o ?ei7@sdZddlZddlmZddlmZddlmZddlmZddlm Z ddlm Z dd lm Z dd lm Z dd lm Z dd lmZdd lmZddlmZddlmZddlmZddlmZddgZedgdGdddejZGdddeZdS)zStudent's t distribution class.N) constant_op)dtypes)ops) tensor_shape) array_ops) check_ops)control_flow_ops)math_ops)nn) random_ops)special_math_ops) distribution)util) deprecation) tf_exportStudentTStudentTWithAbsDfSoftplusScalezdistributions.StudentT)v1cseZdZdZejdddd   d.fdd Zed d Ze d d Z e d dZ e ddZ ddZ ddZddZddZd/ddZddZddZd d!Zd"d#Zd$d%Zed&d'd(Zed)d*d+Zd,d-ZZS)0ra Student's t-distribution. This distribution has parameters: degree of freedom `df`, location `loc`, and `scale`. #### Mathematical details The probability density function (pdf) is, ```none pdf(x; df, mu, sigma) = (1 + y**2 / df)**(-0.5 (df + 1)) / Z where, y = (x - mu) / sigma Z = abs(sigma) sqrt(df pi) Gamma(0.5 df) / Gamma(0.5 (df + 1)) ``` 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`. Samples of this distribution are reparameterized (pathwise differentiable). The derivatives are computed using the approach described in (Figurnov et al., 2018). #### Examples Examples of initialization of one or a batch of distributions. ```python import tensorflow_probability as tfp tfd = tfp.distributions # Define a single scalar Student t distribution. single_dist = tfd.StudentT(df=3) # Evaluate the pdf at 1, returning a scalar Tensor. single_dist.prob(1.) # Define a batch of two scalar valued Student t's. # The first has degrees of freedom 2, mean 1, and scale 11. # The second 3, 2 and 22. multi_dist = tfd.StudentT(df=[2, 3], 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. multi_dist.prob([0, 1.5]) # Get 3 samples, returning a 3 x 2 tensor. multi_dist.sample(3) ``` 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 = tfd.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. dist.prob(3.0) ``` Compute the gradients of samples w.r.t. the parameters: ```python df = tf.constant(2.0) loc = tf.constant(2.0) scale = tf.constant(11.0) dist = tfd.StudentT(df=df, loc=loc, scale=scale) samples = dist.sample(5) # Shape [5] loss = tf.reduce_mean(tf.square(samples)) # Arbitrary loss function # Unbiased stochastic gradients of the loss function grads = tf.gradients(loss, [df, loc, scale]) ``` References: Implicit Reparameterization Gradients: [Figurnov et al., 2018] (http://papers.nips.cc/paper/7326-implicit-reparameterization-gradients) ([pdf](http://papers.nips.cc/paper/7326-implicit-reparameterization-gradients.pdf)) 2019-01-01zThe TensorFlow Distributions library has moved to TensorFlow Probability (https://github.com/tensorflow/probability). You should update all references to use `tfp.distributions` instead of `tf.distributions`.TZ warn_onceFc stt}tj||||gdH}t|rt|gng+tj|dd|_ tj|dd|_ tj|dd|_ t |j |j |j fWdn1sKwYWdn1sZwYt t|j|j jtj||||j |j |j g|ddS)aConstruct Student's t distributions. The distributions have degree of freedom `df`, mean `loc`, and scale `scale`. 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: df: Floating-point `Tensor`. The degrees of freedom of the distribution(s). `df` must contain only positive values. loc: Floating-point `Tensor`. The mean(s) of the distribution(s). scale: Floating-point `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. validate_args: Python `bool`, default `False`. When `True` distribution parameters are checked for validity despite possibly degrading runtime performance. When `False` invalid inputs may silently render incorrect outputs. allow_nan_stats: Python `bool`, 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. name: Python `str` name prefixed to Ops created by this class. Raises: TypeError: if loc and scale are different dtypes. valuesdfnamelocscaleN)dtypeZreparameterization_type validate_argsallow_nan_stats parametersZ graph_parentsr)dictlocalsr name_scopeZcontrol_dependenciesrZassert_positiveridentity_df_loc_scaleZassert_same_float_dtypesuperr__init__rr ZFULLY_REPARAMETERIZEDselfrrrrrrr  __class__n/home/www/facesmatcher.com/pyenv/lib/python3.10/site-packages/tensorflow/python/ops/distributions/student_t.pyr)s2 ,  zStudentT.