tfprobability (version 0.10.0.0)

tfd_covariance: Covariance.

Description

Covariance is (possibly) defined only for non-scalar-event distributions. For example, for a length-k, vector-valued distribution, it is calculated as, Cov[i, j] = Covariance(X_i, X_j) = E[(X_i - E[X_i]) (X_j - E[X_j])] where Cov is a (batch of) k x k matrix, 0 <= (i, j) < k, and E denotes expectation.

Usage

tfd_covariance(distribution, ...)

Arguments

distribution

The distribution being used.

...

Additional parameters passed to Python.

Value

Floating-point Tensor with shape [B1, ..., Bn, k, k] where the first n dimensions are batch coordinates and k = reduce_prod(self.event_shape).

Details

Alternatively, for non-vector, multivariate distributions (e.g., matrix-valued, Wishart), Covariance shall return a (batch of) matrices under some vectorization of the events, i.e., Cov[i, j] = Covariance(Vec(X)_i, Vec(X)_j) = [as above] where Cov is a (batch of) k x k matrices, 0 <= (i, j) < k = reduce_prod(event_shape), and Vec is some function mapping indices of this distribution's event dimensions to indices of a length-k vector.

See Also

Other distribution_methods: tfd_cdf(), tfd_cross_entropy(), tfd_entropy(), tfd_kl_divergence(), tfd_log_cdf(), tfd_log_prob(), tfd_log_survival_function(), tfd_mean(), tfd_mode(), tfd_prob(), tfd_quantile(), tfd_sample(), tfd_stddev(), tfd_survival_function(), tfd_variance()

Examples

# NOT RUN {
d <- tfd_vector_diffeomixture(
 mix_loc = list(c(0, 1)),
 temperature = list(1),
 distribution = tfd_normal(loc = 0, scale = 1),
 loc = list(NULL, rep(2, 5)),
 scale = list(
  tf$linalg$LinearOperatorScaledIdentity(
      num_rows = 5L,
      multiplier = 1.1,
      is_positive_definite = TRUE),
  tf$linalg$LinearOperatorDiag(
      diag = seq(2.5, 3.5,  length.out = 5),
      is_positive_definite = TRUE)))
  d %>% tfd_covariance()
# }