Automatic Differentiation Equipped Variable Elimination for Sensitivity Analysis on Probabilistic Inference Queries

Jeff Druce

Abstract:

Probabilistic Models are a natural framework for describing the stochastic relation-
ships between variables in a system to perform inference tasks, such as estimating
the probability of a specific set of conditions or events. In application it is often
appropriate to perform sensitivity analysis on a model, for example, to assess the
stability of analytical results with respect to the governing parameters. However,
typical programming language are cumbersome for encoding and reasoning with
complex models and current approaches to sensitivity analysis on probabilistic
models are not scalable, as they require repeated computation or estimation of the
derivatives of complex functions. To overcome these limitations, and to enable effi-
cient sensitivity analysis with respect to arbitrary model queries, e.g., P(X|Y = y),
we propose to use Automatic Differentiation to extend the Probabilistic Program-
ming Language Figaro.

TL;DR: Extending probabilistic programming with automatic differentiation

Keywords: automatic differentiation, probabilistic models, probabilistic programming