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We propose a robust inferential procedure for assessing uncertainties of parameter estimation in high-dimensional linear models, where the dimension $p$ can grow exponentially fast with the sample size $n$. Our method combines the…
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…
Fully robust versions of the elastic net estimator are introduced for linear and logistic regression. The algorithms to compute the estimators are based on the idea of repeatedly applying the non-robust classical estimators to data subsets…
Compressed sensing typically deals with the estimation of a system input from its noise-corrupted linear measurements, where the number of measurements is smaller than the number of input components. The performance of the estimation…
It is of importance to develop statistical techniques to analyze high-dimensional data in the presence of both complex dependence and possible outliers in real-world applications such as imaging data analyses. We propose a new robust…
In this work, we propose low-complexity adaptive biased estimation algorithms, called group-based shrinkage estimators (GSEs), for parameter estimation and interference suppression scenarios with mechanisms to automatically adjust the…
Series and polynomial regression are able to approximate the same function classes as neural networks. However, these methods are rarely used in practice, although they offer more interpretability than neural networks. In this paper, we…
Consider the problem of joint parameter estimation and prediction in a Markov random field: i.e., the model parameters are estimated on the basis of an initial set of data, and then the fitted model is used to perform prediction (e.g.,…
In the analysis of survey data, sampling weights are needed for consistent estimation of the population. However, the original inverse probability weights from the survey sample design are typically modified to account for non-response, to…
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…
We consider the multivariate max-linear regression problem where the model parameters $\boldsymbol{\beta}_{1},\dotsc,\boldsymbol{\beta}_{k}\in\mathbb{R}^{p}$ need to be estimated from $n$ independent samples of the (noisy) observations $y =…
The mean squared error loss is widely used in many applications, including auto-encoders, multi-target regression, and matrix factorization, to name a few. Despite computational advantages due to its differentiability, it is not robust to…
Data subject to heavy-tailed errors are commonly encountered in various scientific fields, especially in the modern era with explosion of massive data. To address this problem, procedures based on quantile regression and Least Absolute…
In this study, we consider preliminary test and shrinkage estimation strategies for quantile regression models. In classical Least Squares Estimation (LSE) method, the relationship between the explanatory and explained variables in the…
This paper proposes a new approach to fit a linear regression for symbolic internal-valued variables, which improves both the Center Method suggested by Billard and Diday in \cite{BillardDiday2000} and the Center and Range Method suggested…
A large empirical literature regresses outcomes on empirical Bayes shrinkage estimates of value-added, yet little is known about whether this approach leads to unbiased estimates and valid inference for the downstream regression…
We consider regression problems with binary weights. Such optimization problems are ubiquitous in quantized learning models and digital communication systems. A natural approach is to optimize the corresponding Lagrangian using variants of…
Stochastic heavy ball momentum (SHB) is commonly used to train machine learning models, and often provides empirical improvements over stochastic gradient descent. By primarily focusing on strongly-convex quadratics, we aim to better…
Sparse regression and classification estimators that respect group structures have application to an assortment of statistical and machine learning problems, from multitask learning to sparse additive modeling to hierarchical selection.…
This paper investigates a new approach to estimate the gradient of the conditional probability given the covariates in the binary classification framework. The proposed approach consists in fitting a localized nearest-neighbor logistic…