AVhY5dZddlmZddlmZddlmZddlmZddlmZddlmZddlm Z dd lm Z dd l m Z dd l m Zdd lmZdd lmZdgZdZedgGdde j*Zy)z,The DirichletMultinomial distribution class.)dtypes)ops) array_ops) check_ops)control_flow_ops)math_ops) random_ops)special_math_ops) distribution)util) deprecation) tf_exportDirichletMultinomialaFor each batch of counts, `value = [n_0, ..., n_{K-1}]`, `P[value]` is the probability that after sampling `self.total_count` draws from this Dirichlet-Multinomial distribution, the number of draws falling in class `j` is `n_j`. Since this definition is [exchangeable](https://en.wikipedia.org/wiki/Exchangeable_random_variables); different sequences have the same counts so the probability includes a combinatorial coefficient. Note: `value` must be a non-negative tensor with dtype `self.dtype`, have no fractional components, and such that `tf.reduce_sum(value, -1) = self.total_count`. Its shape must be broadcastable with `self.concentration` and `self.total_count`.z"distributions.DirichletMultinomial)v1cXeZdZdZej ddd dfd ZedZedZ ed Z d Z d Z d Z d ZddZej"edZej"edZdZej"ddZdZdZdZdZxZS)raX Dirichlet-Multinomial compound distribution. The Dirichlet-Multinomial distribution is parameterized by a (batch of) length-`K` `concentration` vectors (`K > 1`) and a `total_count` number of trials, i.e., the number of trials per draw from the DirichletMultinomial. It is defined over a (batch of) length-`K` vector `counts` such that `tf.reduce_sum(counts, -1) = total_count`. The Dirichlet-Multinomial is identically the Beta-Binomial distribution when `K = 2`. #### Mathematical Details The Dirichlet-Multinomial is a distribution over `K`-class counts, i.e., a length-`K` vector of non-negative integer `counts = n = [n_0, ..., n_{K-1}]`. The probability mass function (pmf) is, ```none pmf(n; alpha, N) = Beta(alpha + n) / (prod_j n_j!) / Z Z = Beta(alpha) / N! ``` where: * `concentration = alpha = [alpha_0, ..., alpha_{K-1}]`, `alpha_j > 0`, * `total_count = N`, `N` a positive integer, * `N!` is `N` factorial, and, * `Beta(x) = prod_j Gamma(x_j) / Gamma(sum_j x_j)` is the [multivariate beta function]( https://en.wikipedia.org/wiki/Beta_function#Multivariate_beta_function), and, * `Gamma` is the [gamma function]( https://en.wikipedia.org/wiki/Gamma_function). Dirichlet-Multinomial is a [compound distribution]( https://en.wikipedia.org/wiki/Compound_probability_distribution), i.e., its samples are generated as follows. 1. Choose class probabilities: `probs = [p_0,...,p_{K-1}] ~ Dir(concentration)` 2. Draw integers: `counts = [n_0,...,n_{K-1}] ~ Multinomial(total_count, probs)` The last `concentration` dimension parametrizes a single Dirichlet-Multinomial distribution. When calling distribution functions (e.g., `dist.prob(counts)`), `concentration`, `total_count` and `counts` are broadcast to the same shape. The last dimension of `counts` corresponds single Dirichlet-Multinomial distributions. Distribution parameters are automatically broadcast in all functions; see examples for details. #### Pitfalls The number of classes, `K`, must not exceed: - the largest integer representable by `self.dtype`, i.e., `2**(mantissa_bits+1)` (IEE754), - the maximum `Tensor` index, i.e., `2**31-1`. In other words, ```python K <= min(2**31-1, { tf.float16: 2**11, tf.float32: 2**24, tf.float64: 2**53 }[param.dtype]) ``` Note: This condition is validated only when `self.validate_args = True`. #### Examples ```python alpha = [1., 2., 3.] n = 2. dist = DirichletMultinomial(n, alpha) ``` Creates a 3-class distribution, with the 3rd class is most likely to be drawn. The distribution functions can be evaluated on counts. ```python # counts same shape as alpha. counts = [0., 0., 2.] dist.prob(counts) # Shape [] # alpha will be broadcast to [[1., 2., 3.], [1., 2., 3.]] to match counts. counts = [[1., 1., 0.], [1., 0., 1.]] dist.prob(counts) # Shape [2] # alpha will be broadcast to shape [5, 7, 3] to match counts. counts = [[...]] # Shape [5, 7, 3] dist.prob(counts) # Shape [5, 7] ``` Creates a 2-batch of 3-class distributions. ```python alpha = [[1., 2., 3.], [4., 5., 6.]] # Shape [2, 3] n = [3., 3.] dist = DirichletMultinomial(n, alpha) # counts will be broadcast to [[2., 1., 0.], [2., 1., 0.]] to match alpha. counts = [2., 1., 0.] dist.prob(counts) # Shape [2] ``` z 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`.T) warn_oncec Rtt}tj|||g5}tj|d|_|r$t j|j |_|jtj|d||_ tj|jd|_ dddtt|?