Question

爱德华示例

不推荐使用Edward，并且需要较旧版本的TensorFlow的人可以为以下示例创建专用的虚拟环境

playground::dot_x: # @playground::dot_x
# %bb.0:
    movsd   xmm0, qword ptr [rdi + 8] # xmm0 = mem[0],zero
    subsd   xmm0, qword ptr [rdi + 16]
    addsd   xmm0, qword ptr [rdi + 40]
    subsd   xmm0, qword ptr [rdi + 56]
    ret

我有一个非常简单的最小工作示例，该示例将哈密顿蒙特卡洛与爱德华结合使用，名为$ python3 --version Python 3.6.8 $ python3 -m venv edward $ source edward/bin/activate (edward) $ pip3 install --upgrade pip setuptools wheel (edward) $ cat edward.txt tensorflow==1.7 edward~=1.3 scipy~=1.2 pandas~=0.24 matplotlib~=3.0 (edward) $ pip3 install -r edward.txt

edward_old.py

将通过以下方式生成图

#!/usr/bin/env python3

import numpy as np
import scipy.stats
import tensorflow as tf
import edward as ed
import pandas as pd
import matplotlib.pyplot as plt


def generate_samples(data, n_samples):
    # Pick initial point for MCMC chains based on the data
    low, med, high = np.percentile(data, (16, 50, 84))
    mu_init = np.float32(med)
    t_init = np.float32(np.log(0.5 * (high - low)))

    # Build a very simple model
    mu = ed.models.Uniform(-1.0, 1.0)
    t = ed.models.Uniform(*np.log((0.05, 1.0), dtype=np.float32))
    X = ed.models.Normal(
        loc=tf.fill(data.shape, mu), scale=tf.fill(data.shape, tf.exp(t))
    )

    # Emperical samples of a sclar
    q_mu = ed.models.Empirical(params=tf.Variable(tf.fill((n_samples,), mu_init)))
    q_t = ed.models.Empirical(params=tf.Variable(tf.fill((n_samples,), t_init)))

    # Run inference using HMC to generate samples.
    with tf.Session() as sess:
        inference = ed.HMC({mu: q_mu, t: q_t}, data={X: data})
        inference.run(step_size=0.01, n_steps=10)
        mu_samples, t_samples = sess.run([q_mu.params, q_t.params])
    return mu_samples, t_samples


def visualize(samples, mu_grid, sigma_grid):
    fig, ax = plt.subplots(1, 1, figsize=(6, 5))
    ax.scatter(samples['mu'], samples['sigma'], s=5, lw=0, c='black')
    ax.set_xlim(mu_grid[0], mu_grid[-1])
    ax.set_ylim(sigma_grid[0], sigma_grid[-1])
    ax.set_title('Edward')
    ax.set_xlabel('$\mu$')
    ax.set_ylabel('$\sigma$')
    plt.savefig('edward_old.pdf')


def main():
    np.random.seed(0)
    tf.set_random_seed(0)

    # Generate pseudodata from draws from a single normal distribution
    dist_mean = 0.0
    dist_std = 0.5
    n_events = 5000
    toy_data = scipy.stats.norm.rvs(dist_mean, dist_std, size=n_events)

    mu_samples, t_samples = generate_samples(toy_data, n_events)
    samples = pd.DataFrame({'mu': mu_samples, 'sigma': np.exp(t_samples)})

    n_grid = 50
    mu_grid = np.linspace(*np.percentile(mu_samples, (0.5, 99.5)), n_grid)
    sigma_grid = np.linspace(*np.exp(np.percentile(t_samples, (0.5, 99.5))), n_grid)
    visualize(samples, mu_grid, sigma_grid)


if __name__ == '__main__':
    main()

