An official website of the United States government
Probabilistic programming languages (PPLs) are an expressive means for creating and reasoning about probabilistic models. Unfortunatelyhybridprobabilistic programs that involve both continuous and discrete structures are not well supported by today’s PPLs. In this paper we develop a new approximate inference algorithm for hybrid probabilistic programs that first discretizes the continuous distributions and then performs discrete inference on the resulting program. The key novelty is a form of discretization that we callbit blasting, which uses a binary representation of numbers such that a domain of discretized points can be succinctly represented as a discrete probabilistic program overpoly Boolean random variables. Surprisingly, we prove that many common continuous distributions can be bit blasted in a manner that incurs no loss of accuracy over an explicit discretization and supports efficient probabilistic inference. We have built a probabilistic programming system for hybrid programs calledHyBit, which employs bit blasting followed by discrete probabilistic inference. We empirically demonstrate the benefits of our approach over existing sampling-based and symbolic inference approaches
more »
« less
Semi-symbolic inference for efficient streaming probabilistic programming
A streaming probabilistic program receives a stream of observations and produces a stream of distributions that are conditioned on these observations. Efficient inference is often possible in a streaming context using Rao-Blackwellized particle filters (RBPFs), which exactly solve inference problems when possible and fall back on sampling approximations when necessary. While RBPFs can be implemented by hand to provide efficient inference, the goal of streaming probabilistic programming is to automatically generate such efficient inference implementations given input probabilistic programs. In this work, we propose semi-symbolic inference, a technique for executing probabilistic programs using a runtime inference system that automatically implements Rao-Blackwellized particle filtering. To perform exact and approximate inference together, the semi-symbolic inference system manipulates symbolic distributions to perform exact inference when possible and falls back on approximate sampling when necessary. This approach enables the system to implement the same RBPF a developer would write by hand. To ensure this, we identify closed families of distributions – such as linear-Gaussian and finite discrete models – on which the inference system guarantees exact inference. We have implemented the runtime inference system in the ProbZelus streaming probabilistic programming language. Despite an average 1.6× slowdown compared to the state of the art on existing benchmarks, our evaluation shows that speedups of 3×-87× are obtainable on a new set of challenging benchmarks we have designed to exploit closed families.
more »
« less
- Award ID(s):
- 2029016
- PAR ID:
- 10390779
- Date Published:
- Journal Name:
- Proceedings of the ACM on Programming Languages
- Volume:
- 6
- Issue:
- OOPSLA2
- ISSN:
- 2475-1421
- Page Range / eLocation ID:
- 1668 to 1696
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Exact probabilistic inference is a requirement for many applications of probabilistic programming languages (PPLs) such as in high-consequence settings or verification. However, designing and implementing a PPL with scalable high-performance exact inference is difficult: exact inference engines, much like SAT solvers, are intricate low-level programs that are hard to implement. Due to this implementation challenge, PPLs that support scalable exact inference are restrictive and lack many features of general-purpose languages. This paper presents Roulette, the first discrete probabilistic programming language that combines high-performance exact inference with general-purpose language features. Roulette supports a significant subset of Racket, including data structures, first-class functions, surely-terminating recursion, mutable state, modules, and macros, along with probabilistic features such as finitely supported discrete random variables, conditioning, and top-level inference. The key insight is that there is a close connection between exact probabilistic inference and the symbolic evaluation strategy of Rosette. Building on this connection, Roulette generalizes and extends the Rosette solver-aided programming system to reason about probabilistic rather than symbolic quantities. We prove Roulette sound by generalizing a proof of correctness for Rosette to handle probabilities, and demonstrate its scalability and expressivity on a number of examples.more » « less
-
null (Ed.)For probabilistic programs, it is usually not possible to automatically derive exact information about their properties, such as the distribution of states at a given program point. Instead, one can attempt to derive approximations, such as upper bounds on tail probabilities. Such bounds can be obtained via concentration inequalities, which rely on the moments of a distribution, such as the expectation (the first raw moment) or the variance (the second central moment). Tail bounds obtained using central moments are often tighter than the ones obtained using raw moments, but automatically analyzing central moments is more challenging. This paper presents an analysis for probabilistic programs that automatically derives symbolic upper and lower bounds on variances, as well as higher central moments, of cost accumulators. To overcome the challenges of higher-moment analysis, it generalizes analyses for expectations with an algebraic abstraction that simultaneously analyzes different moments, utilizing relations between them. A key innovation is the notion of moment-polymorphic recursion, and a practical derivation system that handles recursive functions. The analysis has been implemented using a template-based technique that reduces the inference of polynomial bounds to linear programming. Experiments with our prototype central-moment analyzer show that, despite the analyzer’s upper/lower bounds on various quantities, it obtains tighter tail bounds than an existing system that uses only raw moments, such as expectations.more » « less
-
Recursive calls over recursive data are useful for generating probability distributions, and probabilistic programming allows computations over these distributions to be expressed in a modular and intuitive way. Exact inference is also useful, but unfortunately, existing probabilistic programming languages do not perform exact inference on recursive calls over recursive data, forcing programmers to code many applications manually. We introduce a probabilistic language in which a wide variety of recursion can be expressed naturally, and inference carried out exactly. For instance, probabilistic pushdown automata and their generalizations are easy to express, and polynomial-time parsing algorithms for them are derived automatically. We eliminate recursive data types using program transformations related to defunctionalization and refunctionalization. These transformations are assured correct by a linear type system, and a successful choice of transformations, if there is one, is guaranteed to be found by a greedy algorithm.more » « less
-
null (Ed.)Probabilistic Programming offers a concise way to represent stochastic models and perform automated statistical inference. However,many real-world models have discrete or hybrid discrete-continuous distributions, for which existing tools may suffer non-trivial limitations.Inference and parameter estimation can be exceedingly slow for these models because many inference algorithms compute results faster (or exclusively) when the distributions being inferred are continuous. To address this discrepancy, this paper presents Leios. Leios is the first approach for systematically approximating arbitrary probabilistic programs that have discrete, or hybrid discrete-continuous random variables. The approximate programs have all their variables fully continualized. We show that once we have the fully continuous approximate program, we can perform inference and parameter estimation faster by exploiting the existing support that many languages offer for continuous distributions.Furthermore, we show that the estimates obtained when performing inference and parameter estimation on the continuous approximation are still comparably close to both the true parameter values and the estimates obtained when performing inference on the original model.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1145/3563347
