LostTech.TensorFlow : API Documentation

Type MultivariateNormalFullCovariance

Namespace tensorflow.contrib.distributions

Parent MultivariateNormalTriL

Interfaces IMultivariateNormalFullCovariance

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
Show Example 
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]

Properties

Public properties

object allow_nan_stats get;

object allow_nan_stats_dyn get;

TensorShape batch_shape get;

object batch_shape_dyn get;

object bijector get;

object bijector_dyn get;

object distribution get;

object distribution_dyn get;

object dtype get;

object dtype_dyn get;

TensorShape event_shape get;

object event_shape_dyn get;

object loc get;

object loc_dyn get;

string name get;

object name_dyn get;

IDictionary<object, object> parameters get;

object parameters_dyn get;

object PythonObject get;

object reparameterization_type get;

object reparameterization_type_dyn get;

object scale get;

object scale_dyn get;

object validate_args get;

object validate_args_dyn get;