Edward2示例

但是，当我尝试在以下环境中使用TensorFlow Probability和Edward2复制它时

(edward) $ python3 edward_old.py

，以下是$ python3 --version Python 3.6.8 $ python3 -m venv tfp-edward2 $ source tfp-edward2/bin/activate (tfp-edward2) $ pip3 install --upgrade pip setuptools wheel (tfp-edward2) $ cat tfp-edward2.txt tensorflow~=1.13 tensorflow-probability~=0.6 scipy~=1.2 pandas~=0.24 matplotlib~=3.0 (tfp-edward2) $ pip3 install -r tfp-edward2.txt的{{1}}在名为edward_old.py的文件中的更改

generate_samples

运行

edward2.py

表明存在一些明显的问题。我认为我没有正确地制定与#!/usr/bin/env python3 import numpy as np import scipy.stats import tensorflow as tf import tensorflow_probability as tfp from tensorflow_probability import edward2 as ed import pandas as pd import matplotlib.pyplot as plt def generate_samples(data, n_samples): # Pick initial point for MCMC chains based on the data low, med, high = np.percentile(data, (16, 50, 84)) mu_init = np.float32(med) t_init = np.float32(np.log(0.5 * (high - low))) def model(data_shape): mu = ed.Uniform( low=tf.fill(data_shape, -1.0), high=tf.fill(data_shape, 1.0), name="mu" ) t = ed.Uniform( low=tf.log(tf.fill(data_shape, 0.05)), high=tf.log(tf.fill(data_shape, 1.0)), name="t", ) x = ed.Normal(loc=mu, scale=tf.exp(t), name="x") return x log_joint = ed.make_log_joint_fn(model) def target_log_prob_fn(mu, t): """Target log-probability as a function of states.""" return log_joint(data.shape, mu=mu, t=t, x=data) step_size = tf.get_variable( name='step_size', initializer=0.01, use_resource=True, # For TFE compatibility trainable=False, ) num_burnin_steps = 1000 hmc_kernel = tfp.mcmc.HamiltonianMonteCarlo( target_log_prob_fn=target_log_prob_fn, num_leapfrog_steps=5, step_size=step_size, step_size_update_fn=tfp.mcmc.make_simple_step_size_update_policy( num_adaptation_steps=int(num_burnin_steps * 0.8) ), ) # How should these be done? q_mu = tf.random_normal(data.shape, mean=mu_init) q_t = tf.random_normal(data.shape, mean=t_init) states, kernel_results = tfp.mcmc.sample_chain( num_results=n_samples, current_state=[q_mu, q_t], kernel=hmc_kernel, num_burnin_steps=num_burnin_steps, ) # Initialize all constructed variables. init_op = tf.global_variables_initializer() # Run the inference using HMC to generate samples with tf.Session() as sess: init_op.run() states_, results_ = sess.run([states, kernel_results]) mu_samples, t_samples = states_[0][0], states_[1][0] return mu_samples, t_samples等效的公式，因此，如果对此有任何想法或我做错了，那太好了。

我已经尝试遵循“ Upgrading from Edward to Edward2”示例，但是我对它们的理解还不够，无法将其从(tfp-edward2) $ python3 edward2.py模型中使用的示例转移到该示例。 / p>

Answer 1

我为自己创建的问题完全搞乱了分布的形状。起初我没有正确掌握的是，我的current_state中的tfp.mcmc.sample_chain应该是代表链的初始位置的标量（shape==()）。一旦意识到这一点，就可以清楚地知道q_mu和q_t的位置形状非常错误，应该是根据数据确定的位置中的样本的平均值。

q_mu = tf.reduce_mean(tf.random_normal((1000,), mean=mu_init))
q_t = tf.reduce_mean(tf.random_normal((1000,), mean=t_init))

由于这些值是标量，因此我也一直在错误地创建模型的形状。我一直在创建随机变量的样本，这些样本的形状与我的数据相同，但错误地认为这只是将x的形状移动到mu和t的形状。当然，mu和t是来自其各自均匀分布的标量随机变量，然后它们是x的正态分布的参数，从中抽取data.shape样本

def model(data_shape):
    mu = ed.Uniform(low=-1.0, high=1.0, name="mu")
    t = ed.Uniform(low=tf.log(0.05), high=tf.log(1.0), name="t")
    x = ed.Normal(
        loc=tf.fill(data_shape, mu), scale=tf.fill(data_shape, tf.exp(t)), name="x"
    )
    return x

完成此操作后，剩下要做的就是立即正确访问状态

with tf.Session() as sess:
    init_op.run()
    states_, results_ = sess.run([states, kernel_results])
    mu_samples, t_samples = (states_[0], states_[1])

