Z = abs(sigma) sqrt(df pi) Gamma(0.5 df) / Gamma(0.5 (df + 1)) ``` -Notice that `sigma` has semantics more similar to standard deviation than -variance. (Recall that the variance of the Student's t-distribution is -`sigma**2 df / (df - 2)` when `df > 2`.) +where: +* `loc = mu`, +* `scale = sigma`, and, +* `Z` is the normalization constant, and, +* `Gamma` is the [gamma function]( + https://en.wikipedia.org/wiki/Gamma_function). + +The StudentT distribution is a member of the [location-scale family]( +https://en.wikipedia.org/wiki/Location-scale_family), i.e., it can be +constructed as, + +```none +X ~ StudentT(df, loc=0, scale=1) +Y = loc + scale * X +``` + +Notice that `scale` has semantics more similar to standard deviation than +variance. However it is not actually the std. deviation; the Student's +t-distribution std. dev. is `scale sqrt(df / (df - 2))` when `df > 2`. #### Examples @@ -31,8 +46,8 @@ single_dist.pdf(1.) # The first has degrees of freedom 2, mean 1, and scale 11. # The second 3, 2 and 22. multi_dist = tf.contrib.distributions.StudentT(df=[2, 3], - mu=[1, 2.], - sigma=[11, 22.]) + loc=[1, 2.], + scale=[11, 22.]) # Evaluate the pdf of the first distribution on 0, and the second on 1.5, # returning a length two tensor. @@ -47,7 +62,7 @@ Arguments are broadcast when possible. ```python # Define a batch of two Student's t distributions. # Both have df 2 and mean 1, but different scales. -dist = tf.contrib.distributions.StudentT(df=2, mu=1, sigma=[11, 22.]) +dist = tf.contrib.distributions.StudentT(df=2, loc=1, scale=[11, 22.]) # Evaluate the pdf of both distributions on the same point, 3.0, # returning a length 2 tensor. @@ -55,38 +70,40 @@ dist.pdf(3.0) ``` - - - -#### `tf.contrib.distributions.StudentT.__init__(df, mu, sigma, validate_args=False, allow_nan_stats=True, name='StudentT')` {#StudentT.__init__} +#### `tf.contrib.distributions.StudentT.__init__(df, loc, scale, validate_args=False, allow_nan_stats=True, name='StudentT')` {#StudentT.__init__} Construct Student's t distributions. -The distributions have degree of freedom `df`, mean `mu`, and scale `sigma`. +The distributions have degree of freedom `df`, mean `loc`, and scale +`scale`. -The parameters `df`, `mu`, and `sigma` must be shaped in a way that supports -broadcasting (e.g. `df + mu + sigma` is a valid operation). +The parameters `df`, `loc`, and `scale` must be shaped in a way that +supports broadcasting (e.g. `df + loc + scale` is a valid operation). ##### Args: * <b>`df`</b>: Numeric `Tensor`. The degrees of freedom of the distribution(s). `df` must contain only positive values. -* <b>`mu`</b>: Numeric `Tensor`. The mean(s) of the distribution(s). -* <b>`sigma`</b>: Numeric `Tensor`. The scaling factor(s) for the distribution(s). - Note that `sigma` is not technically the standard deviation of this +* <b>`loc`</b>: Numeric `Tensor`. The mean(s) of the distribution(s). +* <b>`scale`</b>: Numeric `Tensor`. The scaling factor(s) for the distribution(s). + Note that `scale` is not technically the standard deviation of this distribution but has semantics more similar to standard deviation than variance. -* <b>`validate_args`</b>: `Boolean`, default `False`. Whether to assert that - `df > 0` and `sigma > 0`. If `validate_args` is `False` and inputs are - invalid, correct behavior is not guaranteed. -* <b>`allow_nan_stats`</b>: `Boolean`, default `True`. If `False`, raise an - exception if a statistic (e.g. mean/mode/etc...) is undefined for any - batch member. If `True`, batch members with valid parameters leading to - undefined statistics will return NaN for this statistic. -* <b>`name`</b>: The name to give Ops created by the initializer. +* <b>`validate_args`</b>: Python `Boolean`, default `False`. When `True` distribution + parameters are checked for validity despite possibly degrading runtime + performance. When `False` invalid inputs may silently render incorrect + outputs. +* <b>`allow_nan_stats`</b>: Python `Boolean`, default `True`. When `True`, + statistics (e.g., mean, mode, variance) use the value "`NaN`" to + indicate the result is undefined. When `False`, an exception is raised + if one or more of the statistic's batch members are undefined. +* <b>`name`</b>: `String` name prefixed to Ops created by this class. ##### Raises: -* <b>`TypeError`</b>: if mu and sigma are different dtypes. +* <b>`TypeError`</b>: if loc and scale are different dtypes. - - - @@ -331,6 +348,13 @@ Indicates that `event_shape == []`. - - - +#### `tf.contrib.distributions.StudentT.loc` {#StudentT.loc} + +Locations of these Student's t distribution(s). + + +- - - + #### `tf.contrib.distributions.StudentT.log_cdf(value, name='log_cdf')` {#StudentT.log_cdf} Log cumulative distribution function. @@ -462,9 +486,9 @@ Mean. Additional documentation from `StudentT`: -The mean of Student's T equals `mu` if `df > 1`, otherwise it is `NaN`. -If `self.allow_nan_stats=True`, then an exception will be raised rather -than returning `NaN`. +The mean of Student's T equals `loc` if `df > 1`, otherwise it is +`NaN`. If `self.allow_nan_stats=True`, then an exception will be raised +rather than returning `NaN`. - - - @@ -476,13 +500,6 @@ Mode. - - - -#### `tf.contrib.distributions.StudentT.mu` {#StudentT.mu} - -Locations of these Student's t distribution(s). - - -- - - - #### `tf.contrib.distributions.StudentT.name` {#StudentT.name} Name prepended to all ops created by this `Distribution`. @@ -655,7 +672,7 @@ sample. - - - -#### `tf.contrib.distributions.StudentT.sigma` {#StudentT.sigma} +#### `tf.contrib.distributions.StudentT.scale` {#StudentT.scale} Scaling factors of these Student's t distribution(s). diff --git a/tensorflow/g3doc/api_docs/python/functions_and_classes/shard6/tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.md b/tensorflow/g3doc/api_docs/python/functions_and_classes/shard1/tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.md index baec79507d..d54ee3678c 100644 --- a/tensorflow/g3doc/api_docs/python/functions_and_classes/shard6/tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.md +++ b/tensorflow/g3doc/api_docs/python/functions_and_classes/shard1/tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.md @@ -1,14 +1,14 @@ -StudentT with `df = floor(abs(df))` and `sigma = softplus(sigma)`. +StudentT with `df = floor(abs(df))` and `scale = softplus(scale)`. