机器学习

This paper introduces a rigorous framework for defining generative diffusion models in infinite dimensions via Doob's h-transform. Rather than relying on time reversal of a noising process, a reference diffusion is forced towards the target…

Adversarial online linear optimization (OLO) is essentially about making performance tradeoffs with respect to the unknown difficulty of the adversary. In the setting of one-dimensional fixed-time OLO on a bounded domain, it has been…

The Sliced Wasserstein Kernel (SWK) for persistence diagrams was introduced in (Carri{\`e}re et al. 2017) as a powerful tool to implicitly embed persistence diagrams in a Hilbert space with reasonable distortion. This kernel is built on the…

Given that machine learning algorithms are increasingly being deployed to aid in high stakes decision-making, uncertainty quantification methods that wrap around these black box models such as conformal prediction have received much…

Techniques for feedforward networks (FFNs) and convolutional networks (CNNs) are frequently reused across families, but the relationship between the underlying model classes is rarely made explicit. We introduce a unified node-level…

Gradient flows of the Kullback--Leibler (KL) divergence, such as the Fokker--Planck equation and Stein Variational Gradient Descent, evolve a distribution toward a target density known only up to a normalizing constant. We introduce new…

Performative predictions influence the very outcomes they aim to forecast. We study performative predictions that affect a sample (e.g., only existing users of an app) and/or the whole population (e.g., all potential app users). This raises…

Time series forecasting is essential in a wide range of real world applications. Recently, frequency-domain methods have attracted increasing interest for their ability to capture global dependencies. However, when applied to non-stationary…

We study matrix and tensor denoising when the underlying signal is \textbf{not} necessarily low-rank. In the tensor setting, we observe \[ Y = X^\ast + Z \in \mathbb{R}^{p_1 \times p_2 \times p_3}, \] where $X^\ast$ is an unknown signal…

While continuous diffusion models excel in modeling continuous distributions, their application to categorical data has been less effective. Recent work has shown that ratio-matching through score-entropy within a continuous-time discrete…

Conformal prediction methodology has recently been extended to the covariate shift setting, where the distribution of covariates differs between training and test data. While existing results ensure that the prediction sets from these…

Directed acyclic graph (DAG) learning is a central task in structure discovery and causal inference. Although the field has witnessed remarkable advances over the past few years, it remains statistically and computationally challenging to…

We consider a causal inference problem frequently encountered in online advertising systems, where a publisher (e.g., Instagram, TikTok) interacts repeatedly with human users and advertisers by sporadically displaying to each user an…

Transformers underpin modern large language models (LLMs) and are commonly assumed to be behaviorally unstructured at random initialization, with all meaningful preferences emerging only through large-scale training. We challenge this…

We introduce Wedge Sampling, a new non-adaptive sampling scheme for low-rank tensor completion. We study recovery of an order-$k$ low-rank tensor of dimension $n \times \cdots \times n$ from a subset of its entries. Unlike the standard…

In this work, we provide a sharp theory of scaling laws for two-layer neural networks trained on a class of hierarchical multi-index targets, in a genuinely representation-limited regime. We derive exact information-theoretic scaling laws…

A simple strategy for improving LLM accuracy, especially in math and reasoning problems, is to sample multiple responses and submit the answer most consistently reached. In this paper we leverage Bayesian prior information to save on…

Effective reinforcement learning (RL) for complex stochastic systems requires leveraging historical data collected in previous iterations to accelerate policy optimization. Classical experience replay treats all past observations uniformly…

We consider the sequential experimental design problem in the predict-then-optimize paradigm. In this paradigm, the outputs of the prediction model are used as coefficient vectors in a downstream linear optimization problem. Traditional…

Riemannian flow matching (RFM) extends flow-based generative modeling to data supported on manifolds by learning a time-dependent tangent vector field whose flow-ODE transports a simple base distribution to the data law. We develop a…