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Evidence Lower Bound (ELBO) for Flow-Based Variational Inference

Source: R/elbo.r
ELBOflow.Rd

Computes the ELBO:

Usage

ELBOflow(flow, Qobs, pxgivenz, nmc = 256)

Arguments

flow

A flow model created by makeflow().

Qobs

Observed empirical distribution (probability vector).

pxgivenz

A function mapping a latent vector z to a categorical pmf.

nmc

Number of Monte Carlo samples.

Value

A numeric ELBO value.

Details

\(\log p(x \| z) + \log p(z) - \log q(z)\)

where:

  • q(z) is the flow-based variational posterior

  • p(z) is a standard Gaussian prior

  • p(x | z) is provided by the user as pxgivenz

The expectation is approximated via Monte Carlo sampling.

Examples

f <- makeflow("planar", list(u = 0.1, w = 0.2, b = 0))
px <- function(z) c(0.3, 0.4, 0.3)
ELBOflow(f, Qobs = c(0.2, 0.5, 0.3), pxgivenz = px, nmc = 100)
#> [1] -1.061949