Probabilistic Programming with Stochastic Probabilities

Abstract

We present a new approach to the design and implementation of probabilistic programming languages (PPLs), based on the idea of stochastically estimating the probability density ratios necessary for probabilistic inference. By relaxing the usual PPL design constraint that these densities be computed exactly, we are able to eliminate many common restrictions in current PPLs, to deliver a language that, for the first time, simultaneously supports first-class constructs for marginalization and nested inference, unrestricted stochastic control flow, continuous and discrete sampling, and programmable inference with custom proposals. At the heart of our approach is a new technique for compiling these expressive probabilistic programs into randomized algorithms for unbiasedly estimating their densities and density reciprocals. We employ these stochastic probability estimators within modified Monte Carlo inference algorithms that are guaranteed to be sound despite their reliance on inexact estimates of density ratios. We establish the correctness of our compiler using logical relations over the semantics of λ SP , a new core calculus for modeling and inference with stochastic probabilities. We also implement our approach in an open-source extension to Gen, called GenSP, and evaluate it on six challenging inference problems adapted from the modeling and inference literature. We find that: (1) ‍can automate fast density estimators for programs with very expensive exact densities; (2) convergence of inference is mostly unaffected by the noise from these estimators; and (3) our sound-by-construction estimators are competitive with hand-coded density estimators, incurring only a small constant-factor overhead.

Suspension Analysis and Selective Continuation-Passing Style for Universal Probabilistic Programming Languages

“…The PPLs Pyro [6], Stan [10,5], Gen [11,27], and Edward [48] either implement inference algorithms that do not require suspension (e.g., Hamiltonian Monte Carlo), or restrict the language in such a way that suspension is explicit and trivially handled by the language implementation. For example, SMC in Pyro 8 and newer versions of Birch require that users explicitly write programs as a step function that the SMC implementation calls iteratively.…”

Probabilistic Programming with Programmable Variational Inference

“…Our full language includes constructs for marginalizing (marginal) and normalizing (normalize) 𝜆 Gen programs, making it possible to express a broader class of models and variational families than in current systems. Our versions of these constructs are designed following Lew et al [39]. • Differentiable stochastic estimators of densities and density reciprocals (Appx.…”

“…This can make it difficult to reason about correctness. Indeed, while the community has made tremendous progress in understanding the compositional correctness arguments of an increasingly broad class of Monte Carlo inference methods for probabilistic programs [9,39,43,75,76], pioneering work on correctness for variational inference [34,35,41] has generally focused on specific properties (e.g., smoothness and absolute continuity) in somewhat restricted languages, and not to end-to-end correctness of gradient estimation for variational inference.…”

“…• System: We contribute genjax.vi, a performant, GPU-accelerated implementation of our approach in JAX [20], which also extends our formal modeling language with constructs for marginalization and normalization ( §7) [39]. We also contribute concise, pedagogical Haskell and Julia versions.…”

Data cleaning and restoring method for vehicle battery big data platform

“…Regression analysis methods can detect and fix the bad data by utilizing the model dependence information [28,29]. However, compared to mechanical and electrical systems, the battery is an integrated electrochemical system with complex external characteristics [33,34].…”