Related papers: Deciding the dimension of effective dimension redu…
High-dimensional compositional data, such as those from human microbiome studies, pose unique statistical challenges due to the simplex constraint and excess zeros. While dimension reduction is indispensable for analyzing such data,…
The development and use of dimension reduction methods is prevalent in modern statistical literature. This paper reviews a class of dimension reduction techniques which aim to simultaneously select relevant predictors and find clusters…
Based on the theories of sliced inverse regression (SIR) and reproducing kernel Hilbert space (RKHS), a new approach RDSIR (RKHS-based Double SIR) to nonlinear dimension reduction for survival data is proposed and discussed. An…
Eluder dimension and information gain are two widely used methods of complexity measures in bandit and reinforcement learning. Eluder dimension was originally proposed as a general complexity measure of function classes, but the common…
This article deals with the analysis of high dimensional data that come from multiple sources (experiments) and thus have different possibly correlated responses, but share the same set of predictors. The measurements of the predictors may…
Experience replay is widely used to improve learning efficiency in reinforcement learning by leveraging past experiences. However, existing experience replay methods, whether based on uniform or prioritized sampling, often suffer from low…
Sufficient dimension reduction (SDR) is a popular tool in regression analysis, which replaces the original predictors with a minimal set of their linear combinations. However, the estimated linear combinations generally contain all original…
High-dimensional vector autoregressive (VAR) models provide a flexible framework for characterizing dynamic dependence in multivariate spatio-temporal systems, but their unrestricted estimation becomes infeasible when multiple variables are…
A key challenge to performing effective analyses of high-dimensional data is finding a signal-rich, low-dimensional representation. For linear subspaces, this is generally performed by decomposing a design matrix (via eigenvalue or singular…
Dimensionality reduction (DR) is a popular method for preparing and analyzing high-dimensional data. Reduced data representations are less computationally intensive and easier to manage and visualize, while retaining a significant…
We introduce a novel sufficient dimension-reduction (SDR) method which is robust against outliers using $\alpha$-distance covariance (dCov) in dimension-reduction problems. Under very mild conditions on the predictors, the central subspace…
Developing interpretable machine learning models has become an increasingly important issue. One way in which data scientists have been able to develop interpretable models has been to use dimension reduction techniques. In this paper, we…
Over the past few decades, we have witnessed a large family of algorithms that have been designed to provide different solutions to the problem of dimensionality reduction (DR). The DR is an essential tool to excavate the important…
High-dimensional statistical inference with general estimating equations are challenging and remain less explored. In this paper, we study two problems in the area: confidence set estimation for multiple components of the model parameters,…
We propose a nonlinear function-on-function regression model where both the covariate and the response are random functions. The nonlinear regression is carried out in two steps: we first construct Hilbert spaces to accommodate the…
The rise in data has led to the need for dimension reduction techniques, especially in the area of non-scalar variables, including time series, natural language processing, and computer vision. In this paper, we specifically investigate…
We present a new method for high-dimensional linear regression when a scale parameter of the additive errors is unknown. The proposed estimator is based on a penalized Huber $M$-estimator, for which theoretical results on estimation error…
The classic Hettmansperger-Randles Estimator has found extensive use in robust statistical inference. However, it cannot be directly applied to high-dimensional data. In this paper, we propose a high-dimensional Hettmansperger-Randles…
A bottleneck of sufficient dimension reduction (SDR) in the modern era is that, among numerous methods, only the sliced inverse regression (SIR) is generally applicable under the high-dimensional settings. The higher-order inverse…
High-dimensional linear regression has been thoroughly studied in the context of independent and identically distributed data. We propose to investigate high-dimensional regression models for independent but non-identically distributed…