Inference Plans for Hybrid Particle Filtering

TL;DR

Siren introduces inference plans to give developers explicit control over how random variables are encoded in hybrid particle filtering, blending symbolic inference with Monte Carlo methods. A static, abstract-interpretation-based satisfiability analysis guarantees that chosen annotations are feasible across all executions, reducing the risk of unpredictable accuracy degradations. Empirical results across a suite of benchmarks show average speedups of $1.76\times$ to reach target accuracy and up to $206\times$ improvements for some plans, along with significant accuracy gains compared to default heuristics. The work provides a unified hybrid inference interface and demonstrates that planning at inference time can yield substantial practical benefits while preserving the modeling-inference separation fundamental to probabilistic programming.

Abstract

Advanced probabilistic programming languages (PPLs) using hybrid particle filtering combine symbolic exact inference and Monte Carlo methods to improve inference performance. These systems use heuristics to partition random variables within the program into variables that are encoded symbolically and variables that are encoded with sampled values, and the heuristics are not necessarily aligned with the developer's performance evaluation metrics. In this work, we present inference plans, a programming interface that enables developers to control the partitioning of random variables during hybrid particle filtering. We further present Siren, a new PPL that enables developers to use annotations to specify inference plans the inference system must implement. To assist developers with statically reasoning about whether an inference plan can be implemented, we present an abstract-interpretation-based static analysis for Siren for determining inference plan satisfiability. We prove the analysis is sound with respect to Siren's semantics. Our evaluation applies inference plans to three different hybrid particle filtering algorithms on a suite of benchmarks. It shows that the control provided by inference plans enables speed ups of 1.76x on average and up to 206x to reach a target accuracy, compared to the inference plans implemented by default heuristics; the results also show that inference plans improve accuracy by 1.83x on average and up to 595x with less or equal runtime, compared to the default inference plans. We further show that our static analysis is precise in practice, identifying all satisfiable inference plans in 27 out of the 33 benchmark-algorithm evaluation settings.

Figures (79)

• Figure 1: Hybrid inference with particle filtering.
• Figure 2: Diagram of a radar tracker.
• Figure 3: A program written in Siren that implements a radar tracking.
• Figure 4: Accuracy and runtime performance of the Figure \ref{['fig:example']} programs. Each scatter plot presents the program execution time and accuracy for particle counts $p$ ranging from 1 to 1024 and multiple inference plans. Each data point is an experiment that -- across 100 runs -- measures the median runtime and the 90th percentile of the Mean Squared Error for the relevant random variable -- or .
• Figure 5: Accuracy of and over 100 timesteps at altitudes, measured as the Squared Error of the estimated value to the true value at that timestep.

Theorems & Definitions (21)

• Definition 4.1: Abstraction Function
• Definition 4.2: Concretization Function
• lemma 1: Terminating Particle Evaluation Soundness
• lemma 2: Preservation
• lemma 3: Particle Evaluation Soundness
• lemma 4: Particle Trace
• theorem 1: Particle Set Evaluation Soundness
• corollary 1: Model Evaluation Soundness
• lemma 5: Weakening
• lemma 6: Abstract Weakening