机器学习

Confidence sequences based on test martingales provide time-uniform uncertainty quantification for the mean of bounded IID observations without parametric distributional assumptions. Their practical efficiency, however, depends strongly on…

Gaussian process (GP) marginal likelihood scores and kernel conditional independence tests are theoretically appealing for nonlinear causal discovery but computationally prohibitive at scale. We present three complementary RFF-based methods…

We study the problem of learning generative models for discrete sequences in a continuous embedding space. Whereas prior approaches typically operate in Euclidean space or on the probability simplex, we instead work on the sphere $\mathbb…

A central challenge in dynamic network analysis is to represent temporal evolution in a way that is both geometrically meaningful and statistically identifiable. One approach embeds a sequence of network snapshots as trajectories in a…

In quantum machine learning (QML), classical data are often encoded as quantum pure states and processed directly as quantum representations, motivating representation-level generative modeling that samples new quantum states from an…

Large language models (LLMs) encode rich semantic knowledge that can be useful for supervised learning, but their outputs are unreliable as statistical priors: they may be noisy, misspecified, or hallucinated. Existing LLM-informed learning…

Exhaustively evaluating many large language models (LLMs) on a large suite of benchmarks is expensive. We cast benchmarking as finite-population inference and, under a fixed query budget, seek tight confidence intervals (CIs) for model…

Pretrained Transformers can perform in-context learning (ICL) from a few demonstrations, but this ability can fail sharply when the test distribution differs from pretraining, a common deployment setting. We study attention temperature as a…

Missing data is a fundamental challenge in data science, significantly hindering analysis and decision-making across a wide range of disciplines, including healthcare, bioinformatics, social science, e-commerce, and industrial monitoring.…

In observational settings where treatment and outcome share unmeasured confounders but an observed mediator remains unconfounded, the front-door (FD) adjustment identifies causal effects through the mediator. We study the heterogeneous…

Estimating causal effects on networks is challenging because treatments may affect both treated units and their neighbors, while network homophily induces dependence and confounding. These challenges are amplified when causal effects are…

Canonical correlation analysis (CCA) is a technique for finding correlated sets of features between two datasets. In this paper, we propose a novel extension of CCA to the online, streaming data setting: Sliding Window Informative Canonical…

This paper introduces an active learning framework for manifold Gaussian Process (GP) regression, combining manifold learning with strategic data selection to improve accuracy in high-dimensional spaces. Our method jointly optimizes a…

The sliced Wasserstein flow (SWF), a nonparametric and implicit generative gradient flow, is transformed into a Liouville partial differential equation (PDE)-based formalism. First, the stochastic diffusive term from the Fokker-Planck…

This paper addresses a fundamental but largely unexplored challenge in sequential changepoint analysis: conducting inference following a detected change. We develop a very general framework to construct confidence sets for the unknown…

Hyperparameter tuning is a key component of machine learning procedures, but when validation data contain sensitive user information, search mechanisms can leak private information through the selected configuration. Existing differentially…

Symmetry is ubiquitous in many real-world phenomena and tasks, such as physics, images, and molecular simulations. Empirical studies have demonstrated that incorporating symmetries into generative models can provide better generalization…

Existing rigorous convergence guarantees for the Hamiltonian Monte Carlo (HMC) algorithm use Gaussian auxiliary momentum variables, which are crucially symmetrically distributed. We present a novel convergence analysis for HMC utilizing new…

We introduce a new variational inference (VI) framework, called energetic variational inference (EVI). It minimizes the VI objective function based on a prescribed energy-dissipation law. Using the EVI framework, we can derive many existing…

$L_1$-Approximating polynomials, i.e., polynomials that approximate indicator functions in $L_1$-norm under certain distributions, are widely used in computational learning theory. We study the existence of \textit{non-negative}…