Related papers: Errors-in-variables Fr\'echet Regression with Low-…
Reduced-rank (RR) regression may be interpreted as a dimensionality reduction technique able to reveal complex relationships among the data parsimoniously. However, RR regression models typically overlook any potential group structure among…
We propose a generic framework based on a new stochastic variance-reduced gradient descent algorithm for accelerating nonconvex low-rank matrix recovery. Starting from an appropriate initial estimator, our proposed algorithm performs…
In this paper, the estimation problem for sparse reduced rank regression (SRRR) model is considered. The SRRR model is widely used for dimension reduction and variable selection with applications in signal processing, econometrics, etc. The…
In many modern applications, a carefully designed primary study provides individual-level data for interpretable modeling, while summary-level external information is available through black-box, efficient, and nonparametric…
Debiasing is a fundamental concept in high-dimensional statistics. While degrees-of-freedom adjustment is the state-of-the-art technique in high-dimensional linear regression, it is limited to i.i.d. samples and sub-Gaussian covariates.…
Missing values in datasets are common in applied statistics. For regression problems, theoretical work thus far has largely considered the issue of missing covariates as distinct from missing responses. However, in practice, many datasets…
We study the problem of learning mixtures of low-rank models, i.e. reconstructing multiple low-rank matrices from unlabelled linear measurements of each. This problem enriches two widely studied settings -- low-rank matrix sensing and mixed…
Variable selection comprises an important step in many modern statistical inference procedures. In the regression setting, when estimators cannot shrink irrelevant signals to zero, covariates without relationships to the response often…
We introduce a novel Bayesian approach for both covariate selection and sparse precision matrix estimation in the context of high-dimensional Gaussian graphical models involving multiple responses. Our approach provides a sparse estimation…
Recently, many machine learning and statistical models such as non-linear regressions, the Single Index, Multi-index, Varying Coefficient Index Models and Two-layer Neural Networks can be reduced to or be seen as a special case of a new…
Error-in-variables regression is a common ingredient in treatment effect estimators using panel data. This includes synthetic control estimators, counterfactual time series forecasting estimators, and combinations. We study high-dimensional…
Segmented regression models offer model flexibility and interpretability as compared to the global parametric and the nonparametric models, and yet are challenging in both estimation and inference. We consider a four-regime segmented model…
In this paper, we present a novel and effective inference approach to conduct both finite- and large-sample inference for high-dimensional linear regression models. This approach is developed under the so-called repro samples framework, in…
Incomplete covariate vectors are known to be problematic for estimation and inferences on model parameters, but their impact on prediction performance is less understood. We develop an imputation-free method that builds on a random…
Random forests are a statistical learning method widely used in many areas of scientific research because of its ability to learn complex relationships between input and output variables and also its capacity to handle high-dimensional…
In this paper we present the framework of symmetry in nonparametric regression. This generalises the framework of covariate sparsity, where the regression function depends only on at most $s < d$ of the covariates, which is a special case…
Regression analysis with missing data is a long-standing and challenging problem, particularly when there are many missing variables with arbitrary missing patterns. Likelihood-based methods, although theoretically appealing, are often…
Functional linear regression analysis aims to model regression relations which include a functional predictor. The analog of the regression parameter vector or matrix in conventional multivariate or multiple-response linear regression…
In practical regression applications, multiple covariates are often measured, but not all may be associated with the response variable. Identifying and including only the relevant covariates in the model is crucial for improving prediction…
This study proposes a mathematical programming-based algorithm for the integrated selection of variable subsets and bandwidth estimation in geographically weighted regression, a local regression method that allows the kernel bandwidth and…