AVh-dZddlmZddlmZddlmZddlmZddlmZddlmZddlm Z dd lm Z dd lm Z dd l m Z dd l mZdd lmZddlmZdgZdZedgGdde j,Zy)z#The Multinomial distribution class.)dtypes)ops) array_ops) check_ops)control_flow_ops)map_fn)math_ops)nn_ops) random_ops) distribution)util) deprecation) tf_export MultinomialaFor each batch of counts, `value = [n_0, ... ,n_{k-1}]`, `P[value]` is the probability that after sampling `self.total_count` draws from this 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.probs` and `self.total_count`.zdistributions.Multinomial)v1ceZdZdZej ddd dfd ZedZedZ ed Z d Z d Z d Z d ZddZej"edZdZdZdZdZdZdZxZS)ra3 Multinomial distribution. This Multinomial distribution is parameterized by `probs`, a (batch of) length-`K` `prob` (probability) vectors (`K > 1`) such that `tf.reduce_sum(probs, -1) = 1`, and a `total_count` number of trials, i.e., the number of trials per draw from the Multinomial. It is defined over a (batch of) length-`K` vector `counts` such that `tf.reduce_sum(counts, -1) = total_count`. The Multinomial is identically the Binomial distribution when `K = 2`. #### Mathematical Details The 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; pi, N) = prod_j (pi_j)**n_j / Z Z = (prod_j n_j!) / N! ``` where: * `probs = pi = [pi_0, ..., pi_{K-1}]`, `pi_j > 0`, `sum_j pi_j = 1`, * `total_count = N`, `N` a positive integer, * `Z` is the normalization constant, and, * `N!` denotes `N` factorial. 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 Create a 3-class distribution, with the 3rd class is most likely to be drawn, using logits. ```python logits = [-50., -43, 0] dist = Multinomial(total_count=4., logits=logits) ``` Create a 3-class distribution, with the 3rd class is most likely to be drawn. ```python p = [.2, .3, .5] dist = Multinomial(total_count=4., probs=p) ``` The distribution functions can be evaluated on counts. ```python # counts same shape as p. counts = [1., 0, 3] dist.prob(counts) # Shape [] # p will be broadcast to [[.2, .3, .5], [.2, .3, .5]] to match counts. counts = [[1., 2, 1], [2, 2, 0]] dist.prob(counts) # Shape [2] # p will be broadcast to shape [5, 7, 3] to match counts. counts = [[...]] # Shape [5, 7, 3] dist.prob(counts) # Shape [5, 7] ``` Create a 2-batch of 3-class distributions. ```python p = [[.1, .2, .7], [.3, .3, .4]] # Shape [2, 3] dist = Multinomial(total_count=[4., 5], probs=p) counts = [[2., 1, 1], [3, 1, 1]] dist.prob(counts) # Shape [2] dist.sample(5) # Shape [5, 2, 3] ``` 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 xtt}tj||||g5}tj|d|_|r$t j|j |_t j||d||\|_ |_ |j dtjf|jz|_ dddtt|C|jj"t$j&||||j |j|jg|y#1swYgxYw) aInitialize a batch of Multinomial distributions. Args: total_count: Non-negative floating point tensor with shape broadcastable to `[N1,..., Nm]` with `m >= 0`. Defines this as a batch of `N1 x ... x Nm` different Multinomial distributions. Its components should be equal to integer values. logits: Floating point tensor representing unnormalized log-probabilities of a positive event with shape broadcastable to `[N1,..., Nm, K]` `m >= 0`, and the same dtype as `total_count`. Defines this as a batch of `N1 x ... x Nm` different `K` class Multinomial distributions. Only one of `logits` or `probs` should be passed in. probs: Positive floating point tensor with shape broadcastable to `[N1,..., Nm, K]` `m >= 0` and same dtype as `total_count`. Defines this as a batch of `N1 x ... x Nm` different `K` class Multinomial distributions. `probs`'s components in the last portion of its shape should sum to `1`. Only one of `logits` or `probs` should be passed in. 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. 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