Tractable Inference for Complex Stochastic Processes

TL;DR

This paper introduces a method for approximate inference in complex stochastic processes that maintains bounded error over time, enabling faster and scalable monitoring of dynamic systems with minimal accuracy loss.

Contribution

It proposes a novel approximation scheme for belief states in dynamic Bayesian networks that ensures error contraction and boundedness over the process lifetime.

Findings

Error in belief state contracts exponentially over time

Approximate inference achieves orders of magnitude speedup

Small accuracy degradation with significant performance gains

Abstract

The monitoring and control of any dynamic system depends crucially on the ability to reason about its current status and its future trajectory. In the case of a stochastic system, these tasks typically involve the use of a belief state- a probability distribution over the state of the process at a given point in time. Unfortunately, the state spaces of complex processes are very large, making an explicit representation of a belief state intractable. Even in dynamic Bayesian networks (DBNs), where the process itself can be represented compactly, the representation of the belief state is intractable. We investigate the idea of maintaining a compact approximation to the true belief state, and analyze the conditions under which the errors due to the approximations taken over the lifetime of the process do not accumulate to make our answers completely irrelevant. We show that the error in a belief state contracts exponentially as the process evolves. Thus, even with multiple approximations, the error in our process remains bounded indefinitely. We show how the additional structure of a DBN can be used to design our approximation scheme, improving its performance significantly. We demonstrate the applicability of our ideas in the context of a monitoring task, showing that orders of magnitude faster inference can be achieved with only a small degradation in accuracy.