Related papers: A Precise Performance Analysis of Support Vector R…
Heteroskedasticity testing in nonparametric regression is a classic statistical problem with important practical applications, yet fundamental limits are unknown. Adopting a minimax perspective, this article considers the testing problem in…
Most linear experimental design problems assume homogeneous variance although heteroskedastic noise is present in many realistic settings. Let a learner have access to a finite set of measurement vectors $\mathcal{X}\subset \mathbb{R}^d$…
Variable selection in linear models plays a pivotal role in modern statistics. Hard-thresholding methods such as $l_0$ regularization are theoretically ideal but computationally infeasible. In this paper, we propose a new approach, called…
Suppose that we observe independent random pairs $(X_1,Y_1)$, $(X_2,Y_2)$, >..., $(X_n,Y_n)$. Our goal is to estimate regression functions such as the conditional mean or $\beta$--quantile of $Y$ given $X$, where $0<\beta <1$. In order to…
A challenge in developing machine learning regression models is that it is difficult to know whether maximal performance has been reached on a particular dataset, or whether further model improvement is possible. In biology this problem is…
Tackling pattern recognition problems in areas such as computer vision, bioinformatics, speech or text recognition is often done best by taking into account task-specific statistical relations between output variables. In structured…
The Full Bayesian Significance Test (FBST) possesses many desirable aspects, such as dismissing the need for hypotheses to have positive prior probability and providing a measure of evidence against $H_0$. Still, few attempts have been made…
Transient stability assessment is an integral part of dynamic security assessment of power systems. Traditional methods of transient stability assessment, such as time domain simulation approach and direct methods, are appropriate for…
Tensor regression is an important tool for tensor data analysis, but existing works have not considered the impact of outliers, making them potentially sensitive to such data points. This paper proposes a low tubal rank robust regression…
Symbolic regression has recently gained traction in AI-driven scientific discovery, aiming to recover explicit closed-form expressions from data that reveal underlying physical laws. Despite recent advances, existing methods remain…
This work introduces an asymptotic study of Hotelling-type tensor deflation in the presence of noise, in the regime of large tensor dimensions. Specifically, we consider a low-rank asymmetric tensor model of the form $\sum_{i=1}^r…
Beta regression models provide an adequate approach for modeling continuous outcomes limited to the interval (0,1). This paper deals with an extension of beta regression models that allow for explanatory variables to be measured with error.…
Robust loss minimization is an important strategy for handling robust learning issue on noisy labels. Current robust loss functions, however, inevitably involve hyperparameter(s) to be tuned, manually or heuristically through cross…
Improvement of statistical learning models in order to increase efficiency in solving classification or regression problems is still a goal pursued by the scientific community. In this way, the support vector machine model is one of the…
There is a growing need for models that are interpretable and have reduced energy and computational cost (e.g., in health care analytics and federated learning). Examples of algorithms to train such models include logistic regression and…
Hypothesis testing procedures are developed to assess linear operator constraints in function-on-scalar regression when incomplete functional responses are observed. The approach enables statistical inferences about the shape and other…
Nowadays Big Data are becoming more and more important. Many sectors of our economy are now guided by data-driven decision processes. Big Data and business intelligence applications are facilitated by the MapReduce programming model while,…
Suppose that we observe $y \in \mathbb{R}^f$ and $X \in \mathbb{R}^{f \times m}$ in the following errors-in-variables model: \begin{eqnarray*} y & = & X_0 \beta^* + \epsilon \\ X & = & X_0 + W \end{eqnarray*} where $X_0$ is a $f \times m$…
Motivated by value function estimation in reinforcement learning, we study statistical linear inverse problems, i.e., problems where the coefficients of a linear system to be solved are observed in noise. We consider penalized estimators,…
Most factor modelling research in vector or matrix-valued time series assume all factors are pervasive/strong and leave weaker factors and their corresponding series to the noise. Weaker factors can in fact be important to a group of…