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.__init__(df, mu, sigma, validate_args=False, allow_nan_stats=True, name='StudentTWithAbsDfSoftplusSigma')` {#StudentTWithAbsDfSoftplusSigma.__init__} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.__init__(df, loc, scale, validate_args=False, allow_nan_stats=True, name='StudentTWithAbsDfSoftplusScale')` {#StudentTWithAbsDfSoftplusScale.__init__} - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.allow_nan_stats` {#StudentTWithAbsDfSoftplusSigma.allow_nan_stats} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.allow_nan_stats` {#StudentTWithAbsDfSoftplusScale.allow_nan_stats} Python boolean describing behavior when a stat is undefined. @@ -29,7 +29,7 @@ undefined. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.batch_shape(name='batch_shape')` {#StudentTWithAbsDfSoftplusSigma.batch_shape} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.batch_shape(name='batch_shape')` {#StudentTWithAbsDfSoftplusScale.batch_shape} Shape of a single sample from a single event index as a 1-D `Tensor`. @@ -49,7 +49,7 @@ independent distributions of this kind the instance represents. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.cdf(value, name='cdf')` {#StudentTWithAbsDfSoftplusSigma.cdf} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.cdf(value, name='cdf')` {#StudentTWithAbsDfSoftplusScale.cdf} Cumulative distribution function. @@ -74,7 +74,7 @@ cdf(x) := P[X <= x] - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.copy(**override_parameters_kwargs)` {#StudentTWithAbsDfSoftplusSigma.copy} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.copy(**override_parameters_kwargs)` {#StudentTWithAbsDfSoftplusScale.copy} Creates a deep copy of the distribution. @@ -97,7 +97,7 @@ intialization arguments. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.covariance(name='covariance')` {#StudentTWithAbsDfSoftplusSigma.covariance} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.covariance(name='covariance')` {#StudentTWithAbsDfSoftplusScale.covariance} Covariance. @@ -141,28 +141,28 @@ length-`k'` vector. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.df` {#StudentTWithAbsDfSoftplusSigma.df} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.df` {#StudentTWithAbsDfSoftplusScale.df} Degrees of freedom in these Student's t distribution(s). - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.dtype` {#StudentTWithAbsDfSoftplusSigma.dtype} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.dtype` {#StudentTWithAbsDfSoftplusScale.dtype} The `DType` of `Tensor`s handled by this `Distribution`. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.entropy(name='entropy')` {#StudentTWithAbsDfSoftplusSigma.entropy} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.entropy(name='entropy')` {#StudentTWithAbsDfSoftplusScale.entropy} Shannon entropy in nats. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.event_shape(name='event_shape')` {#StudentTWithAbsDfSoftplusSigma.event_shape} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.event_shape(name='event_shape')` {#StudentTWithAbsDfSoftplusScale.event_shape} Shape of a single sample from a single batch as a 1-D int32 `Tensor`. @@ -179,7 +179,7 @@ Shape of a single sample from a single batch as a 1-D int32 `Tensor`. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.get_batch_shape()` {#StudentTWithAbsDfSoftplusSigma.get_batch_shape} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.get_batch_shape()` {#StudentTWithAbsDfSoftplusScale.get_batch_shape} Shape of a single sample from a single event index as a `TensorShape`. @@ -193,7 +193,7 @@ Same meaning as `batch_shape`. May be only partially defined. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.get_event_shape()` {#StudentTWithAbsDfSoftplusSigma.get_event_shape} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.get_event_shape()` {#StudentTWithAbsDfSoftplusScale.get_event_shape} Shape of a single sample from a single batch as a `TensorShape`. @@ -207,14 +207,14 @@ Same meaning as `event_shape`. May be only partially defined. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.is_continuous` {#StudentTWithAbsDfSoftplusSigma.is_continuous} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.is_continuous` {#StudentTWithAbsDfSoftplusScale.is_continuous} - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.is_scalar_batch(name='is_scalar_batch')` {#StudentTWithAbsDfSoftplusSigma.is_scalar_batch} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.is_scalar_batch(name='is_scalar_batch')` {#StudentTWithAbsDfSoftplusScale.is_scalar_batch} Indicates that `batch_shape == []`. @@ -231,7 +231,7 @@ Indicates that `batch_shape == []`. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.is_scalar_event(name='is_scalar_event')` {#StudentTWithAbsDfSoftplusSigma.is_scalar_event} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.is_scalar_event(name='is_scalar_event')` {#StudentTWithAbsDfSoftplusScale.is_scalar_event} Indicates that `event_shape == []`. @@ -248,7 +248,14 @@ Indicates that `event_shape == []`. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.log_cdf(value, name='log_cdf')` {#StudentTWithAbsDfSoftplusSigma.log_cdf} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.loc` {#StudentTWithAbsDfSoftplusScale.loc} + +Locations of these Student's t distribution(s). + + +- - - + +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.log_cdf(value, name='log_cdf')` {#StudentTWithAbsDfSoftplusScale.log_cdf} Log cumulative distribution function. @@ -277,7 +284,7 @@ a more accurate answer than simply taking the logarithm of the `cdf` when - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.log_pdf(value, name='log_pdf')` {#StudentTWithAbsDfSoftplusSigma.log_pdf} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.log_pdf(value, name='log_pdf')` {#StudentTWithAbsDfSoftplusScale.log_pdf} Log probability density function. @@ -301,7 +308,7 @@ Log probability density function. