机器学习

We introduce a novel framework for uncertainty quantification in clustering that combines martingale posterior distributions with density-based clustering. Unlike classical model-based approaches, which define clusters at the latent level…

We study robustness verification of neural networks via metric algebraic geometry. For polynomial neural networks, certifying a robustness radius amounts to computing the distance to the algebraic decision boundary. We use the Euclidean…

This paper presents ``randomized SINDy", a sequential machine learning algorithm designed for dynamic data that has a time-dependent structure. It employs a probabilistic approach, with its PAC learning property rigorously proven through…

This paper investigates approximation capabilities of two-dimensional (2D) deep convolutional neural networks (CNNs), with Korobov functions serving as a benchmark. We focus on 2D CNNs, comprising multi-channel convolutional layers with…

We study post-training interpretability for Support Vector Machines (SVMs) built from truncated orthogonal polynomial kernels. Since the associated reproducing kernel Hilbert space is finite-dimensional and admits an explicit tensor-product…

We propose a novel amortized optimization method for predicting optimal transport (OT) plans across multiple pairs of measures by leveraging Kantorovich potentials derived from sliced OT. We introduce two amortization strategies:…

Feature selection is a classical problem in statistics and machine learning, and it continues to remain an extremely challenging problem especially in the context of unknown non-linear relationships with dependent features. On the other…

We study bandit best-arm identification with arbitrary and potentially adversarial rewards. A simple random uniform learner obtains the optimal rate of error in the adversarial scenario. However, this type of strategy is suboptimal when the…

In online clustering problems, there is often a large amount of uncertainty over possible cluster assignments that cannot be resolved until more data are observed. This difficulty is compounded when clusters follow complex distributions, as…

We study a classification problem with three key challenges: pervasive informative missingness, the integration of partial prior expert knowledge into the learning process, and the need for interpretable decision rules. We propose a…

Modern Machine Learning (ML) and Deep Neural Networks (DNNs) often operate on high-dimensional data and rely on overparameterized models, where classical low-dimensional intuitions break down. In particular, the proportional regime where…

We investigate stochastic combinatorial semi-bandits, where the entire joint distribution of outcomes impacts the complexity of the problem instance (unlike in the standard bandits). Typical distributions considered depend on specific…

The robust low-rank tensor completion problem addresses the challenge of recovering corrupted high-dimensional tensor data with missing entries, outliers, and sparse noise commonly found in real-world applications. Existing methodologies…

Clustering and dimensionality reduction have been crucial topics in machine learning and computer vision. Clustering high-dimensional data has been challenging for a long time due to the curse of dimensionality. For that reason, a more…

Causal representation learning (CRL) aims to identify the underlying latent variables from high-dimensional observations, even when variables are dependent with each other. We study this problem for latent variables that follow a…

Rare events such as conformational changes in biomolecules, phase transitions, and chemical reactions are central to the behavior of many physical systems, yet they are extremely difficult to study computationally because unbiased…

Clinical decision-making often involves selecting tests that are costly, invasive, or time-consuming, motivating individualized, sequential strategies for what to measure and when to stop ascertaining. We study the problem of learning…

Stochastic gradient descent (SGD) is central to simulation optimization, stochastic programming, and online M-estimation, where sampling effort is a decision variable. We study the mini-batch gradient noise as a sampling-design object.…

Random walk (RW)-based algorithms have long been popular in distributed systems due to low overheads and scalability, with recent growing applications in decentralized learning. However, their reliance on local interactions makes them…

Predicting potential and counterfactual outcomes from observational data is central to individualized decision-making, particularly in clinical settings where treatment choices must be tailored to each patient rather than guided solely by…