并产生以下图像

(tfp-edward2) $ python3 edward2.py

这与使用Edward的原始版本非常匹配。

完整的脚本在下面

#!/usr/bin/env python3

import numpy as np
import scipy.stats
import tensorflow as tf
import tensorflow_probability as tfp
from tensorflow_probability import edward2 as ed
import pandas as pd
import matplotlib.pyplot as plt


def generate_samples(data, n_samples):
    # Pick initial point for MCMC chains based on the data
    low, med, high = np.percentile(data, (16, 50, 84))
    mu_init = np.float32(med)
    t_init = np.float32(np.log(0.5 * (high - low)))

    def model(data_shape):
        mu = ed.Uniform(low=-1.0, high=1.0, name="mu")
        t = ed.Uniform(low=tf.log(0.05), high=tf.log(1.0), name="t")
        x = ed.Normal(
            loc=tf.fill(data_shape, mu), scale=tf.fill(data_shape, tf.exp(t)), name="x"
        )
        return x

    log_joint = ed.make_log_joint_fn(model)

    def target_log_prob_fn(mu, t):
        """Target log-probability as a function of states."""
        return log_joint(data.shape, mu=mu, t=t, x=data)

    step_size = tf.get_variable(
        name='step_size',
        initializer=0.01,
        use_resource=True,  # For TFE compatibility
        trainable=False,
    )

    num_burnin_steps = 1000

    hmc_kernel = tfp.mcmc.HamiltonianMonteCarlo(
        target_log_prob_fn=target_log_prob_fn,
        num_leapfrog_steps=5,
        step_size=step_size,
        step_size_update_fn=tfp.mcmc.make_simple_step_size_update_policy(
            num_adaptation_steps=int(num_burnin_steps * 0.8)
        ),
    )

    # Initial states of chains
    q_mu = tf.reduce_mean(tf.random_normal((1000,), mean=mu_init))
    q_t = tf.reduce_mean(tf.random_normal((1000,), mean=t_init))

    states, kernel_results = tfp.mcmc.sample_chain(
        num_results=n_samples,
        current_state=[q_mu, q_t],
        kernel=hmc_kernel,
        num_burnin_steps=num_burnin_steps,
    )

    # Initialize all constructed variables.
    init_op = tf.global_variables_initializer()

    # Run the inference using HMC to generate samples
    with tf.Session() as sess:
        init_op.run()
        states_, results_ = sess.run([states, kernel_results])
        mu_samples, t_samples = (states_[0], states_[1])

    return mu_samples, t_samples


def visualize(samples, mu_grid, sigma_grid):
    fig, ax = plt.subplots(1, 1, figsize=(6, 5))
    ax.scatter(samples['mu'], samples['sigma'], s=5, lw=0, c='black')
    ax.set_xlim(mu_grid[0], mu_grid[-1])
    ax.set_ylim(sigma_grid[0], sigma_grid[-1])
    ax.set_title('tfp and Edward2')
    ax.set_xlabel('$\mu$')
    ax.set_ylabel('$\sigma$')
    plt.savefig('tfp-edward2.pdf')
    plt.savefig('tfp-edward2.png')


def main():
    np.random.seed(0)
    tf.set_random_seed(0)

    # Generate pseudodata from draws from a single normal distribution
    dist_mean = 0.0
    dist_std = 0.5
    n_events = 5000
    toy_data = scipy.stats.norm.rvs(dist_mean, dist_std, size=n_events)

    mu_samples, t_samples = generate_samples(toy_data, n_events)
    samples = pd.DataFrame({'mu': mu_samples, 'sigma': np.exp(t_samples)})

    n_grid = 50
    mu_grid = np.linspace(*np.percentile(mu_samples, (0.5, 99.5)), n_grid)
    sigma_grid = np.linspace(*np.exp(np.percentile(t_samples, (0.5, 99.5))), n_grid)
    visualize(samples, mu_grid, sigma_grid)


if __name__ == '__main__':
    main()

具有TensorFlow概率的Edward2的简单哈密顿蒙特卡洛示例

爱德华示例

Edward2示例

1 个答案: