Related papers: Fr\'echet Sufficient Dimension Reduction for Rando…
Inverse problems involving systems of partial differential equations (PDEs) with many measurements or experiments can be very expensive to solve numerically. In a recent paper we examined dimensionality reduction methods, both stochastic…
The present paper continues the study of infinite dimensional calculus via regularization, started by C. Di Girolami and the second named author, introducing the notion of "weak Dirichlet process" in this context. Such a process $\X$,…
The Fr\'echet mean generalizes the concept of a mean to a metric space setting. In this work we consider equivariant estimation of Fr\'echet means for parametric models on metric spaces that are Riemannian manifolds. The geometry and…
Modern metrics for generative learning like Fr\'echet Inception Distance (FID) and DINOv2-Fr\'echet Distance (FD-DINOv2) demonstrate impressive performance. However, they suffer from various shortcomings, like a bias towards specific…
We review sufficient dimension reduction (SDR) estimators with multivariate response in this paper. A wide range of SDR methods are characterized as inverse regression SDR estimators or forward regression SDR estimators. The inverse…
In this paper, we address the inference problem in high-dimensional linear expectile regression. We transform the expectile loss into a weighted-least-squares form and apply a de-biased strategy to establish Wald-type tests for multiple…
It is well-known that the high computational complexity and the insufficient samples in large-scale array signal processing restrict the real-world applications of the conventional full-dimensional adaptive beamforming (sample matrix…
We derive concentration inequalities for the supremum norm of the difference between a kernel density estimator (KDE) and its point-wise expectation that hold uniformly over the selection of the bandwidth and under weaker conditions on the…
Selecting relevant features is an important and necessary step for intelligent machines to maximize their chances of success. However, intelligent machines generally have no enough computing resources when faced with huge volume of data.…
Additive regression models are actively researched in the statistical field because of their usefulness in the analysis of responses determined by non-linear relationships with multivariate predictors. In this kind of statistical models,…
This paper studies kernel ridge regression in high dimensions under covariate shifts and analyzes the role of importance re-weighting. We first derive the asymptotic expansion of high dimensional kernels under covariate shifts. By a…
Data consisting of samples of probability density functions are increasingly prevalent, necessitating the development of methodologies for their analysis that respect the inherent nonlinearities associated with densities. In many…
An inverse elastic source problem with sparse measurements is of concern. A generic mathematical framework is proposed which incorporates a low- dimensional manifold regularization in the conventional source reconstruction algorithms…
In some applications (e.g., in cosmology and economics), the regression E[Z|x] is not adequate to represent the association between a predictor x and a response Z because of multi-modality and asymmetry of f(z|x); using the full density…
Randomized dimensionality reduction has been recognized as one of the fundamental techniques in handling high-dimensional data. Starting with the celebrated Johnson-Lindenstrauss Lemma, such reductions have been studied in depth for the…
To accelerate kernel methods, we propose a near input sparsity time algorithm for sampling the high-dimensional feature space implicitly defined by a kernel transformation. Our main contribution is an importance sampling method for…
Multi-fidelity modelling arises in many situations in computational science and engineering world. It enables accurate inference even when only a small set of accurate data is available. Those data often come from a high-fidelity model,…
In this work, we study distance metric learning (DML) for high dimensional data. A typical approach for DML with high dimensional data is to perform the dimensionality reduction first before learning the distance metric. The main…
Variable screening methods have been shown to be effective in dimension reduction under the ultra-high dimensional setting. Most existing screening methods are designed to rank the predictors according to their individual contributions to…
The vast majority of Dimensionality Reduction (DR) techniques rely on second-order statistics to define their optimization objective. Even though this provides adequate results in most cases, it comes with several shortcomings. The methods…