Expectation Programming

Building on ideas from probabilistic programming, we introduce the concept of an expectation programming framework (EPF) that automates the calculation of expectations. Analogous to a probabilistic program, an expectation program is comprised of a mix of probabilistic constructs and deterministic calculations that define a conditional distribution over its variables. However, the focus of the inference engine in an EPF is to directly estimate the resulting expectation of the program return values, rather than approximate the conditional distribution itself. This distinction allows us to achieve substantial performance improvements over the standard probabilistic programming pipeline by tailoring the inference to the precise expectation we care about. We realize a particular instantiation of our EPF concept by extending the probabilistic programming language Turing to allow so-called target-aware inference to be run automatically, and show that this leads to significant empirical gains compared to conventional posterior-based inference

Amortized Monte Carlo integration

Current approaches to amortizing Bayesian inference focus solely on approximating the posterior distribution. Typically, this approximation is, in turn, used to calculate expectations for one or more target functions{—}a computational pipeline which is inefficient when the target function(s) are known upfront. In this paper, we address this inefficiency by introducing AMCI, a method for amortizing Monte Carlo integration directly. AMCI operates similarly to amortized inference but produces three distinct amortized proposals, each tailored to a different component of the overall expectation calculation. At runtime, samples are produced separately from each amortized proposal, before being combined to an overall estimate of the expectation. We show that while existing approaches are fundamentally limited in the level of accuracy they can achieve, AMCI can theoretically produce arbitrarily small errors for any integrable target function using only a single sample from each proposal at runtime. We further show that it is able to empirically outperform the theoretically optimal selfnormalized importance sampler on a number of example problems. Furthermore, AMCI allows not only for amortizing over datasets but also amortizing over target functions

Amortized Monte Carlo integration

Current approaches to amortizing Bayesian inference focus solely on approximating the posterior distribution. Typically, this approximation is, in turn, used to calculate expectations for one or more target functions{—}a computational pipeline which is inefficient when the target function(s) are known upfront. In this paper, we address this inefficiency by introducing AMCI, a method for amortizing Monte Carlo integration directly. AMCI operates similarly to amortized inference but produces three distinct amortized proposals, each tailored to a different component of the overall expectation calculation. At runtime, samples are produced separately from each amortized proposal, before being combined to an overall estimate of the expectation. We show that while existing approaches are fundamentally limited in the level of accuracy they can achieve, AMCI can theoretically produce arbitrarily small errors for any integrable target function using only a single sample from each proposal at runtime. We further show that it is able to empirically outperform the theoretically optimal selfnormalized importance sampler on a number of example problems. Furthermore, AMCI allows not only for amortizing over datasets but also amortizing over target functions