Covariance.
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.
tfd_covariance(distribution, ...)
distribution |
The distribution being used. |
... |
Additional parameters passed to Python. |
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.
Floating-point Tensor with shape [B1, ..., Bn, k, k] where the first n dimensions
are batch coordinates and k = reduce_prod(self.event_shape).
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()
d <- tfd_normal(loc = c(1, 2), scale = c(1, 0.5)) d %>% tfd_variance()
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