elbo: Compute the evidence lower bound (ELBO)

In survival.svb: Fit High-Dimensional Proportional Hazards Models

Description

Compute the evidence lower bound (ELBO)

Usage

elbo(Y, delta, X, fit, nrep = 10000, center = TRUE)

Arguments

Y	Failure times.
delta	Censoring indicator, 0: censored, 1: uncensored.
X	Design matrix.
fit	Fit model.
nrep	Number of Monte Carlo samples.
center	Should the design matrix be centered.

Value

Returns a list containing:

mean	The mean of the ELBO.
sd	The standard-deviation of the ELBO.
expected.likelihood	The expectation of the likelihood under the variational posterior.
kl	The KL between the variational posterior and prior.

Details

The evidence lower bound (ELBO) is a popular goodness of fit measure used in variational inference. Under the variational posterior the ELBO is given as

ELBO = E_{\tilde{Π}}[\log L_p(β; Y, X, δ)] - KL(\tilde{Π} \| Π)

where \tilde{Π} is the variational posterior, Π is the prior, L_p(β; Y, X, δ) is Cox's partial likelihood. Intuitively, within the ELBO we incur a trade-off between how well we fit to the data (through the expectation of the log-partial-likelihood) and how close we are to our prior (in terms of KL divergence). Ideally we want the ELBO to be as small as possible.

survival.svb documentation built on Jan. 17, 2022, 5:07 p.m.