__init__cCs ttdtj|tjdgdS)N)rrrr)r!ziprZconvert_to_tensorrint32)Z sample_shaper.r.r/ _param_shapesszStudentT._param_shapescC|jS)z8Degrees of freedom in these Student's t distribution(s).)r%r+r.r.r/rz StudentT.dfcCr5)z/Locations of these Student's t distribution(s).)r&r6r.r.r/rr7z StudentT.loccCr5)z5Scaling factors of these Student's t distribution(s).)r'r6r.r.r/rr7zStudentT.scalec Cs,tt|jtt|jt|jSN)rZbroadcast_dynamic_shapeshaperrrr6r.r.r/_batch_shape_tensors  zStudentT._batch_shape_tensorcCs&tt|j|j|jSr8)rZbroadcast_static_shaper get_shaperrr6r.r.r/ _batch_shapes  zStudentT._batch_shapecCstjgtjdS)Nr0)rZconstantr r3r6r.r.r/_event_shape_tensorszStudentT._event_shape_tensorcCs tgSr8)rZ TensorShaper6r.r.r/ _event_shapes zStudentT._event_shapeNc Cst|g|gd}tj||j|d}|jtj||jd}tj|gd|d|jt j |ddd}|t ||}||j |jS)Nr)rseedr0?Z student_t)salt)betarr?)rconcatbatch_shape_tensorr Z random_normalrronesZ random_gammadistribution_utilZ gen_new_seedr Zrsqrtrr)r+nr?r9Z normal_samplerZ gamma_sampleZsamplesr.r.r/ _sample_ns zStudentT._sample_ncCs|||Sr8)_log_unnormalized_prob_log_normalization)r+xr.r.r/ _log_probszStudentT._log_probcCs2||j|j}d|jdt|d|jS)Ng?@)rrrr log1p)r+rKyr.r.r/rI s"zStudentT._log_unnormalized_probcCsVtt|jdt|jdttjtd|jtd|jdS)Nr@rM)r logabsrrnppilgammar6r.r.r/rJszStudentT._log_normalizationcCs\||jt|j}|j|d|j}dtd|jd|}tt|d|d|S)NrNr@grM) rr rRrrZbetaincrwhere_v2less)r+rKrPZx_tZneg_cdfr.r.r/_cdfsz StudentT._cdfcCstj||jddtjf}||jdtjf}t||gdd}tt |j dt|jt |d|jdt d|jdt d|jS)Nr0.rNr@rM)rrErDrZnewaxisrrCr rQrRrr ZlbetaZdigamma)r+vuZbeta_argr.r.r/_entropys$  zStudentT._entropyzThe 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`.c Cs|jtj||jd}|jr7tjtj|j d}t t |j tj||jd|tj||ddSttjtjg|jd|j ddg|S)Nr0nanrz*mean not defined for components of df <= 1message)rrrErDrrrSarrayr]as_numpy_dtyperVr greaterrfillrwith_dependenciesr assert_less)r+meanr]r.r.r/_mean)s*zStudentT._meanz The variance for Student's T equals ``` df / (df - 2), when df > 2 infinity, when 1 < df <= 2 NaN, when df <= 1 ``` c Cstt|jd|jdt|j}tj||jdt |j |j|}t j t j |jd}t|jt|dk|tj||dd}|jrut j t j|jd}tt|jtj||jd|tj||ddSttjtjg|jd|jddg|S)NrNr0infrr]z.variance not defined for components of df <= 1r^)rrVr rbrZ ones_likerErDrZsquarerrSr`rhrarcrr]rrdrre)r+denomvarrhZresult_where_definedr]r.r.r/ _varianceAsF   zStudentT._variancecCs t|jSr8)rr$rr6r.r.r/_modeks zStudentT._mode)FTrr8)__name__ __module__ __qualname____doc__r deprecatedr) staticmethodr4propertyrrrr:r<r=r>rHrLrIrJrXr\rFZAppendDocstringrgrkrl __classcell__r.r.r,r/r*sHc 6        !cs8eZdZdZejdddd   d fdd ZZS) rzBStudentT with `df = floor(abs(df))` and `scale = softplus(scale)`.rzLUse `tfd.StudentT(tf.floor(tf.abs(df)), loc, tf.nn.softplus(scale)) instead.TrFc sxtt}tj|||gd!}tt|jtt ||t j |dd|||dWdn1s2wY||_ dS)NrZsoftplus_scaler)rrrrrr) r!r"rr#r(rr)r floorrRr Zsoftplus _parametersr*r,r.r/r)rs    z'StudentTWithAbsDfSoftplusScale.__init__)FTr)rmrnrorprrqr)rtr.r.r,r/ros )rpnumpyrSZtensorflow.python.frameworkrrrrZtensorflow.python.opsrrrr r r r Z#tensorflow.python.ops.distributionsr rrFZtensorflow.python.utilrZ tensorflow.python.util.tf_exportr__all__ Distributionrrr.r.r.r/s2                F