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

Probabilistic Models are a natural framework for describing the stochastic relation1 ships between variables in a system to perform inference tasks, such as estimating 2 the probability of a specific set of conditions or events. In application it is often 3 appropriate to perform sensitivity analysis on a model, for example, to assess the 4 stability of analytical results with respect to the governing parameters. However, 5 typical programming language are cumbersome for encoding and reasoning with 6 complex models and current approaches to sensitivity analysis on probabilistic 7 models are not scalable, as they require repeated computation or estimation of the 8 derivatives of complex functions. To overcome these limitations, and to enable effi9 cient sensitivity analysis with respect to arbitrary model queries, e.g., P (X|Y = y), 10 we propose to use Automatic Differentiation to extend the Probabilistic Program11 ming Language Figaro. 12