Related papers: A Unified Analysis of Multi-task Functional Linear…
Spatiotemporal matrix-valued data arise frequently in modern applications, yet performing effective regression analysis remains challenging due to complex, dimension-specific dependencies. In this work, we propose a regularized framework…
We study a regression problem on a compact manifold M. In order to take advantage of the underlying geometry and topology of the data, the regression task is performed on the basis of the first several eigenfunctions of the Laplace-Beltrami…
We propose a new class of nonconvex penalty functions, based on data depth functions, for multitask sparse penalized regression. These penalties quantify the relative position of rows of the coefficient matrix from a fixed distribution…
Multi-task learning has shown to significantly enhance the performance of multiple related learning tasks in a variety of situations. We present the fused logistic regression, a sparse multi-task learning approach for binary classification.…
Gaussian graphical regression is a powerful means that regresses the precision matrix of a Gaussian graphical model on covariates, permitting the numbers of the response variables and covariates to far exceed the sample size. Model fitting…
Within the statistical and machine learning literature, regularization techniques are often used to construct sparse (predictive) models. Most regularization strategies only work for data where all predictors are treated identically, such…
We propose a new methodology for parameterized constrained robust optimization, an important class of optimization problems under uncertainty, based on learning with a self-supervised penalty-based loss function. Whereas supervised learning…
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,…
The linear regression model cannot be fitted to high-dimensional data, as the high-dimensionality brings about empirical non-identifiability. Penalized regression overcomes this non-identifiability by augmentation of the loss function by a…
In this paper we study the kernel multiple ridge regression framework, which we refer to as multi-task regression, using penalization techniques. The theoretical analysis of this problem shows that the key element appearing for an optimal…
The paper deals with generalized functional regression. The aim is to estimate the influence of covariates on observations, drawn from an exponential distribution. The link considered has a semiparametric expression: if we are interested in…
Multi-task learning is a framework that enforces different learning tasks to share their knowledge to improve their generalization performance. It is a hot and active domain that strives to handle several core issues; particularly, which…
The function-on-function regression model is fundamental for analyzing relationships between functional covariates and responses. However, most existing function-on-function regression methodologies assume independence between observations,…
We study a functional linear regression model that deals with functional responses and allows for both functional covariates and high-dimensional vector covariates. The proposed model is flexible and nests several functional regression…
This paper develops a general theory on rates of convergence of penalized spline estimators for function estimation when the likelihood functional is concave in candidate functions, where the likelihood is interpreted in a broad sense that…
We study settings where gradient penalties are used alongside risk minimization with the goal of obtaining predictors satisfying different notions of monotonicity. Specifically, we present two sets of contributions. In the first part of the…
We sharply characterize the performance of different penalization schemes for the problem of selecting the relevant variables in the multi-task setting. Previous work focuses on the regression problem where conditions on the design matrix…
In this paper we consider a problem known as multi-task learning, consisting of fitting a set of classifier or regression functions intended for solving different tasks. In our novel formulation, we couple the parameters of these functions,…
While matrix variate regression models have been studied in many existing works, classical statistical and computational methods for the analysis of the regression coefficient estimation are highly affected by high dimensional and noisy…
Probabilistic models must be well calibrated to support reliable decision-making. While calibration in single-output regression is well studied, defining and achieving multivariate calibration in multi-output regression remains considerably…