distributions.py

# Copyright 2020 DeepMind Technologies Limited.
#
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# https://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""Module for all distribution implementations needed for the loss functions."""
import math
import jax
import jax.numpy as jnp


class MultivariateNormalDiag:
  """Multivariate normal distribution on `R^k`."""

  def __init__(
      self,
      loc: jnp.ndarray,
      scale_diag: jnp.ndarray):
    """Initializes a MultivariateNormalDiag distribution.

    Args:
      loc: Mean vector of the distribution. Can also be a batch of vectors.
      scale_diag: Vector of standard deviations.
    """
    super().__init__()
    self._loc = loc
    self._scale_diag = scale_diag

  @property
  def loc(self) -> jnp.ndarray:
    """Mean of the distribution."""
    return self._loc

  @property
  def scale_diag(self) -> jnp.ndarray:
    """Scale of the distribution."""
    return self._scale_diag

  def _num_dims(self) -> int:
    """Dimensionality of the events."""
    return self._scale_diag.shape[-1]

  def _standardize(self, value: jnp.ndarray) -> jnp.ndarray:
    return (value - self._loc) / self._scale_diag

  def log_prob(self, value: jnp.ndarray) -> jnp.ndarray:
    """See `Distribution.log_prob`."""
    log_unnormalized = -0.5 * jnp.square(self._standardize(value))
    log_normalization = 0.5 * math.log(2 * math.pi) + jnp.log(self._scale_diag)
    return jnp.sum(log_unnormalized - log_normalization, axis=-1)

  def mean(self) -> jnp.ndarray:
    """Calculates the mean."""
    return self.loc

  def sample(self, seed: jnp.ndarray) -> jnp.ndarray:
    """Samples an event.

    Args:
      seed: PRNG key or integer seed.

    Returns:
      A sample.
    """
    eps = jax.random.normal(seed, self.loc.shape)
    return self.loc + eps * self.scale_diag