机器学习

Robust estimation of heterogeneous treatment effects is a fundamental challenge for optimal decision-making in domains ranging from personalized medicine to educational policy. In recent years, predictive machine learning has emerged as a…

We propose a novel method for simulating conditioned diffusion processes (diffusion bridges) in Euclidean spaces. By training a neural network to approximate bridge dynamics, our approach eliminates the need for computationally intensive…

Proposed in Hyv\"arinen (2005), score matching is a parameter estimation procedure that does not require computation of distributional normalizing constants. In this work we utilize the geometric median of means to develop a robust score…

We introduce a unified, flexible, and easy-to-implement framework of sufficient dimension reduction that can accommodate both linear and nonlinear dimension reduction, and both the conditional distribution and the conditional mean as the…

Modeling epidemic spread is critical for informing policy decisions aimed at mitigation. Accordingly, in this work we present a new data-driven method based on Gaussian process regression (GPR) to model epidemic spread through the…

We propose a data-driven method to learn the time-dependent probability density of a multivariate stochastic process from sample paths, assuming that the initial probability density is known and can be evaluated. Our method uses a novel…

Clustering and estimating cluster means are core problems in statistics and machine learning, with k-means and Expectation Maximization (EM) being two widely used algorithms. In this work, we provide a theoretical explanation for the…

There has been much recent interest in understanding the continuum from adversarial to stochastic settings in online learning, with various frameworks including smoothed settings proposed to bridge this gap. We consider the more general and…

Flow-based methods for sampling and generative modeling use continuous-time dynamical systems to represent a {transport map} that pushes forward a source measure to a target measure. The introduction of a time axis provides considerable…

Focusing on the expert problem in online learning, this paper studies the interpolation of several performance metrics via $\phi$-regret minimization, which measures the total loss of an algorithm by its regret with respect to an arbitrary…

Low-Rank Adaptation (LoRA) has emerged as a widely adopted parameter-efficient fine-tuning (PEFT) technique for foundation models. Recent work has highlighted an inherent asymmetry in the initialization of LoRA's low-rank factors, which has…

In linear contextual bandits, the objective is to select actions that maximize cumulative rewards, modeled as a linear function with unknown parameters. Although Thompson Sampling performs well empirically, it does not achieve optimal…

Causal effect estimation seeks to determine the impact of an intervention from observational data. However, the existing causal inference literature primarily addresses treatment effects on frequently occurring events. But what if we are…

In this paper, we develop a wide class Mirror Descent (MD) algorithms, which play a key role in machine learning. For this purpose we formulated the constrained optimization problem, in which we exploits the Bregman divergence with the…

Anomaly detection (AD) is a critical task across domains such as cybersecurity and healthcare. In the unsupervised setting, an effective and theoretically-grounded principle is to train classifiers to distinguish normal data from…

We address the regression problem under the constraint of demographic parity, a commonly used fairness definition. Recent studies have revealed fair minimax optimal regression algorithms, the most accurate algorithms that adhere to the…

Most existing literature on supervised machine learning assumes that the training dataset is drawn from an i.i.d. sample. However, many real-world problems exhibit temporal dependence and strong correlations between the marginal…

Cooperative game theory has become a cornerstone of post-hoc interpretability in machine learning, largely through the use of Shapley values. Yet, despite their widespread adoption, Shapley-based methods often rest on axiomatic…

We study finite-armed semiparametric bandits, where each arm's reward combines a linear component with an unknown, potentially adversarial shift. This model strictly generalizes classical linear bandits and reflects complexities common in…

Forward uncertainty quantification in dynamical systems is challenging due to non-smooth or locally oscillating nonlinear behaviors. Spline dimensional decomposition (SDD) addresses such nonlinearity by partitioning input coordinates via…