Related papers: PULasso: High-dimensional variable selection with …
In this paper, we introduce a novel high-dimensional Factor-Adjusted sparse Partially Linear regression Model (FAPLM), to integrate the linear effects of high-dimensional latent factors with the nonparametric effects of low-dimensional…
Let $(Y,X_1,...,X_m)$ be a random vector. It is desired to predict $Y$ based on $(X_1,...,X_m)$. Examples of prediction methods are regression, classification using logistic regression or separating hyperplanes, and so on. We consider the…
Machine learning methods are used to discover complex nonlinear relationships in biological and medical data. However, sophisticated learning models are computationally unfeasible for data with millions of features. Here we introduce the…
Model selection consistency in the high-dimensional regression setting can be achieved only if strong assumptions are fulfilled. We therefore suggest to pursue a different goal, which we call a minimal class of models. The minimal class of…
We study the problem of high-dimensional regression when there may be interacting variables. Approaches using sparsity-inducing penalty functions such as the Lasso can be useful for producing interpretable models. However, when the number…
The pattern of zero entries in the inverse covariance matrix of a multivariate normal distribution corresponds to conditional independence restrictions between variables. Covariance selection aims at estimating those structural zeros from…
Sparse modelling or model selection with categorical data is challenging even for a moderate number of variables, because one parameter is roughly needed to encode one category or level. The Group Lasso is a well known efficient algorithm…
We consider the problem of recovering conditional independence relationships between $p$ jointly distributed Hilbertian random elements given $n$ realizations thereof. We operate in the sparse high-dimensional regime, where $n \ll p$ and no…
The $\ell_1$-penalized method, or the Lasso, has emerged as an important tool for the analysis of large data sets. Many important results have been obtained for the Lasso in linear regression which have led to a deeper understanding of…
Penalized (or regularized) regression, as represented by Lasso and its variants, has become a standard technique for analyzing high-dimensional data when the number of variables substantially exceeds the sample size. The performance of…
The Lasso is one of the most ubiquitous methods for variable selection in high-dimensional linear regression and has been studied extensively under different regimes. In a particular asymptotic setup entailing $n/p\to \text{constant}$, an…
To deal with high-dimensional unlabeled datasets in many areas, principal component analysis (PCA) has become a rising technique for unsupervised feature selection (UFS). However, most existing PCA-based methods only consider the structure…
We consider regression problems where the number of predictors greatly exceeds the number of observations. We propose a method for variable selection that first estimates the regression function, yielding a "pre-conditioned" response…
Detecting influential features in non-linear and/or high-dimensional data is a challenging and increasingly important task in machine learning. Variable selection methods have thus been gaining much attention as well as post-selection…
This thesis responds to the challenges of using a large number, such as thousands, of features in regression and classification problems. There are two situations where such high dimensional features arise. One is when high dimensional…
Latent Gaussian models have a rich history in statistics and machine learning, with applications ranging from factor analysis to compressed sensing to time series analysis. The classical method for maximizing the likelihood of these models…
Penalized likelihood approaches are widely used for high-dimensional regression. Although many methods have been proposed and the associated theory is now well-developed, the relative efficacy of different approaches in finite-sample…
This research deals with the estimation and imputation of missing data in longitudinal models with a Poisson response variable inflated with zeros. A methodology is proposed that is based on the use of maximum likelihood, assuming that data…
Ranking and comparing items is crucial for collecting information about preferences in many areas, from marketing to politics. The Mallows rank model is among the most successful approaches to analyse rank data, but its computational…
Clustering, a fundamental activity in unsupervised learning, is notoriously difficult when the feature space is high-dimensional. Fortunately, in many realistic scenarios, only a handful of features are relevant in distinguishing clusters.…