# tfp.trainable_distributions.poisson

Constructs a trainable `tfd.Poisson` distribution. (deprecated)

``````tfp.trainable_distributions.poisson(
*args,
**kwargs
)
``````

This function creates a Poisson distribution parameterized by log rate. Using default args, this function is mathematically equivalent to:

``````Y = Poisson(log_rate=matmul(W, x) + b)

where,
W in R^[d, n]
b in R^d
``````

#### Examples

This can be used as a Poisson regression loss.

``````# This example fits a poisson regression loss.
import numpy as np
import tensorflow as tf
import tensorflow_probability as tfp

# Create fictitious training data.
dtype = np.float32
n = 3000    # number of samples
x_size = 4  # size of single x
def make_training_data():
np.random.seed(142)
x = np.random.randn(n, x_size).astype(dtype)
w = np.random.randn(x_size).astype(dtype)
b = np.random.randn(1).astype(dtype)
true_log_rate = np.tensordot(x, w, axes=[[-1], [-1]]) + b
y = np.random.poisson(lam=np.exp(true_log_rate)).astype(dtype)
return y, x
y, x = make_training_data()

# Build TF graph for fitting Poisson maximum likelihood estimator.
poisson = tfp.trainable_distributions.poisson(x)
loss = -tf.reduce_mean(poisson.log_prob(y))
mse = tf.reduce_mean(tf.squared_difference(y, poisson.mean()))
init_op = tf.global_variables_initializer()

# Run graph 1000 times.
num_steps = 1000
loss_ = np.zeros(num_steps)   # Style: `_` to indicate sess.run result.
mse_ = np.zeros(num_steps)
with tf.Session() as sess:
sess.run(init_op)
for it in xrange(loss_.size):
_, loss_[it], mse_[it] = sess.run([train_op, loss, mse])
if it % 200 == 0 or it == loss_.size - 1:
print("iteration:{}  loss:{}  mse:{}".format(it, loss_[it], mse_[it]))

# ==> iteration:0    loss:37.0814208984  mse:6359.41259766
#     iteration:200  loss:1.42010736465  mse:40.7654914856
#     iteration:400  loss:1.39027583599  mse:8.77660560608
#     iteration:600  loss:1.3902695179   mse:8.78443241119
#     iteration:800  loss:1.39026939869  mse:8.78443622589
#     iteration:999  loss:1.39026939869  mse:8.78444766998
``````

#### Args:

• `x`: `Tensor` with floating type. Must have statically defined rank and statically known right-most dimension.
• `layer_fn`: Python `callable` which takes input `x` and `int` scalar `d` and returns a transformation of `x` with shape `tf.concat([tf.shape(x)[:-1], [1]], axis=0)`. Default value: `tf.layers.dense`.
• `log_rate_fn`: Python `callable` which transforms the `log_rate` parameter. Takes a (batch of) length-`dims` vectors and returns a `Tensor` of same shape and `dtype`. Default value: `lambda x: x`.
• `name`: A `name_scope` name for operations created by this function. Default value: `None` (i.e., "poisson").

#### Returns:

• `poisson`: An instance of `tfd.Poisson`.