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We propose a new exact approach for solving integer linear programming (ILP) problems which we will call projective splitting algorithms (PSAs). Unlike classical methods for solving ILP problems, PSAs conduct the search for the optimal…

Maximum pseudolikelihood (MPL) estimators are useful alternatives to maximum likelihood (ML) estimators when likelihood functions are more difficult to manipulate than their marginal and conditional components. Furthermore, MPL estimators…

As large language models (LLMs) are increasingly deployed to perform tasks with minimal human oversight, it is crucial that these models operate robustly. In particular, a model that can solve a given problem should not fail simply because…

A major trend in academia and data science is the rapid adoption of Bayesian statistics for data analysis and modeling, leading to the development of probabilistic programming languages (PPL). A PPL provides a framework that allows users to…

Probabilistic programming languages and modeling toolkits are two modular ways to build and reuse stochastic models and inference procedures. Combining strengths of both, we express models and inference as generalized coroutines in the same…

Dynamic Programming (DP) suffers from the well-known ``curse of dimensionality'', further exacerbated by the need to compute expectations over process noise in stochastic models. This paper presents a Monte Carlo-based sampling approach for…

Dynamic languages (such as Python and JavaScript) offer flexibility and simplified type handling for programming, but this can also lead to an increase in type-related errors and additional overhead for compile-time type inference. As a…

Monte Carlo methods to evaluate and maximize the likelihood function enable the construction of confidence intervals and hypothesis tests, facilitating scientific investigation using models for which the likelihood function is intractable.…

Probabilistic programming languages can simplify the development of machine learning techniques, but only if inference is sufficiently scalable. Unfortunately, Bayesian parameter estimation for highly coupled models such as regressions and…

In this paper, we evaluate the capability of transformer-based language models in making inferences over uncertain text that includes uncertain rules of reasoning. We cover both Pre-trained Language Models (PLMs) and generative Large…

Sequential Monte Carlo is a family of algorithms for sampling from a sequence of distributions. Some of these algorithms, such as particle filters, are widely used in the physics and signal processing researches. More recent developments…

Hypothesis tests calibrated by (re)sampling methods (such as permutation, rank and bootstrap tests) are useful tools for statistical analysis, at the computational cost of requiring Monte-Carlo sampling for calibration. It is common and…

Recent advancements in large language models (LLMs) integrating explicit reasoning, such as OpenAI's o3-mini, DeepSeek-R1, and QWQ-32B, enable smaller models to solve complex tasks by generating intermediate reasoning steps prior to…

Probabilistic systems are an important theme in AI domain. As the specification language, the logic PCTL is now the default logic for reasoning about probabilistic properties. In this paper, we present a natural and succinct probabilistic…

Probabilistic inference is fundamentally hard, yet many tasks require optimization on top of inference, which is even harder. We present a new optimization-via-compilation strategy to scalably solve a certain class of such problems. In…

Consider testing multiple hypotheses using tests that can only be evaluated by simulation, such as permutation tests or bootstrap tests. This article introduces MMCTest, a sequential algorithm which gives, with arbitrarily high probability,…

Recent advances in preference optimization have demonstrated significant potential for improving mathematical reasoning capabilities in large language models (LLMs). While current approaches leverage high-quality pairwise preference data…

Pre-trained language models (PLMs) have become a prevalent technique in deep learning for code, utilizing a two-stage pre-training and fine-tuning procedure to acquire general knowledge about code and specialize in a variety of downstream…

Probabilistic inference procedures are usually coded painstakingly from scratch, for each target model and each inference algorithm. We reduce this effort by generating inference procedures from models automatically. We make this code…

To model combinatorial decision problems involving uncertainty and probability, we extend the stochastic constraint programming framework proposed in [Walsh, 2002] along a number of important dimensions (e.g. to multiple chance constraints…