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Parameter reduction can enable otherwise infeasible design and uncertainty studies with modern computational science models that contain several input parameters. In statistical regression, techniques for sufficient dimension reduction…
Symbolic regression (SR) is an area of interpretable machine learning that aims to identify mathematical expressions, often composed of simple functions, that best fit in a given set of covariates $X$ and response $y$. In recent years, deep…
Seeking to improve model generalization, we consider a new approach based on distributionally robust learning (DRL) that applies stochastic gradient descent to the outer minimization problem. Our algorithm efficiently estimates the gradient…
We propose a novel method for semi-supervised learning (SSL) based on data-driven distributionally robust optimization (DRO) using optimal transport metrics. Our proposed method enhances generalization error by using the unlabeled data to…
We introduce a new method of nowcasting using regression on path signatures. Path signatures capture the geometric properties of sequential data. Because signatures embed observations in continuous time, they naturally handle mixed…
Symbolic regression (SR) is a powerful technique for discovering the analytical mathematical expression from data, finding various applications in natural sciences due to its good interpretability of results. However, existing methods face…
Learning representations that capture both intrinsic data geometry and target-relevant structure remains a fundamental challenge, particularly in settings where data reduction must balance compression with predictive fidelity. While…
Structured additive distributional regression models offer a versatile framework for estimating complete conditional distributions by relating all parameters of a parametric distribution to covariates. Although these models efficiently…
Aiming to generalize the label knowledge from a source domain with continuous outputs to an unlabeled target domain, Domain Adaptation Regression (DAR) is developed for complex practical learning problems. However, due to the continuity…
We consider the distributionally robust optimization (DRO) problem with spectral risk-based uncertainty set and $f$-divergence penalty. This formulation includes common risk-sensitive learning objectives such as regularized condition…
We describe a new approach for managing aleatoric uncertainty in the Reinforcement Learning (RL) paradigm. Instead of selecting actions according to a single statistic, we propose a distributional method based on the second-order stochastic…
Sparse deep learning has become a popular technique for improving the performance of deep neural networks in areas such as uncertainty quantification, variable selection, and large-scale network compression. However, most existing research…
Stochastic convex optimization algorithms are the most popular way to train machine learning models on large-scale data. Scaling up the training process of these models is crucial, but the most popular algorithm, Stochastic Gradient Descent…
The large communication cost for exchanging gradients between different nodes significantly limits the scalability of distributed training for large-scale learning models. Motivated by this observation, there has been significant recent…
Sampling is ubiquitous in machine learning methodologies. Due to the growth of large datasets and model complexity, we want to learn and adapt the sampling process while training a representation. Towards achieving this grand goal, a…
In this study, we propose a method Distributionally Robust Safe Screening (DRSS), for identifying unnecessary samples and features within a DR covariate shift setting. This method effectively combines DR learning, a paradigm aimed at…
Over-parameterized deep models usually over-fit to a given training distribution, which makes them sensitive to small changes and out-of-distribution samples at inference time, leading to low generalization performance. To this end, several…
Domain Adaptation (DA) has recently received significant attention due to its potential to adapt a learning model across source and target domains with mismatched distributions. Since DA methods rely exclusively on the given source and…
We focus on the distribution regression problem: regressing to vector-valued outputs from probability measures. Many important machine learning and statistical tasks fit into this framework, including multi-instance learning and point…
Sufficient dimension reduction (SDR) is continuing an active research field nowadays for high dimensional data. It aims to estimate the central subspace (CS) without making distributional assumption. To overcome the large-$p$-small-$n$…