Related papers: A globally convergent algorithm for lasso-penalize…
A regularized minimization model with $l_1$-norm penalty (RP) is introduced for training the autoencoders that belong to a class of two-layer neural networks. We show that the RP can act as an exact penalty model which shares the same…
We propose a shrinkage procedure for simultaneous variable selection and estimation in generalized linear models (GLMs) with an explicit predictive motivation. The procedure estimates the coefficients by minimizing the Kullback-Leibler…
We consider a high dimensional binary classification problem and construct a classification procedure by minimizing the empirical misclassification risk with a penalty on the number of selected features. We derive non-asymptotic probability…
In this paper, we study norm-based regularization methods for neural networks. We compare existing penalization approaches and introduce two regularization strategies that extend classical ridge- and lasso-type penalties to neural network…
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…
Variable (feature, gene, model, which we use interchangeably) selections for regression with high-dimensional BIGDATA have found many applications in bioinformatics, computational biology, image processing, and engineering. One appealing…
We study the complexity of the entire regularization path for least squares regression with 1-norm penalty, known as the Lasso. Every regression parameter in the Lasso changes linearly as a function of the regularization value. The number…
A multiple interval-valued linear regression model considering all the cross-relationships between the mids and spreads of the intervals has been introduced recently. A least-squares estimation of the regression parameters has been carried…
This work is motivated by analyses of longitudinal data collected from participants in the Quebec Longitudinal Study of Child Development (QLSCD) and the Quebec Newborn Twin Study (QNTS) to identify important genetic predictors for…
To conduct regression analysis for data contaminated with outliers, many approaches have been proposed for simultaneous outlier detection and robust regression, so is the approach proposed in this manuscript. This new approach is called…
We present a new approach to solve the sparse approximation or best subset selection problem, namely find a $k$-sparse vector ${\bf x}\in\mathbb{R}^d$ that minimizes the $\ell_2$ residual $\lVert A{\bf x}-{\bf y} \rVert_2$. We consider a…
Aligning generative models with human preference via RLHF typically suffers from overoptimization, where an imperfectly learned reward model can misguide the generative model to output undesired responses. We investigate this problem in a…
Standard likelihood penalties to learn Gaussian graphical models are based on regularising the off-diagonal entries of the precision matrix. Such methods, and their Bayesian counterparts, are not invariant to scalar multiplication of the…
We propose an approach for fitting linear regression models that splits the set of covariates into groups. The optimal split of the variables into groups and the regularized estimation of the regression coefficients are performed by…
Motivated by penalized likelihood maximization in complex models, we study optimization problems where neither the function to optimize nor its gradient have an explicit expression, but its gradient can be approximated by a Monte Carlo…
We consider the problem of automatic variable selection in a linear model with asymmetric or heavy-tailed errors when the number of explanatory variables diverges with the sample size. For this high-dimensional model, the penalized least…
We propose a new randomized algorithm for solving convex optimization problems that have a large number of constraints (with high probability). Existing methods like interior-point or Newton-type algorithms are hard to apply to such…
We propose a novel model selection algorithm based on a penalized maximum likelihood estimator (PMLE) for functional hidden dynamic geostatistical models (f-HDGM). These models employ a classic mixed-effect regression structure with…
In this paper, we study a popular method for inference of the Bradley-Terry model parameters, namely the MM algorithm, for maximum likelihood estimation and maximum a posteriori probability estimation. This class of models includes the…
We propose a penalized likelihood method to fit the linear discriminant analysis model when the predictor is matrix valued. We simultaneously estimate the means and the precision matrix, which we assume has a Kronecker product…