| # Copyright 2017 The TensorFlow Authors. All Rights Reserved. |
| # |
| # 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 |
| # |
| # http://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. |
| # ============================================================================== |
| """Multivariate Normal distribution class initialized with a full covariance.""" |
| |
| from __future__ import absolute_import |
| from __future__ import division |
| from __future__ import print_function |
| |
| from tensorflow.contrib.distributions.python.ops import mvn_tril |
| from tensorflow.python.framework import ops |
| from tensorflow.python.ops import array_ops |
| from tensorflow.python.ops import check_ops |
| from tensorflow.python.ops import control_flow_ops |
| from tensorflow.python.ops import linalg_ops |
| from tensorflow.python.util import deprecation |
| |
| |
| __all__ = [ |
| "MultivariateNormalFullCovariance", |
| ] |
| |
| |
| class MultivariateNormalFullCovariance(mvn_tril.MultivariateNormalTriL): |
| """The multivariate normal distribution on `R^k`. |
| |
| The Multivariate Normal distribution is defined over `R^k` and parameterized |
| by a (batch of) length-`k` `loc` vector (aka "mu") and a (batch of) `k x k` |
| `covariance_matrix` matrices that are the covariance. |
| This is different than the other multivariate normals, which are parameterized |
| by a matrix more akin to the standard deviation. |
| |
| #### Mathematical Details |
| |
| The probability density function (pdf) is, with `@` as matrix multiplication, |
| |
| ```none |
| pdf(x; loc, covariance_matrix) = exp(-0.5 y) / Z, |
| y = (x - loc)^T @ inv(covariance_matrix) @ (x - loc) |
| Z = (2 pi)**(0.5 k) |det(covariance_matrix)|**(0.5). |
| ``` |
| |
| where: |
| |
| * `loc` is a vector in `R^k`, |
| * `covariance_matrix` is an `R^{k x k}` symmetric positive definite matrix, |
| * `Z` denotes the normalization constant. |
| |
| Additional leading dimensions (if any) in `loc` and `covariance_matrix` allow |
| for batch dimensions. |
| |
| The MultivariateNormal distribution is a member of the [location-scale |
| family](https://en.wikipedia.org/wiki/Location-scale_family), i.e., it can be |
| constructed e.g. as, |
| |
| ```none |
| X ~ MultivariateNormal(loc=0, scale=1) # Identity scale, zero shift. |
| scale = Cholesky(covariance_matrix) |
| Y = scale @ X + loc |
| ``` |
| |
| #### Examples |
| |
| ```python |
| import tensorflow_probability as tfp |
| tfd = tfp.distributions |
| |
| # Initialize a single 3-variate Gaussian. |
| mu = [1., 2, 3] |
| cov = [[ 0.36, 0.12, 0.06], |
| [ 0.12, 0.29, -0.13], |
| [ 0.06, -0.13, 0.26]] |
| mvn = tfd.MultivariateNormalFullCovariance( |
| loc=mu, |
| covariance_matrix=cov) |
| |
| mvn.mean().eval() |
| # ==> [1., 2, 3] |
| |
| # Covariance agrees with covariance_matrix. |
| mvn.covariance().eval() |
| # ==> [[ 0.36, 0.12, 0.06], |
| # [ 0.12, 0.29, -0.13], |
| # [ 0.06, -0.13, 0.26]] |
| |
| # Compute the pdf of an observation in `R^3` ; return a scalar. |
| mvn.prob([-1., 0, 1]).eval() # shape: [] |
| |
| # Initialize a 2-batch of 3-variate Gaussians. |
| mu = [[1., 2, 3], |
| [11, 22, 33]] # shape: [2, 3] |
| covariance_matrix = ... # shape: [2, 3, 3], symmetric, positive definite. |
| mvn = tfd.MultivariateNormalFullCovariance( |
| loc=mu, |
| covariance=covariance_matrix) |
| |
| # Compute the pdf of two `R^3` observations; return a length-2 vector. |
| x = [[-0.9, 0, 0.1], |
| [-10, 0, 9]] # shape: [2, 3] |
| mvn.prob(x).eval() # shape: [2] |
