Probabilistic programming is an approach to reasoning under uncertainty by encoding inference problems as programs. In order to solve these inference problems, probabilistic programming languages (PPLs) employ different inference algorithms, such as sequential Monte Carlo (SMC), Markov chain Monte Carlo (MCMC), or variational methods. Existing research on such algorithms mainly concerns their implementation and efficiency, rather than the correctness of the algorithms themselves when applied in the context of expressive PPLs. To remedy this, we give a correctness proof for SMC methods in the context of an expressive PPL calculus, representative of popular PPLs such as WebPPL, Anglican, and Birch. Previous work have studied correctness of MCMC using an operational semantics, and correctness of SMC and MCMC in a denotational setting without term recursion. However, for SMC inference—one of the most commonly used algorithms in PPLs as of today—no formal correctness proof exists in an operational setting. In particular, an open question is if the resample locations in a probabilistic program affects the correctness of SMC. We solve this fundamental problem, and make four novel contributions: (i) we extend an untyped PPL lambda calculus and operational semantics to include explicit resample terms, expressing synchronization points in SMC inference; (ii) we prove, for the first time, that subject to mild restrictions, any placement of the explicit resample terms is valid for a generic form of SMC inference; (iii) as a result of (ii), our calculus benefits from classic results from the SMC literature: a law of large numbers and an unbiased estimate of the model evidence; and (iv) we formalize the bootstrap particle filter for the calculus and discuss how our results can be further extended to other SMC algorithms. 

Probabilistic programming languages (PPLs) allow users to encode arbitrary inference problems, and PPL implementations provide general-purpose automatic inference for these problems. However, constructing inference implementations that are efficient enough is challenging for many real-world problems. Often, this is due to PPLs not fully exploiting available parallelization and optimization opportunities. For example, handling probabilistic checkpoints in PPLs through continuation-passing style transformations or non-preemptive multitasking—as is done in many popular PPLs—often disallows compilation to low-level languages required for high-performance platforms such as GPUs. To solve the checkpoint problem, we introduce the concept of PPL control-flow graphs (PCFGs)—a simple and efficient approach to checkpoints in low-level languages. We use this approach to implement RootPPL: a low-level PPL built on CUDA and C++ with OpenMP, providing highly efficient and massively parallel SMC inference. We also introduce a general method of compiling universal high-level PPLs to PCFGs and illustrate its application when compiling Miking CorePPL—a high-level universal PPL—to RootPPL. The approach is the first to compile a universal PPL to GPUs with SMC inference. We evaluate RootPPL and the CorePPL compiler through a set of real-world experiments in the domains of phylogenetics and epidemiology, demonstrating up to 6x speedups over state-of-the-art PPLs implementing SMC inference.

Probabilistic Programming Languages (PPLs) allow users to encode statistical inference problems and automatically apply an inference algorithm to solve them. Popular inference algorithms for PPLs, such as sequential Monte Carlo (SMC) and Markov chain Monte Carlo (MCMC), are built around checkpoints—relevant events for the inference algorithm during the execution of a probabilistic program. Deciding the location of checkpoints is, in current PPLs, not done optimally. To solve this problem, we present a static analysis technique that automatically determines checkpoints in programs, relieving PPL users of this task. The analysis identifies a set of checkpoints that execute in the same order in every program run—they are aligned. We formalize alignment, prove the correctness of the analysis, and implement the analysis as part of the higher-order functional PPL Miking CorePPL. By utilizing the alignment analysis, we design two novel inference algorithm variants: aligned SMC and aligned lightweight MCMC. We show, through real-world experiments, that they significantly improve inference execution time and accuracy compared to standard PPL versions of SMC and MCMC.

Probabilistic programming languages (PPLs) make encoding and automatically solving statistical inference problems relatively easy by separating models from the inference algorithm. A popular choice for solving inference problems is to use Monte Carlo inference algorithms. For higher-order functional PPLs, these inference algorithms rely on execution suspension to perform inference, most often enabled through a full continuation-passing style (CPS) transformation. However, standard CPS transformations for PPL compilers introduce significant overhead, a problem the community has generally overlooked. State-of-the-art solutions either perform complete CPS transformations with performance penalties due to unnecessary closure allocations or use efficient, but complex, low-level solutions that are often not available in high-level languages. In contrast to prior work, we develop a new approach that is both efficient and easy to implement using higher-order languages. Specifically, we design a novel static suspension analysis technique that determines the parts of a program that require suspension, given a particular inference algorithm. The analysis result allows selectively CPS transforming the program only where necessary. We formally prove the correctness of the suspension analysis and implement both the suspension analysis and selective CPS transformation in the Miking CorePPL compiler. We evaluate the implementation for a large number of Monte Carlo inference algorithms on real-world models from phylogenetics, epidemiology, and topic modeling. The evaluation results demonstrate significant improvements across all models and inference algorithms.