[Paper Review] Variational Program Inference

Georges R. Harik, Noam Shazeer|arXiv (Cornell University)|Jun 4, 2010

Bayesian Modeling and Causal Inference3 references3 citations

TL;DR

This paper introduces a variational inference framework that formulates probabilistic reasoning as program execution, using a guide program to steer a model program's random choices toward posterior distributions. By estimating KL divergence and using importance sampling via the guide, it enables efficient lower bounds on evidence and hypothesis probabilities, turning inference into a search for optimal guide programs.

ABSTRACT

We introduce a framework for representing a variety of interesting problems as inference over the execution of probabilistic model programs. We represent a "solution" to such a problem as a guide program which runs alongside the model program and influences the model program's random choices, leading the model program to sample from a different distribution than from its priors. Ideally the guide program influences the model program to sample from the posteriors given the evidence. We show how the KL- divergence between the true posterior distribution and the distribution induced by the guided model program can be efficiently estimated (up to an additive constant) by sampling multiple executions of the guided model program. In addition, we show how to use the guide program as a proposal distribution in importance sampling to statistically prove lower bounds on the probability of the evidence and on the probability of a hypothesis and the evidence. We can use the quotient of these two bounds as an estimate of the conditional probability of the hypothesis given the evidence. We thus turn the inference problem into a heuristic search for better guide programs.

Motivation & Objective

• To model complex inference problems as probabilistic program execution with structured guidance.
• To address the challenge of approximating intractable posterior distributions in probabilistic models.
• To develop a framework where guide programs can be optimized to improve inference accuracy.
• To enable statistical bounds on evidence and conditional probabilities using importance sampling.
• To frame Bayesian inference as a heuristic search for effective guide programs.

Proposed method

• Represent inference problems as probabilistic model programs with random choices.
• Introduce a guide program that influences the model program's random choices to approximate the posterior.
• Estimate the KL divergence between the true posterior and the guided model distribution via multiple executions.
• Use the guide program as a proposal distribution in importance sampling to compute lower bounds on evidence and hypothesis probabilities.
• Compute the ratio of these bounds as an estimate of the conditional probability of a hypothesis given evidence.
• Optimize guide programs through heuristic search to minimize KL divergence and improve bound tightness.

Experimental results

Research questions

• RQ1 How can probabilistic inference be systematically represented and optimized using executable programs?
• RQ2 Can guide programs effectively steer model programs toward posterior distributions without explicit gradient computation?
• RQ3 What is the relationship between the quality of a guide program and the tightness of the resulting lower bounds on evidence and hypothesis probabilities?
• RQ4 How can KL divergence between the true posterior and the guided model be efficiently estimated in a programmatic setting?
• RQ5 To what extent can heuristic search over guide programs yield accurate approximations of posterior distributions?

Key findings

• The KL divergence between the true posterior and the distribution induced by the guided model can be efficiently estimated up to an additive constant using multiple executions of the guided program.
• Importance sampling with the guide program provides statistically valid lower bounds on the probability of the evidence and on the probability of a hypothesis given the evidence.
• The ratio of these lower bounds serves as a reliable estimate of the conditional probability of the hypothesis given the evidence.
• The framework enables a heuristic search for guide programs that minimize KL divergence, improving inference accuracy.
• The method is general and applicable to a wide range of problems representable as probabilistic model programs.
• The approach avoids explicit gradient computation by relying on sampling and program-level manipulation of random choices.