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.log_pmf(value, name='log_pmf')` {#StudentTWithAbsDfSoftplusSigma.log_pmf} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.log_pmf(value, name='log_pmf')` {#StudentTWithAbsDfSoftplusScale.log_pmf} Log probability mass function. @@ -325,7 +332,7 @@ Log probability mass function. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.log_prob(value, name='log_prob')` {#StudentTWithAbsDfSoftplusSigma.log_prob} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.log_prob(value, name='log_prob')` {#StudentTWithAbsDfSoftplusScale.log_prob} Log probability density/mass function (depending on `is_continuous`). @@ -344,7 +351,7 @@ Log probability density/mass function (depending on `is_continuous`). - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.log_survival_function(value, name='log_survival_function')` {#StudentTWithAbsDfSoftplusSigma.log_survival_function} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.log_survival_function(value, name='log_survival_function')` {#StudentTWithAbsDfSoftplusScale.log_survival_function} Log survival function. @@ -373,41 +380,34 @@ survival function, which are more accurate than `1 - cdf(x)` when `x >> 1`. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.mean(name='mean')` {#StudentTWithAbsDfSoftplusSigma.mean} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.mean(name='mean')` {#StudentTWithAbsDfSoftplusScale.mean} Mean. Additional documentation from `StudentT`: -The mean of Student's T equals `mu` if `df > 1`, otherwise it is `NaN`. -If `self.allow_nan_stats=True`, then an exception will be raised rather -than returning `NaN`. +The mean of Student's T equals `loc` if `df > 1`, otherwise it is +`NaN`. If `self.allow_nan_stats=True`, then an exception will be raised +rather than returning `NaN`. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.mode(name='mode')` {#StudentTWithAbsDfSoftplusSigma.mode} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.mode(name='mode')` {#StudentTWithAbsDfSoftplusScale.mode} Mode. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.mu` {#StudentTWithAbsDfSoftplusSigma.mu} - -Locations of these Student's t distribution(s). - - -- - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.name` {#StudentTWithAbsDfSoftplusSigma.name} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.name` {#StudentTWithAbsDfSoftplusScale.name} Name prepended to all ops created by this `Distribution`. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.param_shapes(cls, sample_shape, name='DistributionParamShapes')` {#StudentTWithAbsDfSoftplusSigma.param_shapes} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.param_shapes(cls, sample_shape, name='DistributionParamShapes')` {#StudentTWithAbsDfSoftplusScale.param_shapes} Shapes of parameters given the desired shape of a call to `sample()`. @@ -431,7 +431,7 @@ Subclasses should override class method `_param_shapes`. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.param_static_shapes(cls, sample_shape)` {#StudentTWithAbsDfSoftplusSigma.param_static_shapes} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.param_static_shapes(cls, sample_shape)` {#StudentTWithAbsDfSoftplusScale.param_static_shapes} param_shapes with static (i.e. `TensorShape`) shapes. @@ -461,14 +461,14 @@ constant-valued tensors when constant values are fed. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.parameters` {#StudentTWithAbsDfSoftplusSigma.parameters} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.parameters` {#StudentTWithAbsDfSoftplusScale.parameters} Dictionary of parameters used to instantiate this `Distribution`. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.pdf(value, name='pdf')` {#StudentTWithAbsDfSoftplusSigma.pdf} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.pdf(value, name='pdf')` {#StudentTWithAbsDfSoftplusScale.pdf} Probability density function. @@ -492,7 +492,7 @@ Probability density function. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.pmf(value, name='pmf')` {#StudentTWithAbsDfSoftplusSigma.pmf} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.pmf(value, name='pmf')` {#StudentTWithAbsDfSoftplusScale.pmf} Probability mass function. @@ -516,7 +516,7 @@ Probability mass function. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.prob(value, name='prob')` {#StudentTWithAbsDfSoftplusSigma.prob} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.prob(value, name='prob')` {#StudentTWithAbsDfSoftplusScale.prob} Probability density/mass function (depending on `is_continuous`). @@ -535,7 +535,7 @@ Probability density/mass function (depending on `is_continuous`). - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.reparameterization_type` {#StudentTWithAbsDfSoftplusSigma.reparameterization_type} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.reparameterization_type` {#StudentTWithAbsDfSoftplusScale.reparameterization_type} Describes how samples from the distribution are reparameterized. @@ -550,7 +550,7 @@ or `distributions.NOT_REPARAMETERIZED`. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.sample(sample_shape=(), seed=None, name='sample')` {#StudentTWithAbsDfSoftplusSigma.sample} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.sample(sample_shape=(), seed=None, name='sample')` {#StudentTWithAbsDfSoftplusScale.sample} Generate samples of the specified shape. @@ -572,14 +572,14 @@ sample. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.sigma` {#StudentTWithAbsDfSoftplusSigma.sigma} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.scale` {#StudentTWithAbsDfSoftplusScale.scale} Scaling factors of these Student's t distribution(s). - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.stddev(name='stddev')` {#StudentTWithAbsDfSoftplusSigma.stddev} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.stddev(name='stddev')` {#StudentTWithAbsDfSoftplusScale.stddev} Standard deviation. @@ -606,7 +606,7 @@ denotes expectation, and `stddev.shape = batch_shape + event_shape`. