chainer.distributions.Independent¶

class chainer.distributions.Independent(distribution, reinterpreted_batch_ndims=None)[source]¶

Independent distribution.

Parameters

distribution (Distribution) – The base distribution instance to transform.
reinterpreted_batch_ndims (int) – Integer number of rightmost batch dims which will be regarded as event dims. When None all but the first batch axis (batch axis 0) will be transferred to event dimensions.

Methods

cdf(x)[source]¶

Evaluates the cumulative distribution function at the given points.

Parameters: x (Variable or N-dimensional array) – Data points in the domain of the distribution
Returns: Cumulative distribution function value evaluated at x.
Return type: Variable

icdf(x)[source]¶

The inverse cumulative distribution function for multivariate variable.

Cumulative distribution function for multivariate variable is not invertible. This function always raises RuntimeError.

Parameters: x (Variable or N-dimensional array) – Data points in the codomain of the distribution
Raises: RuntimeError –

log_cdf(x)[source]¶

Evaluates the log of cumulative distribution function at the given points.

Parameters: x (Variable or N-dimensional array) – Data points in the domain of the distribution
Returns: Logarithm of cumulative distribution function value evaluated at x.
Return type: Variable

log_prob(x)[source]¶

Evaluates the logarithm of probability at the given points.

Parameters: x (Variable or N-dimensional array) – Data points in the domain of the distribution
Returns: Logarithm of probability evaluated at x.
Return type: Variable

log_survival_function(x)[source]¶

Evaluates the logarithm of survival function at the given points.

Parameters: x (Variable or N-dimensional array) – Data points in the domain of the distribution
Returns: Logarithm of survival function value evaluated at x.
Return type: Variable

perplexity(x)[source]¶

Evaluates the perplexity function at the given points.

Parameters: x (Variable or N-dimensional array) – Data points in the domain of the distribution
Returns: Perplexity function value evaluated at x.
Return type: Variable

prob(x)[source]¶

Evaluates probability at the given points.

Parameters: x (Variable or N-dimensional array) – Data points in the domain of the distribution
Returns: Probability evaluated at x.
Return type: Variable

sample(sample_shape=())[source]¶

Samples random points from the distribution.

This function calls sample_n and reshapes a result of sample_n to sample_shape + batch_shape + event_shape. On implementing sampling code in an inherited distribution class, it is not recommended that you override this function. Instead of doing this, it is preferable to override sample_n.

Parameters: sample_shape (tuple of int) – Sampling shape.
Returns: Sampled random points.
Return type: Variable

sample_n(n)[source]¶

Samples n random points from the distribution.

This function returns sampled points whose shape is (n,) + batch_shape + event_shape. When implementing sampling code in a subclass, it is recommended that you override this method.

Parameters: n (int) – Sampling size.
Returns: sampled random points.
Return type: Variable

survival_function(x)[source]¶

Evaluates the survival function at the given points.

Parameters: x (Variable or N-dimensional array) – Data points in the domain of the distribution
Returns: Survival function value evaluated at x.
Return type: Variable

__eq__()¶: Return self==value.

__ne__()¶: Return self!=value.

__lt__()¶: Return self<value.

__le__()¶: Return self<=value.

__gt__()¶: Return self>value.

__ge__()¶: Return self>=value.

Attributes

batch_shape¶

Returns the shape of a batch.

Returns: The shape of a sample that is not identical and independent.
Return type: tuple

covariance¶

The covariance of the independent distribution.

By definition, the covariance of the new distribution becomes block diagonal matrix. Let \(\Sigma_{\mathbf{x}}\) be the covariance matrix of the original random variable \(\mathbf{x} \in \mathbb{R}^d\), and \(\mathbf{x}^{(1)}, \mathbf{x}^{(2)}, \cdots \mathbf{x}^{(m)}\) be the \(m\) i.i.d. random variables, new covariance matrix \(\Sigma_{\mathbf{y}}\) of \(\mathbf{y} = [\mathbf{x}^{(1)}, \mathbf{x}^{(2)}, \cdots, \mathbf{x}^{(m)}] \in \mathbb{R}^{md}\) can be written as

\[\begin{split}\left[\begin{array}{ccc} \Sigma_{\mathbf{x}^{1}} & & 0 \\ & \ddots & \\ 0 & & \Sigma_{\mathbf{x}^{m}} \end{array} \right].\end{split}\]

Note that this relationship holds only if the covariance matrix of the original distribution is given analytically.

Returns: The covariance of the distribution.
Return type: Variable

distribution¶

entropy¶

Returns the entropy of the distribution.

Returns: The entropy of the distribution.
Return type: Variable

event_shape¶

Returns the shape of an event.

Returns: The shape of a sample that is not identical and independent.
Return type: tuple

mean¶

Returns the mean of the distribution.

Returns: The mean of the distribution.
Return type: Variable

mode¶

Returns the mode of the distribution.

Returns: The mode of the distribution.
Return type: Variable

params¶

Returns the parameters of the distribution.

Returns: The parameters of the distribution.
Return type: dict

reinterpreted_batch_ndims¶

stddev¶

Returns the standard deviation of the distribution.

Returns: The standard deviation of the distribution.
Return type: Variable

support¶

Returns the support of the distribution.

Returns: String that means support of this distribution.
Return type: str

variance¶

Returns the variance of the distribution.

Returns: The variance of the distribution.
Return type: Variable

xp¶

Array module for the distribution.

Depending on which of CPU/GPU this distribution is on, this property returns numpy or cupy.