机器学习
This work develops an active learning framework to intelligently enrich data-driven reduced-order models (ROMs) of parametric dynamical systems, which can serve as the foundation of virtual assets in a digital twin. Data-driven ROMs are…
In the Newsvendor problem, the goal is to guess the number that will be drawn from some distribution, with asymmetric consequences for guessing too high vs. too low. In the data-driven version, the distribution is unknown, and one must work…
In this paper, we propose a probabilistic reduced-dimensional vector autoregressive (PredVAR) model to extract low-dimensional dynamics from high-dimensional noisy data. The model utilizes an oblique projection to partition the measurement…
Simultaneous feature selection and non-linear function estimation is challenging in modeling, especially in high-dimensional settings where the number of variables exceeds the available sample size. In this article, we investigate the…
We consider the problem of conditional density estimation, which is a major topic of interest in the fields of statistical and machine learning. Our method, called Marginal Contrastive Discrimination, MCD, reformulates the conditional…
Higher-order ODE solvers have become a standard tool for accelerating diffusion probabilistic model (DPM) sampling, motivating the widespread view that first-order methods are inherently slower and that increasing discretization order is…
As generative AI systems are increasingly deployed in real-world applications, regulating multiple dimensions of model behavior has become essential. We focus on test-time filtering: a lightweight mechanism for behavior control that…
Stochastic gradient Langevin dynamics and its variants approximate the likelihood of an entire dataset, via random (and typically much smaller) subsets, in the setting of Bayesian sampling. Due to the (often substantial) improvement of the…
In this paper, we construct a class of stochastic interpolation neural network operators (SINNOs) with random coefficients activated by sigmoidal functions. We establish their boundedness, interpolation accuracy, and approximation…
Denoising and score estimation have long been known to be linked via the classical Tweedie's formula. In this work, we first extend the latter to a wider range of distributions often called "energy models" and denoted elliptical…
We study the optimization and sample complexity of gradient-based training of a two-layer neural network with quadratic activation function in the high-dimensional regime, where the data is generated as $f_*(\boldsymbol{x}) \propto…
This paper addresses the problem of robust estimation in gossip algorithms over arbitrary communication graphs. Gossip algorithms are fully decentralized, relying only on local neighbor-to-neighbor communication, making them well-suited for…
Machine Learning (ML) is gaining popularity for hypothesis-free discovery of risk and protective factors in healthcare studies. ML is strong at discovering nonlinearities and interactions, but this power is compromised by a lack of reliable…
With the recent development of new geometric and angular-radial frameworks for multivariate extremes, reliably simulating from angular variables in moderate-to-high dimensions is of increasing importance. Empirical approaches have the…
We derive novel concentration inequalities that bound the statistical error for a large class of stochastic optimization problems, focusing on the case of unbounded objective functions. Our derivations utilize the following key tools: 1) A…
Conformal prediction provides a framework for uncertainty quantification, specifically in the forms of prediction intervals and sets with distribution-free guaranteed coverage. While recent cross-conformal techniques such as CV+ and…
We propose a novel deep neural network methodology for density estimation on product Riemannian manifold domains. In our approach, the network directly parameterizes the unknown density function and is trained using a penalized maximum…
Contrastive representation learning is a modern paradigm for learning representations of unlabeled data via augmentations -- precisely, contrastive models learn to embed semantically similar pairs of samples (positive pairs) closer than…
High-dimensional linear bandits with low-dimensional structure have received considerable attention in recent studies due to their practical significance. The most common structure in the literature is sparsity. However, it may not be…
This paper introduces an iterative algorithm for training nonparametric additive models that enjoys favorable memory storage and computational requirements. The algorithm can be viewed as the functional counterpart of stochastic gradient…