Quadrature Compound: An approximating family of distributions
Abstract
Compound distributions allow construction of a rich set of distributions. Typically
they involve an intractable integral. Here we use a quadrature approximation to that
integral to define the quadrature compound family. Special care is taken that this
approximation is suitable for computation of gradients with respect to distribution pa-
rameters. This technique is applied to discrete (Poisson LogNormal) and continuous
distributions. In the continuous case, quadrature compound family naturally makes use
of parameterized transformations of unparameterized distributions (a.k.a “reparame-
terization”), allowing for gradients of expectations to be estimated as the gradient of
a sample mean. This is demonstrated in a novel distribution, the diffeomixture, which
is is a reparameterizable approximation to a mixture distribution.
they involve an intractable integral. Here we use a quadrature approximation to that
integral to define the quadrature compound family. Special care is taken that this
approximation is suitable for computation of gradients with respect to distribution pa-
rameters. This technique is applied to discrete (Poisson LogNormal) and continuous
distributions. In the continuous case, quadrature compound family naturally makes use
of parameterized transformations of unparameterized distributions (a.k.a “reparame-
terization”), allowing for gradients of expectations to be estimated as the gradient of
a sample mean. This is demonstrated in a novel distribution, the diffeomixture, which
is is a reparameterizable approximation to a mixture distribution.
Research Areas