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.survival_function(value, name='survival_function')` {#StudentTWithAbsDfSoftplusSigma.survival_function} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.survival_function(value, name='survival_function')` {#StudentTWithAbsDfSoftplusScale.survival_function} Survival function. @@ -632,14 +632,14 @@ survival_function(x) = P[X > x] - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.validate_args` {#StudentTWithAbsDfSoftplusSigma.validate_args} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.validate_args` {#StudentTWithAbsDfSoftplusScale.validate_args} Python boolean indicated possibly expensive checks are enabled. - - - -#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusSigma.variance(name='variance')` {#StudentTWithAbsDfSoftplusSigma.variance} +#### `tf.contrib.distributions.StudentTWithAbsDfSoftplusScale.variance(name='variance')` {#StudentTWithAbsDfSoftplusScale.variance} Variance. diff --git a/tensorflow/g3doc/api_docs/python/functions_and_classes/shard8/tf.contrib.distributions.NormalWithSoftplusSigma.md b/tensorflow/g3doc/api_docs/python/functions_and_classes/shard3/tf.contrib.distributions.NormalWithSoftplusScale.md index 8c43860b37..675a961a82 100644 --- a/tensorflow/g3doc/api_docs/python/functions_and_classes/shard8/tf.contrib.distributions.NormalWithSoftplusSigma.md +++ b/tensorflow/g3doc/api_docs/python/functions_and_classes/shard3/tf.contrib.distributions.NormalWithSoftplusScale.md @@ -1,14 +1,14 @@ -Normal with softplus applied to `sigma`. +Normal with softplus applied to `scale`. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.__init__(mu, sigma, validate_args=False, allow_nan_stats=True, name='NormalWithSoftplusSigma')` {#NormalWithSoftplusSigma.__init__} +#### `tf.contrib.distributions.NormalWithSoftplusScale.__init__(loc, scale, validate_args=False, allow_nan_stats=True, name='NormalWithSoftplusScale')` {#NormalWithSoftplusScale.__init__} - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.allow_nan_stats` {#NormalWithSoftplusSigma.allow_nan_stats} +#### `tf.contrib.distributions.NormalWithSoftplusScale.allow_nan_stats` {#NormalWithSoftplusScale.allow_nan_stats} Python boolean describing behavior when a stat is undefined. @@ -29,7 +29,7 @@ undefined. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.batch_shape(name='batch_shape')` {#NormalWithSoftplusSigma.batch_shape} +#### `tf.contrib.distributions.NormalWithSoftplusScale.batch_shape(name='batch_shape')` {#NormalWithSoftplusScale.batch_shape} Shape of a single sample from a single event index as a 1-D `Tensor`. @@ -49,7 +49,7 @@ independent distributions of this kind the instance represents. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.cdf(value, name='cdf')` {#NormalWithSoftplusSigma.cdf} +#### `tf.contrib.distributions.NormalWithSoftplusScale.cdf(value, name='cdf')` {#NormalWithSoftplusScale.cdf} Cumulative distribution function. @@ -74,7 +74,7 @@ cdf(x) := P[X <= x] - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.copy(**override_parameters_kwargs)` {#NormalWithSoftplusSigma.copy} +#### `tf.contrib.distributions.NormalWithSoftplusScale.copy(**override_parameters_kwargs)` {#NormalWithSoftplusScale.copy} Creates a deep copy of the distribution. @@ -97,7 +97,7 @@ intialization arguments. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.covariance(name='covariance')` {#NormalWithSoftplusSigma.covariance} +#### `tf.contrib.distributions.NormalWithSoftplusScale.covariance(name='covariance')` {#NormalWithSoftplusScale.covariance} Covariance. @@ -141,21 +141,21 @@ length-`k'` vector. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.dtype` {#NormalWithSoftplusSigma.dtype} +#### `tf.contrib.distributions.NormalWithSoftplusScale.dtype` {#NormalWithSoftplusScale.dtype} The `DType` of `Tensor`s handled by this `Distribution`. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.entropy(name='entropy')` {#NormalWithSoftplusSigma.entropy} +#### `tf.contrib.distributions.NormalWithSoftplusScale.entropy(name='entropy')` {#NormalWithSoftplusScale.entropy} Shannon entropy in nats. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.event_shape(name='event_shape')` {#NormalWithSoftplusSigma.event_shape} +#### `tf.contrib.distributions.NormalWithSoftplusScale.event_shape(name='event_shape')` {#NormalWithSoftplusScale.event_shape} Shape of a single sample from a single batch as a 1-D int32 `Tensor`. @@ -172,7 +172,7 @@ Shape of a single sample from a single batch as a 1-D int32 `Tensor`. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.get_batch_shape()` {#NormalWithSoftplusSigma.get_batch_shape} +#### `tf.contrib.distributions.NormalWithSoftplusScale.get_batch_shape()` {#NormalWithSoftplusScale.get_batch_shape} Shape of a single sample from a single event index as a `TensorShape`. @@ -186,7 +186,7 @@ Same meaning as `batch_shape`. May be only partially defined. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.get_event_shape()` {#NormalWithSoftplusSigma.get_event_shape} +#### `tf.contrib.distributions.NormalWithSoftplusScale.get_event_shape()` {#NormalWithSoftplusScale.get_event_shape} Shape of a single sample from a single batch as a `TensorShape`. @@ -200,14 +200,14 @@ Same meaning as `event_shape`. May be only partially defined. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.is_continuous` {#NormalWithSoftplusSigma.is_continuous} +#### `tf.contrib.distributions.NormalWithSoftplusScale.is_continuous` {#NormalWithSoftplusScale.is_continuous} - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.is_scalar_batch(name='is_scalar_batch')` {#NormalWithSoftplusSigma.is_scalar_batch} +#### `tf.contrib.distributions.NormalWithSoftplusScale.is_scalar_batch(name='is_scalar_batch')` {#NormalWithSoftplusScale.is_scalar_batch} Indicates that `batch_shape == []`. @@ -224,7 +224,7 @@ Indicates that `batch_shape == []`. