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python - n-batch > 1 的多元正态分布

问题描述

我试图将如何在最新版本的 Tensorflow中使用 MultiVariateNormal 分布中给出的示例概括为二维但不止一批的正态分布。当我运行以下命令时：

from tensorflow_probability import distributions as tfd
import tensorflow as tf

tf.compat.v1.enable_eager_execution()

mu = [[1, 2],
        [-1,-2]]

cov = [[1, 3./5],
        [3./5, 2]]

cov = [cov, cov] # for demonstration purpose, use same cov for both batches

mvn = tfd.MultivariateNormalFullCovariance(
        loc=mu,
        covariance_matrix=cov)

# generate the pdf
X, Y = tf.meshgrid(tf.range(-3, 3, 0.1), tf.range(-3, 3, 0.1))
idx = tf.concat([tf.reshape(X, [-1, 1]), tf.reshape(Y,[-1,1])], axis =1)
prob = tf.reshape(mvn.prob(idx), tf.shape(X))

我收到不兼容的形状错误：

tensorflow.python.framework.errors_impl.InvalidArgumentError: Incompatible shapes: [3600,2] vs. [2,2] [Op:Sub] name: MultivariateNormalFullCovariance/log_prob/affine_linear_operator/inverse/sub/

我对文档（https://www.tensorflow.org/api_docs/python/tf/contrib/distributions/MultivariateNormalFullCovariance）的理解是，要计算 pdf，需要一个 [n_observation, n_dimensions] 张量（在这个例子：idx.shape= TensorShape([Dimension(3600), Dimension(2)])）。我数学错了吗？

标签： pythontensorflowtensorflow-probability

解决方案

您需要idx在倒数第二个位置的张量中添加一个批处理轴，因为 60x60 不能针对mvn.batch_shapeof 进行广播(2,)。

# TF/TFP Imports
!pip install --quiet tfp-nightly tf-nightly
import tensorflow.compat.v2 as tf
tf.enable_v2_behavior()
import tensorflow_probability as tfp
tfd = tfp.distributions

mu = [[1, 2],
      [-1, -2]]

cov = [[1, 3./5],
       [3./5, 2]]

cov = [cov, cov] # for demonstration purpose, use same cov for both batches

mvn = tfd.MultivariateNormalFullCovariance(
    loc=mu, covariance_matrix=cov)
print(mvn.batch_shape, mvn.event_shape)

# generate the pdf
X, Y = tf.meshgrid(tf.range(-3, 3, 0.1), tf.range(-3, 3, 0.1))
print(X.shape)
idx = tf.stack([X, Y], axis=-1)[..., tf.newaxis, :]
print(idx.shape)

probs = mvn.prob(idx)
print(probs.shape)

输出：

(2,) (2,)   # mvn.batch_shape, mvn.event_shape
(60, 60)    # X.shape
(60, 60, 1, 2)   # idx.shape == X.shape + (1 "broadcast against batch", 2 "event")
(60, 60, 2)  # probs.shape == X.shape + (2 "mvn batch shape")

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