Abstract Dantzig-Wolfe (DW) decomposition is a well-known technique in mixed-integer programming (MIP) for decomposing and convexifying constraints to obtain potentially strong dual bounds. We investigate cutting planes that can be derived using the DW decomposition algorithm and show that these cuts can provide the same dual bounds as DW decomposition. …
Abstract: This talk will take up the task of designing the provably best possible gradient method for smooth convex optimization. Methods with big-O optimal worst-case guarantees were (famously) discovered in the 80s by Nesterov. Methods with exactly minimax optimal worst-case guarantees were developed in the last decade. As a first …
Abstract: How do you reconstruct an image of a black hole using only noisy telescope measurements in the Fourier domain? How do you predict the cure state of a carbon fibre aircraft wing as it cures in an autoclave using a few faulty thermocouples? In theory, Bayesian probabilistic models are …
Abstract: In this talk, we advocate for the development of rigorous statistical foundations for large language models (LLMs). We begin by elaborating two key features that motivate statistical perspectives for LLMs: (1) the probabilistic, autoregressive nature of next-token prediction, and (2) the complexity and black box nature of Transformer architectures. …
Abstract: As a computational alternative to Markov chain Monte Carlo approaches, variational inference (VI) is becoming increasingly popular for approximating intractable posterior distributions in large-scale Bayesian models due to its comparable efficacy and superior efficiency. Several recent works provide theoretical justifications of VI by proving its statistical optimality for parameter …
Abstract: Nuclear fusion holds the promise of limitless clean energy and would solve many of the world’s grand challenges. The most promising approach to date uses tokamaks, but we have not yet been able to sustain plasmas at the temperatures, pressures, and durations needed to make fusion power viable. This …
Abstract: Markov Chain Monte Carlo (MCMC) and local-search optimization methods have been extensively used in the practice of statistical research for many decades now. However, their exact theoretical performance has been strikingly eluding even for simple parametric estimation tasks. This is in stark contrast to other classes of estimators such …
Abstract: We are interested in the problem of unit-level counterfactual inference in the presence of unobserved confounders owing to the increasing importance of personalized decision-making in many domains: consider a recommender system interacting with a user over time where each user is provided recommendations based on observed demographics, prior engagement …
Abstract: This talk examines the theoretical foundations of Graph Neural Networks (GNNs), focusing on polynomial GNNs (Poly-GNNs). We start with empirical evidence challenging the need for complex GNN architectures in semi-supervised node classification, showing simpler methods often perform comparably. We then analyze Poly-GNNs within a contextual stochastic block model, addressing …
Abstract: We are witnessing a paradigm shift in AI, transitioning from deep learning models to the era of Large Language Models (LLMs). This shift signifies a transformative advancement in AI, enabling it to be applied to diverse real-world safety-critical applications. Despite these impressive achievements, a fundamental question remains: are …