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.is_scalar_event(name='is_scalar_event')` {#NormalWithSoftplusSigma.is_scalar_event} +#### `tf.contrib.distributions.NormalWithSoftplusScale.is_scalar_event(name='is_scalar_event')` {#NormalWithSoftplusScale.is_scalar_event} Indicates that `event_shape == []`. @@ -241,7 +241,14 @@ Indicates that `event_shape == []`. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.log_cdf(value, name='log_cdf')` {#NormalWithSoftplusSigma.log_cdf} +#### `tf.contrib.distributions.NormalWithSoftplusScale.loc` {#NormalWithSoftplusScale.loc} + +Distribution parameter for the mean. + + +- - - + +#### `tf.contrib.distributions.NormalWithSoftplusScale.log_cdf(value, name='log_cdf')` {#NormalWithSoftplusScale.log_cdf} Log cumulative distribution function. @@ -270,7 +277,7 @@ a more accurate answer than simply taking the logarithm of the `cdf` when - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.log_pdf(value, name='log_pdf')` {#NormalWithSoftplusSigma.log_pdf} +#### `tf.contrib.distributions.NormalWithSoftplusScale.log_pdf(value, name='log_pdf')` {#NormalWithSoftplusScale.log_pdf} Log probability density function. @@ -294,7 +301,7 @@ Log probability density function. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.log_pmf(value, name='log_pmf')` {#NormalWithSoftplusSigma.log_pmf} +#### `tf.contrib.distributions.NormalWithSoftplusScale.log_pmf(value, name='log_pmf')` {#NormalWithSoftplusScale.log_pmf} Log probability mass function. @@ -318,7 +325,7 @@ Log probability mass function. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.log_prob(value, name='log_prob')` {#NormalWithSoftplusSigma.log_prob} +#### `tf.contrib.distributions.NormalWithSoftplusScale.log_prob(value, name='log_prob')` {#NormalWithSoftplusScale.log_prob} Log probability density/mass function (depending on `is_continuous`). @@ -337,7 +344,7 @@ Log probability density/mass function (depending on `is_continuous`). - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.log_survival_function(value, name='log_survival_function')` {#NormalWithSoftplusSigma.log_survival_function} +#### `tf.contrib.distributions.NormalWithSoftplusScale.log_survival_function(value, name='log_survival_function')` {#NormalWithSoftplusScale.log_survival_function} Log survival function. @@ -366,35 +373,28 @@ survival function, which are more accurate than `1 - cdf(x)` when `x >> 1`. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.mean(name='mean')` {#NormalWithSoftplusSigma.mean} +#### `tf.contrib.distributions.NormalWithSoftplusScale.mean(name='mean')` {#NormalWithSoftplusScale.mean} Mean. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.mode(name='mode')` {#NormalWithSoftplusSigma.mode} +#### `tf.contrib.distributions.NormalWithSoftplusScale.mode(name='mode')` {#NormalWithSoftplusScale.mode} Mode. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.mu` {#NormalWithSoftplusSigma.mu} - -Distribution parameter for the mean. - - -- - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.name` {#NormalWithSoftplusSigma.name} +#### `tf.contrib.distributions.NormalWithSoftplusScale.name` {#NormalWithSoftplusScale.name} Name prepended to all ops created by this `Distribution`. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.param_shapes(cls, sample_shape, name='DistributionParamShapes')` {#NormalWithSoftplusSigma.param_shapes} +#### `tf.contrib.distributions.NormalWithSoftplusScale.param_shapes(cls, sample_shape, name='DistributionParamShapes')` {#NormalWithSoftplusScale.param_shapes} Shapes of parameters given the desired shape of a call to `sample()`. @@ -418,7 +418,7 @@ Subclasses should override class method `_param_shapes`. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.param_static_shapes(cls, sample_shape)` {#NormalWithSoftplusSigma.param_static_shapes} +#### `tf.contrib.distributions.NormalWithSoftplusScale.param_static_shapes(cls, sample_shape)` {#NormalWithSoftplusScale.param_static_shapes} param_shapes with static (i.e. `TensorShape`) shapes. @@ -448,14 +448,14 @@ constant-valued tensors when constant values are fed. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.parameters` {#NormalWithSoftplusSigma.parameters} +#### `tf.contrib.distributions.NormalWithSoftplusScale.parameters` {#NormalWithSoftplusScale.parameters} Dictionary of parameters used to instantiate this `Distribution`. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.pdf(value, name='pdf')` {#NormalWithSoftplusSigma.pdf} +#### `tf.contrib.distributions.NormalWithSoftplusScale.pdf(value, name='pdf')` {#NormalWithSoftplusScale.pdf} Probability density function. @@ -479,7 +479,7 @@ Probability density function. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.pmf(value, name='pmf')` {#NormalWithSoftplusSigma.pmf} +#### `tf.contrib.distributions.NormalWithSoftplusScale.pmf(value, name='pmf')` {#NormalWithSoftplusScale.pmf} Probability mass function. @@ -503,7 +503,7 @@ Probability mass function. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.prob(value, name='prob')` {#NormalWithSoftplusSigma.prob} +#### `tf.contrib.distributions.NormalWithSoftplusScale.prob(value, name='prob')` {#NormalWithSoftplusScale.prob} Probability density/mass function (depending on `is_continuous`). @@ -522,7 +522,7 @@ Probability density/mass function (depending on `is_continuous`). - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.reparameterization_type` {#NormalWithSoftplusSigma.reparameterization_type} +#### `tf.contrib.distributions.NormalWithSoftplusScale.reparameterization_type` {#NormalWithSoftplusScale.reparameterization_type} Describes how samples from the distribution are reparameterized. @@ -537,7 +537,7 @@ or `distributions.NOT_REPARAMETERIZED`. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.sample(sample_shape=(), seed=None, name='sample')` {#NormalWithSoftplusSigma.sample} +#### `tf.contrib.distributions.NormalWithSoftplusScale.sample(sample_shape=(), seed=None, name='sample')` {#NormalWithSoftplusScale.sample} Generate samples of the specified shape. @@ -559,14 +559,14 @@ sample. