机器学习

We study the problem of denoising when only the noise level is known, not the noise distribution. Independent noise $Z$ corrupts a signal $X$, yielding the observation $Y = X + \sigma Z$ with known $\sigma \in (0,1)$. We propose…

This paper studies optimization on networks modeled as metric graphs. Motivated by applications where the objective function is expensive to evaluate or only available as a black box, we develop Bayesian optimization algorithms that…

We demonstrate how supervised learning can be decomposed into a two-stage procedure, where (1) all model parameters are selected in an unsupervised manner, and (2) the outputs y are added to the model, without changing the parameter values.…

A key capability of modern neural networks is their capacity to simultaneously learn underlying rules and memorize specific facts or exceptions. Yet, theoretical understanding of this dual capability remains limited. We introduce the…

Tensors provide a structured representation for multidimensional data, yet discretization can obscure important information when such data originates from continuous processes. We address this limitation by introducing a functional Tucker…

We study statistical estimation in a student--teacher setting, where predictions from a pre-trained teacher are used to guide a student model. A standard approach is to train the student to directly match the teacher's outputs, which we…

Probabilistic forecasting provides a principled framework for uncertainty quantification in dynamical systems by representing predictions as probability distributions rather than deterministic trajectories. However, existing forecasting…

Efficient global optimization (EGO) is one of the most widely used noise-free Bayesian optimization algorithms.It comprises the Gaussian process (GP) surrogate model and expected improvement (EI) acquisition function. In practice, when EGO…

Demographic parity (DP) is a widely used group fairness criterion requiring predictive distributions to be invariant across sensitive groups. While natural in classification, full distributional DP is often overly restrictive in regression…

As a representative continuous-depth neural network approach, stochastic differential equation (SDE)-based Bayesian neural networks (BNNs) have attracted considerable attention due to their solid theoretical foundations and strong potential…

Mixture-of-Experts (MoE) architectures decompose prediction tasks into specialized expert sub-networks selected by a gating mechanism. This letter adopts a communication-theoretic view of MoE gating, modeling the gate as a stochastic…

We introduce the $\widetilde{\rho}$-posterior, a modified version of the $\rho$-posterior, obtained by replacing the supremum over competitor parameters with a softmax aggregation. This modification allows a PAC-Bayesian analysis of the…

Generative diffusion models have emerged as a powerful class of models in machine learning, yet a unified theoretical understanding of their operation is still developing. This paper provides an integrated perspective on generative…

We introduce the first best-of-both-worlds algorithm for contextual combinatorial semi-bandits that simultaneously guarantees $\widetilde{\mathcal{O}}(\sqrt{T})$ regret in the adversarial regime and $\widetilde{\mathcal{O}}(\ln T)$ regret…

The widespread use of generative models has created a feedback loop, in which each generation of models is trained on data partially produced by its predecessors. This process has raised concerns about model collapse: A critical degradation…

We introduce kernel density machines (KDM), an agnostic kernel-based framework for learning the Radon-Nikodym derivative (density) between probability measures under minimal assumptions. KDM applies to general measurable spaces and avoids…

In recent years, signSGD has garnered interest as both a practical optimizer as well as a simple model to understand adaptive optimizers like Adam. Though there is a general consensus that signSGD acts to precondition optimization and…

Constrained optimization in high-dimensional black-box settings is difficult due to expensive evaluations, the lack of gradient information, and complex feasibility regions. In this work, we propose a Bayesian optimization method that…

Understanding how biomarker distributions evolve over time is a central challenge in digital health and chronic disease monitoring. In diabetes, changes in the distribution of glucose measurements can reveal patterns of disease progression…

Privacy and algorithmic fairness have become two central issues in modern machine learning. Although each has separately emerged as a rapidly growing research area, their joint effect remains comparatively under-explored. In this paper, we…