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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. 

Probabilistic programming languages aid developers performing Bayesian inference. These languages provide programming constructs and tools for probabilistic modeling and automated inference. Prior work introduced a probabilistic programming language, ProbZelus, to extend probabilistic programming functionality to unbounded streams of data. This work demonstrated that the delayed sampling inference algorithm could be extended to work in a streaming context. ProbZelus showed that while delayed sampling could be effectively deployed on some programs, depending on the probabilistic model under consideration, delayed sampling is not guaranteed to use a bounded amount of memory over the course of the execution of the program. In this paper, we the present conditions on a probabilistic program’s execution under which delayed sampling will execute in bounded memory. The two conditions are dataflow properties of the core operations of delayed sampling: the m -consumed property and the unseparated paths property . A program executes in bounded memory under delayed sampling if, and only if, it satisfies the m -consumed and unseparated paths properties. We propose a static analysis that abstracts over these properties to soundly ensure that any program that passes the analysis satisfies these properties, and thus executes in bounded memory under delayed sampling. 

Modern web browsers rely on layout engines to convert HTML documents to layout trees that specify color, size, and position. However, existing layout engines are notoriously difficult to maintain because of the complexity of web standards. This is especially true for incremental layout engines, which are designed to improve performance by updating only the parts of the layout tree that need to be changed. In this paper, we propose Medea, a new framework for automatically generating incremental layout engines. Medea separates the specification of the layout engine from its incremental implementation, and guarantees correctness through layout engine synthesis. The synthesis is driven by a new iterative algorithm based on detecting conflicts that prevent optimality of the incremental algorithm. We evaluated Medea on a fragment of HTML layout that includes challenging features such as margin collapse, floating layout, and absolute positioning. Medea successfully synthesized an incremental layout engine for this fragment. The synthesized layout engine is both correct and efficient. In particular, we demonstrated that it avoids real-world bugs that have been reported in the layout engines of Chrome, Firefox, and Safari. The incremental layout engine synthesized by Medea is up to 1.82× faster than a naive incremental baseline. We also demonstrated that our conflict-driven algorithm produces engines that are 2.74× faster than a baseline without conflict analysis. 

A Reduction – an accumulation over a set of values, using an associative and commutative operator – is a common computation in many numerical computations, including scientific computations, machine learning, computer vision, and financial analytics. Contemporary polyhedral-based compilation techniques make it possible to optimize reductions, such as prefix sums, in which each component of the reduction’s output potentially shares computation with another component in the reduction. Therefore an optimizing compiler can identify the computation shared between multiple components and generate code that computes the shared computation only once. These techniques, however, do not support reductions that – when phrased in the language of the polyhedral model – span multiple dependent statements. In such cases, existing approaches can generate incorrect code that violates the data dependences of the original, unoptimized program. In this work, we identify and formalize the optimization of dependent reductions as an integer bilinear program. We present a heuristic optimization algorithm that uses an affine sequential schedule of the program to determine how to simplfy reductions yet still preserve the program’s dependences. We demonstrate that the algorithm provides optimal complexity for a set of benchmark programs from the literature on probabilistic inference algorithms, whose performance critically relies on simplifying these reductions. The complexities for 10 of the 11 programs improve siginifcantly by factors at least of the sizes of the input data, which are in the range of 10 4 to 10 6 for typical real application inputs. We also confirm the significance of the improvement by showing speedups in wall-clock time that range from 1.1x to over 10 6 x.