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.sigma` {#NormalWithSoftplusSigma.sigma} +#### `tf.contrib.distributions.NormalWithSoftplusScale.scale` {#NormalWithSoftplusScale.scale} Distribution parameter for standard deviation. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.stddev(name='stddev')` {#NormalWithSoftplusSigma.stddev} +#### `tf.contrib.distributions.NormalWithSoftplusScale.stddev(name='stddev')` {#NormalWithSoftplusScale.stddev} Standard deviation. @@ -593,7 +593,7 @@ denotes expectation, and `stddev.shape = batch_shape + event_shape`. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.survival_function(value, name='survival_function')` {#NormalWithSoftplusSigma.survival_function} +#### `tf.contrib.distributions.NormalWithSoftplusScale.survival_function(value, name='survival_function')` {#NormalWithSoftplusScale.survival_function} Survival function. @@ -619,14 +619,14 @@ survival_function(x) = P[X > x] - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.validate_args` {#NormalWithSoftplusSigma.validate_args} +#### `tf.contrib.distributions.NormalWithSoftplusScale.validate_args` {#NormalWithSoftplusScale.validate_args} Python boolean indicated possibly expensive checks are enabled. - - - -#### `tf.contrib.distributions.NormalWithSoftplusSigma.variance(name='variance')` {#NormalWithSoftplusSigma.variance} +#### `tf.contrib.distributions.NormalWithSoftplusScale.variance(name='variance')` {#NormalWithSoftplusScale.variance} Variance. diff --git a/tensorflow/g3doc/api_docs/python/functions_and_classes/shard9/tf.contrib.distributions.normal_conjugates_known_sigma_predictive.md b/tensorflow/g3doc/api_docs/python/functions_and_classes/shard4/tf.contrib.distributions.normal_conjugates_known_scale_predictive.md index ebeaa66888..6349d89fb0 100644 --- a/tensorflow/g3doc/api_docs/python/functions_and_classes/shard9/tf.contrib.distributions.normal_conjugates_known_sigma_predictive.md +++ b/tensorflow/g3doc/api_docs/python/functions_and_classes/shard4/tf.contrib.distributions.normal_conjugates_known_scale_predictive.md @@ -1,15 +1,15 @@ -### `tf.contrib.distributions.normal_conjugates_known_sigma_predictive(prior, sigma, s, n)` {#normal_conjugates_known_sigma_predictive} +### `tf.contrib.distributions.normal_conjugates_known_scale_predictive(prior, scale, s, n)` {#normal_conjugates_known_scale_predictive} Posterior predictive Normal distribution w. conjugate prior on the mean. This model assumes that `n` observations (with sum `s`) come from a -Normal with unknown mean `mu` (described by the Normal `prior`) -and known variance `sigma^2`. The "known sigma predictive" +Normal with unknown mean `loc` (described by the Normal `prior`) +and known variance `scale^2`. The "known scale predictive" is the distribution of new observations, conditioned on the existing observations and our prior. Accepts a prior Normal distribution object, having parameters -`mu0` and `sigma0`, as well as known `sigma` values of the predictive +`loc0` and `scale0`, as well as known `scale` values of the predictive distribution(s) (also assumed Normal), and statistical estimates `s` (the sum(s) of the observations) and `n` (the number(s) of observations). @@ -17,12 +17,12 @@ and statistical estimates `s` (the sum(s) of the observations) and Calculates the Normal distribution(s) `p(x | sigma^2)`: ``` - p(x | sigma^2) = int N(x | mu, sigma^2) N(mu | prior.mu, prior.sigma^2) dmu - = N(x | prior.mu, 1/(sigma^2 + prior.sigma^2)) +p(x | sigma^2) = int N(x | mu, sigma^2) N(mu | prior.loc, prior.scale**2) dmu + = N(x | prior.loc, 1/(sigma^2 + prior.scale**2)) ``` Returns the predictive posterior distribution object, with parameters -`(mu', sigma'^2)`, where: +`(loc', scale'^2)`, where: ``` sigma_n^2 = 1/(1/sigma0^2 + n/sigma^2), @@ -30,15 +30,15 @@ mu' = (mu0/sigma0^2 + s/sigma^2) * sigma_n^2. sigma'^2 = sigma_n^2 + sigma^2, ``` -Distribution parameters from `prior`, as well as `sigma`, `s`, and `n`. +Distribution parameters from `prior`, as well as `scale`, `s`, and `n`. will broadcast in the case of multidimensional sets of parameters. ##### Args: * <b>`prior`</b>: `Normal` object of type `dtype`: - the prior distribution having parameters `(mu0, sigma0)`. -* <b>`sigma`</b>: tensor of type `dtype`, taking values `sigma > 0`. + the prior distribution having parameters `(loc0, scale0)`. +* <b>`scale`</b>: tensor of type `dtype`, taking values `scale > 0`. The known stddev parameter(s). * <b>`s`</b>: Tensor of type `dtype`. The sum(s) of observations. * <b>`n`</b>: Tensor of type `int`. The number(s) of observations. diff --git a/tensorflow/g3doc/api_docs/python/functions_and_classes/shard6/tf.contrib.distributions.Laplace.md b/tensorflow/g3doc/api_docs/python/functions_and_classes/shard6/tf.contrib.distributions.Laplace.md index 41b3eab89d..23f403b471 100644 --- a/tensorflow/g3doc/api_docs/python/functions_and_classes/shard6/tf.contrib.distributions.Laplace.md +++ b/tensorflow/g3doc/api_docs/python/functions_and_classes/shard6/tf.contrib.distributions.Laplace.md @@ -1,13 +1,27 @@ -The Laplace distribution with location and scale > 0 parameters. +The Laplace distribution with location `loc` and `scale` parameters. #### Mathematical details -The PDF of this distribution is: +The probability density function (pdf) of this distribution is, -```f(x | mu, b, b > 0) = 0.5 / b exp(-|x - mu| / b)``` +```none +pdf(x; mu, sigma) = exp(-|x - mu| / sigma) / Z +Z = 2 sigma +``` + +where `loc = mu`, `scale = sigma`, and `Z` is the normalization constant. Note that the Laplace distribution can be thought of two exponential distributions spliced together "back-to-back." + +The Lpalce distribution is a member of the [location-scale family]( +https://en.wikipedia.org/wiki/Location-scale_family), i.e., it can be +constructed as, + +```none +X ~ Laplace(loc=0, scale=1) +Y = loc + scale * X +``` - - - #### `tf.contrib.distributions.Laplace.