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python - TensorFlow Probability MCMC with Bernoulli distribution

问题描述

I need to use TensorFlow Probability to implement Markov Chain Monte Carlo with sampling from a Bernoulli distribution. However, my attempts are showing results not consistent with what I would expect from a Bernoulli distribution.

I modified the example given in the documentation of tfp.mcmc.sample_chain (sampling from a diagonal-variance Gaussian) example here to draw from a Bernoulli distribution. Since the Bernoulli distribution is discrete, I used the RandomWalkMetropolis transition kernel instead of the Hamiltonian Monte Carlo kernel, which I expect would not work since it computes a gradient.

Here is the code:

import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
import tensorflow as tf
import tensorflow_probability as tfp
tfd = tfp.distributions

def make_likelihood(event_prob):
    return tfd.Bernoulli(probs=event_prob,dtype=tf.float32)


dims=1
event_prob = 0.3
num_results = 30000
likelihood = make_likelihood(event_prob)


states, kernel_results = tfp.mcmc.sample_chain(
    num_results=num_results,
    current_state=tf.zeros(dims),
    kernel = tfp.mcmc.RandomWalkMetropolis(
              target_log_prob_fn=likelihood.log_prob,
              new_state_fn=tfp.mcmc.random_walk_normal_fn(scale=1.0),
              seed=124
             ),
    num_burnin_steps=5000)

chain_vals = states

# Compute sample stats.
sample_mean = tf.reduce_mean(states, axis=0)
sample_var = tf.reduce_mean(
    tf.squared_difference(states, sample_mean),
    axis=0)

#initialize the variable
init_op = tf.global_variables_initializer()

#run the graph
with tf.Session() as sess:
    sess.run(init_op) 
    [sample_mean_, sample_var_, chain_vals_] = sess.run([sample_mean,sample_var,chain_vals])

chain_samples = (chain_vals_[:] )   
print ('Sample mean = {}'.format(sample_mean_))
print ('Sample var = {}'.format(sample_var_))
fig, axes = plt.subplots(2, 1)
fig.set_size_inches(12, 10)

axes[0].plot(chain_samples[:])
axes[0].title.set_text("values sample chain tfd.Bernoulli")
sns.kdeplot(chain_samples[:,0], ax=axes[1], shade=True)
axes[1].title.set_text("chain tfd.Bernoulli distribution")
fig.tight_layout()
plt.show()

I expected to see values for the states of the Markov chain in the interval [0,1].

The result for the Markov chain values does not look like what is expected for a Bernoulli distribution, nor does the KDE plot, as shown in this figure:

enter image description here

Do I have a conceptual flaw with my example, or mistake in using the TensorFlow Probability API ?

Or is there possibly an issue with the TF.Probability implementation of Markov Chain Monte Carlo using a discrete distribution such as the Bernoulli distribution?

标签： pythontensorflow

解决方案

我认为您令人困惑的经历的根源在于您在RandomWalkMetropolis过渡期间仍在使用连续提案分发。TensorFlow Probability 中整数分布（包括Bernoulli）的约定是默认实现连续松弛。IIRC，对于伯努利来说，就是pdf(x) ~ p ** x * (1 - p) ** (1 - x); 正如您所观察到的，一旦x变为负数，这将稳定地将您的随机游走马尔可夫链推向。-inf

您可以对此做几件事：

  1. 使用传递validate_args=True给Bernoulli构造函数。如果不是 0 或 1，这将崩溃x，帮助您检测问题（但如果您想要区间 [0, 1] 中的非整数结果，请不要这样做）。
  2. 使用不同的提案函数，例如 0 和 1 之间的独立统一。编写自己的提案并不难——这是您使用的高斯漂移提案函数的代码：https ://github.com/tensorflow/概率/blob/master/tensorflow_probability/python/mcmc/random_walk_metropolis.py#L97-L107。请注意，提案需要对称才能与RandomWalkMetropolis.
  3. 完全使用不同的 MCMC 转换运算符。

我还提交了一张关于为独立提案制作 TransitionKernel 的票（比如我想你可能需要的）：https ://github.com/tensorflow/probability/issues/218

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