Related papers: Lasso regularization for mixture experiments with …
Among the most popular variable selection procedures in high-dimensional regression, Lasso provides a solution path to rank the variables and determines a cut-off position on the path to select variables and estimate coefficients. In this…
Bayesian optimization has been challenged by datasets with large-scale, high-dimensional, and non-stationary characteristics, which are common in real-world scenarios. Recent works attempt to handle such input by applying neural networks…
We introduce a novel class of Bayesian mixtures for normal linear regression models which incorporates a further Gaussian random component for the distribution of the predictor variables. The proposed cluster-weighted model aims to…
These notes aim at clarifying different strategies to perform linear regression from given dataset. Methods like the weighted and ordinary least squares, ridge regression or LASSO are proposed in the literature. The present article is my…
In linear models it is common to have situations where several regression coefficients are zero. In these situations a common tool to perform regression is a variable selection operator. One of the most common such operators is the LASSO…
We introduce the localized Lasso, which is suited for learning models that are both interpretable and have a high predictive power in problems with high dimensionality $d$ and small sample size $n$. More specifically, we consider a function…
Additive or multiplicative stationary noise recently became an important issue in applied fields such as microscopy or satellite imaging. Relatively few works address the design of dedicated denoising methods compared to the usual white…
Gaussian processes are a flexible Bayesian nonparametric modelling approach that has been widely applied but poses computational challenges. To address the poor scaling of exact inference methods, approximation methods based on sparse…
Regularized linear models, such as Lasso, have attracted great attention in statistical learning and data science. However, there is sporadic work on constructing efficient data collection for regularized linear models. In this work, we…
Variable selection is one of the most important tasks in statistics and machine learning. To incorporate more prior information about the regression coefficients, the constrained Lasso model has been proposed in the literature. In this…
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…
Relevant methods of variable selection have been proposed in model-based clustering and classification. These methods are making use of backward or forward procedures to define the roles of the variables. Unfortunately, these stepwise…
In this work, we investigate data fitting problems with random noises. A randomized progressive iterative regularization method is proposed. It works well for large-scale matrix computations and converges in expectation to the least-squares…
Mixtures-of-Experts models and their maximum likelihood estimation (MLE) via the EM algorithm have been thoroughly studied in the statistics and machine learning literature. They are subject of a growing investigation in the context of…
In this note, we propose to use sparse methods (e.g. LASSO, Post-LASSO, sqrt-LASSO, and Post-sqrt-LASSO) to form first-stage predictions and estimate optimal instruments in linear instrumental variables (IV) models with many instruments in…
Using Kalman techniques, it is possible to perform optimal estimation in linear Gaussian state-space models. We address here the case where the noise probability density functions are of unknown functional form. A flexible Bayesian…
We study the problem of variable selection in convex nonparametric least squares (CNLS). Whereas the least absolute shrinkage and selection operator (Lasso) is a popular technique for least squares, its variable selection performance is…
Large-scale empirical data, the sample size and the dimension are high, often exhibit various characteristics. For example, the noise term follows unknown distributions or the model is very sparse that the number of critical variables is…
It is well known that the Lasso can be interpreted as a Bayesian posterior mode estimate with a Laplacian prior. Obtaining samples from the full posterior distribution, the Bayesian Lasso, confers major advantages in performance as compared…
This article presents a re-structuring of spatial econometric models in a linear mixed model framework. To that end, it proposes low rank spatial econometric models that are robust to the existence of noise (i.e., measurement error), and…