__init__(loc, scale, validate_args=False, allow_nan_stats=True, name='Laplace')` {#Laplace.__init__} @@ -24,14 +38,15 @@ broadcasting (e.g., `loc / scale` is a valid operation). of the distribution. * <b>`scale`</b>: Positive floating point tensor which characterizes the spread of the distribution. -* <b>`validate_args`</b>: `Boolean`, default `False`. Whether to validate input - with asserts. If `validate_args` is `False`, and the inputs are - invalid, correct behavior is not guaranteed. -* <b>`allow_nan_stats`</b>: `Boolean`, default `True`. If `False`, raise an - exception if a statistic (e.g. mean/mode/etc...) is undefined for any - batch member. If `True`, batch members with valid parameters leading to - undefined statistics will return NaN for this statistic. -* <b>`name`</b>: The name to give Ops created by the initializer. +* <b>`validate_args`</b>: Python `Boolean`, default `False`. When `True` distribution + parameters are checked for validity despite possibly degrading runtime + performance. When `False` invalid inputs may silently render incorrect + outputs. +* <b>`allow_nan_stats`</b>: Python `Boolean`, default `True`. When `True`, + statistics (e.g., mean, mode, variance) use the value "`NaN`" to + indicate the result is undefined. When `False`, an exception is raised + if one or more of the statistic's batch members are undefined. +* <b>`name`</b>: `String` name prefixed to Ops created by this class. ##### Raises: diff --git a/tensorflow/g3doc/api_docs/python/functions_and_classes/shard7/tf.contrib.distributions.Normal.md b/tensorflow/g3doc/api_docs/python/functions_and_classes/shard7/tf.contrib.distributions.Normal.md index 73a42eb421..0dab0bfa73 100644 --- a/tensorflow/g3doc/api_docs/python/functions_and_classes/shard7/tf.contrib.distributions.Normal.md +++ b/tensorflow/g3doc/api_docs/python/functions_and_classes/shard7/tf.contrib.distributions.Normal.md @@ -1,10 +1,25 @@ -The scalar Normal distribution with mean and stddev parameters mu, sigma. +The Normal distribution with location `loc` and `scale` parameters. #### Mathematical details -The PDF of this distribution is: +The probability density function (pdf) is, -```f(x) = sqrt(1/(2*pi*sigma^2)) exp(-(x-mu)^2/(2*sigma^2))``` +```none +pdf(x; mu, sigma) = exp(-0.5 (x - mu)**2 / sigma**2) / Z +Z = (2 pi sigma**2)**0.5 +``` + +where `loc = mu` is the mean, `scale = sigma` is the std. deviation, and, `Z` +is the normalization constant. + +The Normal distribution is a member of the [location-scale family]( +https://en.wikipedia.org/wiki/Location-scale_family), i.e., it can be +constructed as, + +```none +X ~ Normal(loc=0, scale=1) +Y = loc + scale * X +``` #### Examples @@ -12,14 +27,14 @@ Examples of initialization of one or a batch of distributions. ```python # Define a single scalar Normal distribution. -dist = tf.contrib.distributions.Normal(mu=0., sigma=3.) +dist = tf.contrib.distributions.Normal(loc=0., scale=3.) # Evaluate the cdf at 1, returning a scalar. dist.cdf(1.) # Define a batch of two scalar valued Normals. # The first has mean 1 and standard deviation 11, the second 2 and 22. -dist = tf.contrib.distributions.Normal(mu=[1, 2.], sigma=[11, 22.]) +dist = tf.contrib.distributions.Normal(loc=[1, 2.], scale=[11, 22.]) # Evaluate the pdf of the first distribution on 0, and the second on 1.5, # returning a length two tensor. @@ -34,7 +49,7 @@ Arguments are broadcast when possible. ```python # Define a batch of two scalar valued Normals. # Both have mean 1, but different standard deviations. -dist = tf.contrib.distributions.Normal(mu=1., sigma=[11, 22.]) +dist = tf.contrib.distributions.Normal(loc=1., scale=[11, 22.]) # Evaluate the pdf of both distributions on the same point, 3.0, # returning a length 2 tensor. @@ -42,32 +57,33 @@ dist.pdf(3.0) ``` - - - -#### `tf.contrib.distributions.Normal.__init__(mu, sigma, validate_args=False, allow_nan_stats=True, name='Normal')` {#Normal.__init__} +#### `tf.contrib.distributions.Normal.__init__(loc, scale, validate_args=False, allow_nan_stats=True, name='Normal')` {#Normal.__init__} -Construct Normal distributions with mean and stddev `mu` and `sigma`. +Construct Normal distributions with mean and stddev `loc` and `scale`. -The parameters `mu` and `sigma` must be shaped in a way that supports -broadcasting (e.g. `mu + sigma` is a valid operation). +The parameters `loc` and `scale` must be shaped in a way that supports +broadcasting (e.g. `loc + scale` is a valid operation). ##### Args: -* <b>`mu`</b>: Floating point tensor, the means of the distribution(s). -* <b>`sigma`</b>: Floating point tensor, the stddevs of the distribution(s). - sigma must contain only positive values. -* <b>`validate_args`</b>: `Boolean`, default `False`. Whether to assert that - `sigma > 0`. If `validate_args` is `False`, correct output is not - guaranteed when input is invalid. -* <b>`allow_nan_stats`</b>: `Boolean`, default `True`. If `False`, raise an - exception if a statistic (e.g. mean/mode/etc...) is undefined for any - batch member. If `True`, batch members with valid parameters leading to - undefined statistics will return NaN for this statistic. -* <b>`name`</b>: The name to give Ops created by the initializer. +* <b>`loc`</b>: Floating point tensor; the means of the distribution(s). +* <b>`scale`</b>: Floating point tensor; the stddevs of the distribution(s). + Must contain only positive values. +* <b>`validate_args`</b>: Python `Boolean`, default `False`. When `True` distribution + parameters are checked for validity despite possibly degrading runtime + performance. When `False` invalid inputs may silently render incorrect + outputs. +* <b>`allow_nan_stats`</b>: Python `Boolean`, default `True`. When `True`, + statistics (e.g., mean, mode, variance) use the value "`NaN`" to + indicate the result is undefined. When `False`, an exception is raised + if one or more of the statistic's batch members are undefined. +* <b>`name`</b>: `String` name prefixed to Ops created by this class. ##### Raises: -* <b>`TypeError`</b>: if mu