Related papers: Dimensionality Reduction and Wasserstein Stability…

We study posterior rates of contraction in Gaussian process regression with unbounded covariate domain. Our argument relies on developing a Gaussian approximation to the posterior of the leading coefficients of a Karhunen--Lo\'{e}ve…

This paper introduces a new unsupervised method for dimensionality reduction via regression (DRR). The algorithm belongs to the family of invertible transforms that generalize Principal Component Analysis (PCA) by using curvilinear instead…

Principal component analysis (PCA) is a widely employed statistical tool used primarily for dimensionality reduction. However, it is known to be adversely affected by the presence of outlying observations in the sample, which is quite…

Composite quantile regression has been used to obtain robust estimators of regression coefficients in linear models with good statistical efficiency. By revealing an intrinsic link between the composite quantile regression loss function and…

Wasserstein distributionally robust optimization (WDRO) strengthens statistical learning under model uncertainty by minimizing the local worst-case risk within a prescribed ambiguity set. Although WDRO has been extensively studied in…

We consider the distributionally robust optimization (DRO) model of principal component analysis (PCA) to account for uncertainty in the underlying probability distribution. The resulting formulation leads to a nonsmooth constrained min-max…

This paper develops a method to detect model structural changes by applying a Corrected Kernel Principal Component Analysis (CKPCA) to construct the so-called central distribution deviation subspaces. This approach can efficiently identify…

We address high-dimensional zero-one random parameters in two-stage convex conic optimization problems. Such parameters typically represent failures of network elements and constitute rare, high-impact random events in several applications.…

Computer vision systems that are deployed in safety-critical applications need to quantify their output uncertainty. We study regression from images to parameter values and here it is common to detect uncertainty by predicting probability…

Diffusion models have revolutionized various application domains, including computer vision and audio generation. Despite the state-of-the-art performance, diffusion models are known for their slow sample generation due to the extensive…

Dimension reduction (DR) methods provide systematic approaches for analyzing high-dimensional data. A key requirement for DR is to incorporate global dependencies among original and embedded samples while preserving clusters in the…

Fitting a function by using linear combinations of a large number $N$ of `simple' components is one of the most fruitful ideas in statistical learning. This idea lies at the core of a variety of methods, from two-layer neural networks to…

Regularized empirical risk minimization using kernels and their corresponding reproducing kernel Hilbert spaces (RKHSs) plays an important role in machine learning. However, the actually used kernel often depends on one or on a few…

Kernel methods are powerful learning methodologies that allow to perform non-linear data analysis. Despite their popularity, they suffer from poor scalability in big data scenarios. Various approximation methods, including random feature…

Persistence diagrams are a useful tool from topological data analysis which can be used to provide a concise description of a filtered topological space. What makes them even more useful in practice is that they come with a notion of a…

In scientific applications, multivariate observations often come in tandem with temporal or spatial covariates, with which the underlying signals vary smoothly. The standard approaches such as principal component analysis and factor…

Due to the growing adoption of deep neural networks in many fields of science and engineering, modeling and estimating their uncertainties has become of primary importance. Despite the growing literature about uncertainty quantification in…

Sufficient dimension reduction aims for reduction of dimensionality of a regression without loss of information by replacing the original predictor with its lower-dimensional subspace. Partial (sufficient) dimension reduction arises when…

The celebrated Nadaraya-Watson kernel estimator is among the most studied method for nonparametric regression. A classical result is that its rate of convergence depends on the number of covariates and deteriorates quickly as the dimension…

In this paper, we consider a partial deconvolution kernel estimator for nonparametric regression when some covariates are measured with error while others are observed without error. We focus on a general and realistic setting in which the…