机器学习

Band-limited functions are fundamental objects that are widely used in systems theory and signal processing. In this paper we refine a recent nonparametric, nonasymptotic method for constructing simultaneous confidence regions for…

Recent developments in generative artificial intelligence (AI) rely on machine learning techniques such as deep learning and generative modeling to achieve state-of-the-art performance across wide-ranging domains. These methods' surprising…

In this paper, we solve stochastic partial differential equations (SPDEs) numerically by using (possibly random) neural networks in the truncated Wiener chaos expansion of their corresponding solution. Moreover, we provide some…

Reliable confidence measures of metrics derived from medical imaging reconstruction pipelines would improve the standard of decision-making in many clinical workflows. Conformal Prediction (CP) provides a robust framework for producing…

Surrogate models are statistical or conceptual approximations for more complex simulation models. In this context, it is crucial to propagate the uncertainty induced by limited simulation budget and surrogate approximation error to…

It is often of interest to infer lower-dimensional structure underlying complex data. As a flexible class of non-linear structures, it is common to focus on Riemannian manifolds. Most existing manifold learning algorithms replace the…

This paper investigates two fundamental descriptors of data, i.e., density distribution versus mass distribution, in the context of clustering. Density distribution has been the de facto descriptor of data distribution since the…

We study variance reduction for score estimation and diffusion-based sampling in settings where the clean (target) score is available or can be approximated. Starting from the Target Score Identity (TSI), which expresses the noisy marginal…

We propose a kernel-based nonparametric framework for mean-variance optimization that enables inference on economically motivated shape constraints in finance, including positivity, monotonicity, and convexity. Many central hypotheses in…

We propose \textbf{Temporal Conformal Prediction (TCP)}, a distribution-free framework for constructing well-calibrated prediction intervals in nonstationary time series. TCP couples a modern quantile forecaster with a rolling…

We study an online dynamic pricing problem where the potential demand at each time period $t=1,2,\ldots, T$ is stochastic and dependent on the price. However, a perishable inventory is imposed at the beginning of each time $t$, censoring…

We consider a general model for high-dimensional empirical risk minimization whereby the data $\mathbf{x}_i$ are $d$-dimensional Gaussian vectors, the model is parametrized by $\mathbf{\Theta}\in\mathbb{R}^{d\times k}$, and the loss depends…

We introduce the spiked mixture model (SMM) to address the problem of estimating a set of signals from many randomly scaled and noisy observations. Subsequently, we design a novel expectation-maximization (EM) algorithm to recover all…

It is increasingly common to collect data of multiple different types on the same set of samples. Our focus is on studying relationships between such multiview features and responses. A motivating application arises in the context of…

Deep neural networks (DNNs) typically involve a large number of parameters and are trained to achieve zero or near-zero training error. Despite such interpolation, they often exhibit strong generalization performance on unseen data, a…

Functional bilevel optimization (FBO) provides a powerful framework for hierarchical learning in function spaces, yet current methods are limited to static offline settings and perform suboptimally in online, non-stationary scenarios. We…

Estimating Heterogeneous Treatment Effects (HTE) in industrial applications such as AdTech and healthcare presents a dual challenge: extreme class imbalance and heavy-tailed outcome distributions. While the X-Learner framework effectively…

Conformal Test Martingales (CTMs) are a standard method within the Conformal Prediction framework for testing the crucial assumption of data exchangeability by monitoring deviations from uniformity in the p-value sequence. Although…

We propose a Likelihood Matching approach for training diffusion models by first establishing an equivalence between the likelihood of the target data distribution and a likelihood along the sample path of the reverse diffusion. To…

We introduce a new class of generative diffusion models that, unlike conventional denoising diffusion models, achieve a time-homogeneous structure for both the noising and denoising processes, allowing the number of steps to adaptively…