and sigma are different dtypes. +* <b>`TypeError`</b>: if `loc` and `scale` have different `dtype`. - - - @@ -305,6 +321,13 @@ Indicates that `event_shape == []`. - - - +#### `tf.contrib.distributions.Normal.loc` {#Normal.loc} + +Distribution parameter for the mean. + + +- - - + #### `tf.contrib.distributions.Normal.log_cdf(value, name='log_cdf')` {#Normal.log_cdf} Log cumulative distribution function. @@ -444,13 +467,6 @@ Mode. - - - -#### `tf.contrib.distributions.Normal.mu` {#Normal.mu} - -Distribution parameter for the mean. - - -- - - - #### `tf.contrib.distributions.Normal.name` {#Normal.name} Name prepended to all ops created by this `Distribution`. @@ -623,7 +639,7 @@ sample. - - - -#### `tf.contrib.distributions.Normal.sigma` {#Normal.sigma} +#### `tf.contrib.distributions.Normal.scale` {#Normal.scale} Distribution parameter for standard deviation. diff --git a/tensorflow/g3doc/api_docs/python/functions_and_classes/shard3/tf.contrib.distributions.normal_conjugates_known_sigma_posterior.md b/tensorflow/g3doc/api_docs/python/functions_and_classes/shard8/tf.contrib.distributions.normal_conjugates_known_scale_posterior.md index ae8eb00890..9b2cce1cc4 100644 --- a/tensorflow/g3doc/api_docs/python/functions_and_classes/shard3/tf.contrib.distributions.normal_conjugates_known_sigma_posterior.md +++ b/tensorflow/g3doc/api_docs/python/functions_and_classes/shard8/tf.contrib.distributions.normal_conjugates_known_scale_posterior.md @@ -1,20 +1,20 @@ -### `tf.contrib.distributions.normal_conjugates_known_sigma_posterior(prior, sigma, s, n)` {#normal_conjugates_known_sigma_posterior} +### `tf.contrib.distributions.normal_conjugates_known_scale_posterior(prior, scale, s, n)` {#normal_conjugates_known_scale_posterior} Posterior Normal distribution with conjugate prior on the mean. This model assumes that `n` observations (with sum `s`) come from a -Normal with unknown mean `mu` (described by the Normal `prior`) -and known variance `sigma^2`. The "known sigma posterior" is -the distribution of the unknown `mu`. +Normal with unknown mean `loc` (described by the Normal `prior`) +and known variance `scale^2`. The "known scale posterior" is +the distribution of the unknown `loc`. Accepts a prior Normal distribution object, having parameters -`mu0` and `sigma0`, as well as known `sigma` values of the predictive +`loc0` and `scale0`, as well as known `scale` values of the predictive distribution(s) (also assumed Normal), and statistical estimates `s` (the sum(s) of the observations) and `n` (the number(s) of observations). Returns a posterior (also Normal) distribution object, with parameters -`(mu', sigma'^2)`, where: +`(loc', scale'^2)`, where: ``` mu ~ N(mu', sigma'^2) @@ -22,15 +22,15 @@ sigma'^2 = 1/(1/sigma0^2 + n/sigma^2), mu' = (mu0/sigma0^2 + s/sigma^2) * sigma'^2. ``` -Distribution parameters from `prior`, as well as `sigma`, `s`, and `n`. +Distribution parameters from `prior`, as well as `scale`, `s`, and `n`. will broadcast in the case of multidimensional sets of parameters. ##### Args: * <b>`prior`</b>: `Normal` object of type `dtype`: - the prior distribution having parameters `(mu0, sigma0)`. -* <b>`sigma`</b>: tensor of type `dtype`, taking values `sigma > 0`. + the prior distribution having parameters `(loc0, scale0)`. +* <b>`scale`</b>: tensor of type `dtype`, taking values `scale > 0`. The known stddev parameter(s). * <b>`s`</b>: Tensor of type `dtype`. The sum(s) of observations. * <b>`n`</b>: Tensor of type `int`. The number(s) of observations. @@ -38,7 +38,7 @@ will broadcast in the case of multidimensional sets of parameters. ##### Returns: A new Normal posterior distribution object for the unknown observation - mean `mu`. + mean `loc`. ##### Raises: diff --git a/tensorflow/g3doc/api_docs/python/index.md b/tensorflow/g3doc/api_docs/python/index.md index ebabc187f4..f52fdfd89e 100644 --- a/tensorflow/g3doc/api_docs/python/index.md +++ b/tensorflow/g3doc/api_docs/python/index.md @@ -769,16 +769,16 @@ * [`MultivariateNormalDiagWithSoftplusStDev`](../../api_docs/python/contrib.distributions.md#MultivariateNormalDiagWithSoftplusStDev) * [`MultivariateNormalFull`](../../api_docs/python/contrib.distributions.md#MultivariateNormalFull) * [`Normal`](../../api_docs/python/contrib.distributions.md#Normal) - * [`normal_conjugates_known_sigma_posterior`](../../api_docs/python/contrib.distributions.md#normal_conjugates_known_sigma_posterior) - * [`normal_conjugates_known_sigma_predictive`](../../api_docs/python/contrib.distributions.md#normal_conjugates_known_sigma_predictive) - * [`NormalWithSoftplusSigma`](../../api_docs/python/contrib.distributions.md#NormalWithSoftplusSigma) + * [`normal_conjugates_known_scale_posterior`](../../api_docs/python/contrib.distributions.md#normal_conjugates_known_scale_posterior) + * [`normal_conjugates_known_scale_predictive`](../../api_docs/python/contrib.distributions.md#normal_conjugates_known_scale_predictive) + * [`NormalWithSoftplusScale`](../../api_docs/python/contrib.distributions.md#NormalWithSoftplusScale) * [`Poisson`](../../api_docs/python/contrib.distributions.md#Poisson) * [`QuantizedDistribution`](../../api_docs/python/contrib.distributions.md#QuantizedDistribution) * [`RegisterKL`](../../api_docs/python/contrib.distributions.md#RegisterKL) * [`ReparameterizationType`](../../api_docs/python/contrib.distributions.md#ReparameterizationType) * [`softplus_inverse`](../../api_docs/python/contrib.distributions.md#softplus_inverse) * [`StudentT`](../../api_docs/python/contrib.distributions.md#StudentT) - * [`StudentTWithAbsDfSoftplusSigma`](../../api_docs/python/contrib.distributions.md#StudentTWithAbsDfSoftplusSigma) + * [`StudentTWithAbsDfSoftplusScale`](../../api_docs/python/contrib.distributions.md#StudentTWithAbsDfSoftplusScale) * [`TransformedDistribution`](../../api_docs/python/contrib.distributions.md#TransformedDistribution) * [`Uniform`](../../api_docs/python/contrib.distributions.md#Uniform) * [`WishartCholesky`](../../api_docs/python/contrib.distributions.md#WishartCholesky) |