These approximate inference strategies can scale well in many cases, but they Distributions on integers are ubiquitous in probabilistic struggle to find valid sampling regions in the presence of modeling but remain challenging for many low-probability observations and non-differentiability (e.g., of today's probabilistic programming languages observing the sum of two large random integers to be a (PPLs). The core challenge comes from discrete constant) [Gelman et al., 2015, Bingham et al., 2019, Dillon structure: many of today's PPL inference strategies et al., 2017]. Exact inference strategies work by preserving rely on enumeration, sampling, or differentiation the global structure of the distribution, but here there is a in order to scale, which fail for high-dimensional challenge: what is the right strategy for efficiently representing complex discrete distributions involving integers.

TypeScript and Python are two programming languages that support optional type annotations, which are useful but tedious to introduce and maintain. This has motivated automated type prediction: given an untyped program, produce a well-typed output program. Large language models (LLMs) are promising for type prediction, but there are challenges: fill-in-the-middle performs poorly, programs may not fit into the context window, generated types may not type check, and it is difficult to measure how well-typed the output program is. We address these challenges by building OpenTau, a search-based approach for type prediction that leverages large language models. We propose a new metric for type prediction quality, give a tree-based program decomposition that searches a space of generated types, and present fill-in-the-type fine-tuning for LLMs. We evaluate our work with a new dataset for TypeScript type prediction, and show that 47.4% of files type check (14.5% absolute improvement) with an overall rate of 3.3 type errors per file. All code, data, and models are available at: https://github.com/GammaTauAI/opentau.

Probabilistic programming is emerging as a popular and effective means of probabilistic modeling and an alternative to probabilistic graphical models. Probabilistic programs provide greater expressivity and flexibility in modeling probabilistic systems than graphical models, but this flexibility comes at a cost: there remains a significant disparity in performance between specialized Bayesian network solvers and probabilistic program inference algorithms. In this work we present a program analysis and associated optimization, flip-hoisting, that collapses repetitious parameters in discrete probabilistic programs to improve inference performance. flip-hoisting generalizes parameter sharing - a well-known important optimization from discrete graphical models - to probabilistic programs. We implement flip-hoisting in an existing probabilistic programming language and show empirically that it significantly improves inference performance, narrowing the gap between the performances of probabilistic programs and probabilistic graphical models.

Scaling probabilistic models to large realistic problems and datasets is a key challenge in machine learning. Central to this effort is the development of tractable probabilistic models (TPMs): models whose structure guarantees efficient probabilistic inference algorithms. The current landscape of TPMs is fragmented: there exist various kinds of TPMs with different strengths and weaknesses. Two of the most prominent classes of TPMs are determinantal point processes (DPPs) and probabilistic circuits (PCs). This paper provides the first systematic study of their relationship. We propose a unified analysis and shared language for discussing DPPs and PCs. Then we establish theoretical barriers for the unification of these two families, and prove that there are cases where DPPs have no compact representation as a class of PCs. We close with a perspective on the central problem of unifying these tractable models.

Lifted inference scales to large probability models by exploiting symmetry. However, existing exact lifted inference techniques do not apply to general factor graphs, as they require a relational representation. In this work we provide a theoretical framework and algorithm for performing exact lifted inference on symmetric factor graphs by computing colored graph automorphisms, as is often done for approximate lifted inference. Our key insight is to represent variable assignments directly in the colored factor graph encoding. This allows us to generate representatives and compute the size of each orbit of the symmetric distribution. In addition to exact inference, we use this encoding to implement an MCMC algorithm that explores the space of orbits quickly by uniform orbit sampling.

This abstract is proposing a challenging problem: to infer a human's mental state — intent and belief — from an observed RGBD video for human-robot interaction. The task is to integrate symbolic reasoning, a field well-studied within A.I. domains, with the uncertainty native to computer vision strategies. Traditional A.I. strategies for plan inference typically rely on first-order logic and closed world assumptions which struggle to take into account the inherent uncertainty of noisy observations within a scene. Computer vision relies on pattern-recognition strategies that have difficulty accounting for higher-level reasoning and abstract representation of world knowledge. By combining these two approaches in a principled way under a probabilistic programming framework, we define new computer vision tasks such as actor intent prediction and belief inference from an observed video sequence. Through inferring a human's theory of mind, a robotic agent can automatically determine a human's goals to collaborate with them.