| |
| ``` |
| |
| """ |
| |
| @deprecation.deprecated( |
| "2018-10-01", |
| "The TensorFlow Distributions library has moved to " |
| "TensorFlow Probability " |
| "(https://github.com/tensorflow/probability). You " |
| "should update all references to use `tfp.distributions` " |
| "instead of `tf.contrib.distributions`.", |
| warn_once=True) |
| def __init__(self, |
| loc=None, |
| covariance_matrix=None, |
| validate_args=False, |
| allow_nan_stats=True, |
| name="MultivariateNormalFullCovariance"): |
| """Construct Multivariate Normal distribution on `R^k`. |
| |
| The `batch_shape` is the broadcast shape between `loc` and |
| `covariance_matrix` arguments. |
| |
| The `event_shape` is given by last dimension of the matrix implied by |
| `covariance_matrix`. The last dimension of `loc` (if provided) must |
| broadcast with this. |
| |
| A non-batch `covariance_matrix` matrix is a `k x k` symmetric positive |
| definite matrix. In other words it is (real) symmetric with all eigenvalues |
| strictly positive. |
| |
| Additional leading dimensions (if any) will index batches. |
| |
| Args: |
| loc: Floating-point `Tensor`. If this is set to `None`, `loc` is |
| implicitly `0`. When specified, may have shape `[B1, ..., Bb, k]` where |
| `b >= 0` and `k` is the event size. |
| covariance_matrix: Floating-point, symmetric positive definite `Tensor` of |
| same `dtype` as `loc`. The strict upper triangle of `covariance_matrix` |
| is ignored, so if `covariance_matrix` is not symmetric no error will be |
| raised (unless `validate_args is True`). `covariance_matrix` has shape |
| `[B1, ..., Bb, k, k]` where `b >= 0` and `k` is the event size. |
| validate_args: Python `bool`, default `False`. When `True` distribution |
| parameters are checked for validity despite possibly degrading runtime |
| performance. When `False` invalid inputs may silently render incorrect |
| outputs. |
| allow_nan_stats: Python `bool`, default `True`. When `True`, |
| statistics (e.g., mean, mode, variance) use the value "`NaN`" to |
| indicate the result is undefined. When `False`, an exception is raised |
| if one or more of the statistic's batch members are undefined. |
| name: Python `str` name prefixed to Ops created by this class. |
| |
| Raises: |
| ValueError: if neither `loc` nor `covariance_matrix` are specified. |
| """ |
| parameters = dict(locals()) |
| |
| # Convert the covariance_matrix up to a scale_tril and call MVNTriL. |
| with ops.name_scope(name) as name: |
| with ops.name_scope("init", values=[loc, covariance_matrix]): |
| if covariance_matrix is None: |
| scale_tril = None |
| else: |
| covariance_matrix = ops.convert_to_tensor( |
| covariance_matrix, name="covariance_matrix") |
| if validate_args: |
| covariance_matrix = control_flow_ops.with_dependencies([ |
| check_ops.assert_near( |
| covariance_matrix, |
| array_ops.matrix_transpose(covariance_matrix), |
| message="Matrix was not symmetric")], covariance_matrix) |
| # No need to validate that covariance_matrix is non-singular. |
| # LinearOperatorLowerTriangular has an assert_non_singular method that |
| # is called by the Bijector. |
| # However, cholesky() ignores the upper triangular part, so we do need |
| # to separately assert symmetric. |
| scale_tril = linalg_ops.cholesky(covariance_matrix) |
| super(MultivariateNormalFullCovariance, self).__init__( |
| loc=loc, |
| scale_tril=scale_tril, |
| validate_args=validate_args, |
| allow_nan_stats=allow_nan_stats, |
| name=name) |
| self._parameters = parameters |