|jj ||t"j$||j |jg|y#1swY\xYw)aInitialize a batch of DirichletMultinomial distributions. Args: total_count: Non-negative floating point tensor, whose dtype is the same as `concentration`. The shape is broadcastable to `[N1,..., Nm]` with `m >= 0`. Defines this as a batch of `N1 x ... x Nm` different Dirichlet multinomial distributions. Its components should be equal to integer values. concentration: Positive floating point tensor, whose dtype is the same as `n` with shape broadcastable to `[N1,..., Nm, K]` `m >= 0`. Defines this as a batch of `N1 x ... x Nm` different `K` class Dirichlet multinomial distributions. 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. )values total_count)name concentrationN)dtype validate_argsallow_nan_statsreparameterization_type parameters graph_parentsr)dictlocalsr name_scopeconvert_to_tensor _total_countdistribution_util$embed_check_nonnegative_integer_form!_maybe_assert_valid_concentration_concentrationr reduce_sum_total_concentrationsuperr__init__rr NOT_REPARAMETERIZED)selfrrrrrr __class__s i/home/dcms/DCMS/lib/python3.12/site-packages/tensorflow/python/ops/distributions/dirichlet_multinomial.pyr+zDirichletMultinomial.__init__sHfhJ k=%A BOd// -Pd   B B!! # !BB   %4 6 d#+"5"5d6I6I2"Nd%O& .!!''#' , @ @((**, /'OOs BDD&c|jS)z,Number of trials used to construct a sample.)r#r-s r/rz DirichletMultinomial.total_counts   c|jS)zCConcentration parameter; expected prior counts for that coordinate.)r'r1s r/rz"DirichletMultinomial.concentrations   r2c|jS)z+Sum of last dim of concentration parameter.)r)r1s r/total_concentrationz(DirichletMultinomial.total_concentrations  $ $$r2c@tj|jSN)rshaper5r1s r/_batch_shape_tensorz(DirichletMultinomial._batch_shape_tensors ??433 44r2c6|jjSr7)r5 get_shaper1s r/ _batch_shapez!DirichletMultinomial._batch_shapes  # # - - //r2cFtj|jddS)Nr)rr8rr1s r/_event_shape_tensorz(DirichletMultinomial._event_shape_tensors ??4-- .rs 33r2cZ|jjjdddS)Nr)rr;with_rank_at_leastr1s r/ _event_shapez!DirichletMultinomial._event_shapes)    ' ' ) <   t11#77Y=N=N8NO P QQr2aThe covariance for each batch member is defined as the following: ```none Var(X_j) = n * alpha_j / alpha_0 * (1 - alpha_j / alpha_0) * (n + alpha_0) / (1 + alpha_0) ``` where `concentration = alpha` and `total_concentration = alpha_0 = sum_j alpha_j`. The covariance between elements in a batch is defined as: ```none Cov(X_i, X_j) = -n * alpha_i * alpha_j / alpha_0 ** 2 * (n + alpha_0) / (1 + alpha_0) ``` c |j|jz}tjt j |dtj f|dtj ddf |jSrk)_variance_scale_termrmrmatrix_set_diagrmatmulrl _variance)r-r\s r/ _covariancez DirichletMultinomial._covariance%su& !!#djjl2A  $ $  c9$$$ % c9$$a' ( * *   r2cr|j}||jz}||j|z|z zSr7)rormr)r-scaler\s r/rrzDirichletMultinomial._variance@s;  % % 'E  A   5(1, --r2c|jdtjf}tjd||j z zd|zz S)zFHelper to `_covariance` and `_variance` which computes a shared scale..g?)r5rrlrsqrtr)r-c0s r/roz)DirichletMultinomial._variance_scale_termEsG  ! !#y'8'8"8 9B =="rD$4$444bA BBr2c|s|Stj|}tjt j |dg|S)z3Checks the validity of the concentration parameter.z)Concentration parameter must be positive.message)r$#embed_check_categorical_event_shaperwith_dependenciesrassert_positive)r-rrs r/r&z6DirichletMultinomial._maybe_assert_valid_concentrationLsP  %IIM  - -!! ? A/  r2c |js|Stj|}tjt j |jtj|ddg|S)zBCheck counts for proper shape, values, then return tensor version.rz4counts last-dimension must sum to `self.total_count`rz) rr$r%rr}r assert_equalrrr(rhs r/r`z/DirichletMultinomial._maybe_assert_valid_sampleXsg    m  C CF KF  - -   h11&"=J L/  r2)FTrr7)__name__ __module__ __qualname____doc__r deprecatedr+propertyrrr5r9r<r>rBr^r$AppendDocstring"_dirichlet_multinomial_sample_notererirmrsrrror&r` __classcell__)r.s@r/rr2s$k^;' ##* 88t     % %504E(&%$$%GH"I"%$$%GH0I0Q%$$  $% $. C  r2N)rtensorflow.python.frameworkrrtensorflow.python.opsrrrrr r #tensorflow.python.ops.distributionsr r r$tensorflow.python.utilr tensorflow.python.util.tf_exportr__all__r Distributionrr2r/rso3.+++2*,2<I.6  &5" 345n<44n6nr2