Related papers: Slicing-free Inverse Regression in High-dimensiona…
As its name suggests, sufficient dimension reduction (SDR) targets to estimate a subspace from data that contains all information sufficient to explain a dependent variable. Ample approaches exist to SDR, some of the most recent of which…
In this paper, we propose new sampling approaches for the Shrinkage Inverse-Wishart (SIW) distribution, a generalized family of the Inverse-Wishart distribution originally proposed by Berger et al. (2020, Annals of Statistics). It offers a…
A wide range of applications arising in machine learning and signal processing can be cast as convex optimization problems. These problems are often ill-posed, i.e., the optimal solution lacks a desired property such as uniqueness or…
The application of standard sufficient dimension reduction methods for reducing the dimension space of predictors without losing regression information requires inverting the covariance matrix of the predictors. This has posed a number of…
The spherical-radial decomposition (SRD) is an efficient method for estimating probabilistic functions and their gradients defined over finite-dimensional elliptical distributions. In this work, we generalize the SRD to infinite stochastic…
The inverse scattering problems have been popular for the past thirty years. While very successful in many cases, progress has lagged when only {\em limited-aperture} measurement is available. In this paper, we perform some elementary study…
Most data sets comprise of measurements on continuous and categorical variables. In regression and classification Statistics literature, modeling high-dimensional mixed predictors has received limited attention. In this paper we study the…
Bayesian methods have received increasing attention in medical research, where sensitivity analysis of prior distributions is essential. Such analyses typically require the evaluation of the posterior distribution of a parameter under…
Metric learning has attracted extensive interest for its ability to provide personalized recommendations based on the importance of observed user-item interactions. Current metric learning methods aim to push negative items away from the…
Single Index Models (SIMs) are simple yet flexible semi-parametric models for machine learning, where the response variable is modeled as a monotonic function of a linear combination of features. Estimation in this context requires learning…
We introduce an innovative method for incremental nonparametric probabilistic inference in high-dimensional state spaces. Our approach leverages \slices from high-dimensional surfaces to efficiently approximate posterior distributions of…
Supervised dimensionality reduction strategies have been of great interest. However, current supervised dimensionality reduction approaches are difficult to scale for situations characterized by large datasets given the high computational…
We present the Deep Picard Iteration (DPI) method, a new deep learning approach for solving high-dimensional partial differential equations (PDEs). The core innovation of DPI lies in its use of Picard iteration to reformulate the typically…
This paper introduces two variational inference approaches for infinite-dimensional inverse problems, developed through gradient descent with a constant learning rate. The proposed methods enable efficient approximate sampling from the…
Current metric learning approaches for image retrieval are usually based on learning a space of informative latent representations where simple approaches such as the cosine distance will work well. Recent state of the art methods such as…
We introduce a discriminative regression approach to supervised classification in this paper. It estimates a representation model while accounting for discriminativeness between classes, thereby enabling accurate derivation of categorical…
High-dimensional data is common in multiple areas, such as health care and genomics, where the number of features can be tens of thousands. In such scenarios, the large number of features often leads to inefficient learning. Constraint…
This paper is concerned with developing an efficient numerical algorithm for fast implementation of the sparse grid method for computing the $d$-dimensional integral of a given function. The new algorithm, called the MDI-SG ({\em multilevel…
Bayesian inverse problems use observed data to update a prior probability distribution for an unknown state or parameter of a scientific system to a posterior distribution conditioned on the data. In many applications, the unknown parameter…
We reformulate unsupervised dimension reduction problem (UDR) in the language of tempered distributions, i.e. as a problem of approximating an empirical probability density function by another tempered distribution, supported in a…