Delta-AI: Local objectives for amortized inference in sparse graphical models

TL;DR

Delta-AI introduces a local, efficient amortized inference algorithm for sparse PGMs that leverages local credit assignment and generative flow network principles to improve training speed and inference accuracy.

Contribution

It proposes a novel $ ext{ extDelta}$-amortized inference method that uses local constraints and off-policy training to efficiently learn samplers for sparse PGMs.

Findings

Effective in sampling from synthetic PGMs

Speeds up training of latent variable models with sparse structure

Accurately recovers marginals and conditional distributions

Abstract

We present a new algorithm for amortized inference in sparse probabilistic graphical models (PGMs), which we call $\Delta$-amortized inference ($\Delta$-AI). Our approach is based on the observation that when the sampling of variables in a PGM is seen as a sequence of actions taken by an agent, sparsity of the PGM enables local credit assignment in the agent's policy learning objective. This yields a local constraint that can be turned into a local loss in the style of generative flow networks (GFlowNets) that enables off-policy training but avoids the need to instantiate all the random variables for each parameter update, thus speeding up training considerably. The $\Delta$-AI objective matches the conditional distribution of a variable given its Markov blanket in a tractable learned sampler, which has the structure of a Bayesian network, with the same conditional distribution under the target PGM. As such, the trained sampler recovers marginals and conditional distributions of interest and enables inference of partial subsets of variables. We illustrate $\Delta$-AI's effectiveness for sampling from synthetic PGMs and training latent variable models with sparse factor structure.