Related papers: On a class of high dimensional linear regression m…
Linear regression is a fundamental and popular statistical method. There are various kinds of linear regression, such as mean regression and quantile regression. In this paper, we propose a new one called distribution regression, which…
This paper deals with sparse feature selection and grouping for classification and regression. The classification or regression problems under consideration consists in minimizing a convex empirical risk function subject to an $\ell^1$…
Unsupervised and self-supervised learning approaches have become a crucial tool to learn representations for downstream prediction tasks. While these approaches are widely used in practice and achieve impressive empirical gains, their…
The Lasso is a popular regression method for high-dimensional problems in which the number of parameters $\theta_1,\dots,\theta_N$, is larger than the number $n$ of samples: $N>n$. A useful heuristics relates the statistical properties of…
Regularization is widely used in statistics and machine learning to prevent overfitting and gear solution towards prior information. In general, a regularized estimation problem minimizes the sum of a loss function and a penalty term. The…
The least-square regression problems or inverse problems have been widely studied in many fields such as compressive sensing, signal processing, and image processing. To solve this kind of ill-posed problems, a regularization term (i.e.,…
Ensemble learning has been a focal point of machine learning research due to its potential to improve predictive performance. This study revisits the foundational work on ensemble error decomposition, historically confined to…
We propose and analyze a regularization approach for structured prediction problems. We characterize a large class of loss functions that allows to naturally embed structured outputs in a linear space. We exploit this fact to design…
We develop a unifying framework for Bayesian nonparametric regression to study the rates of contraction with respect to the integrated $L_2$-distance without assuming the regression function space to be uniformly bounded. The framework is…
A common challenge in regression is that for many problems, the degrees of freedom required for a high-quality solution also allows for overfitting. Regularization is a class of strategies that seek to restrict the range of possible…
Regression methods are fundamental for scientific and technological applications. However, fitted models can be highly unreliable outside of their training domain, and hence the quantification of their uncertainty is crucial in many of…
Cellwise contamination remains a challenging problem for data scientists, particularly in research fields that require the selection of sparse features. Traditional robust methods may not be feasible nor efficient in dealing with such…
In most practical applications such as recommendation systems, display advertising, and so forth, the collected data often contains missing values and those missing values are generally missing-not-at-random, which deteriorates the…
Concerning bivariate least squares linear regression, the classical approach pursued for functional models in earlier attempts is reviewed using a new formalism in terms of deviation (matrix) traces. Within the framework of classical error…
A deraining network can be interpreted as a conditional generator that aims at removing rain streaks from image. Most existing image deraining methods ignore model errors caused by uncertainty that reduces embedding quality. Unlike existing…
Large-scale linear models are ubiquitous throughout machine learning, with contemporary application as surrogate models for neural network uncertainty quantification; that is, the linearised Laplace method. Alas, the computational cost…
High-dimensional statistical inference deals with models in which the the number of parameters p is comparable to or larger than the sample size n. Since it is usually impossible to obtain consistent procedures unless $p/n\rightarrow0$, a…
The Minimum Description Length (MDL) principle states that the optimal model for a given data set is that which compresses it best. Due to practial limitations the model can be restricted to a class such as linear regression models, which…
Current online learning methods suffer issues such as lower convergence rates and limited capability to select important features compared to their offline counterparts. In this paper, a novel framework for online learning based on running…
Regression, the task of predicting a continuous scalar target y based on some features x is one of the most fundamental tasks in machine learning and statistics. It has been observed and theoretically analyzed that the classical approach,…