Related papers: Safe Screening Rules for Generalized Double Sparsi…
We present safe active incremental feature selection~(SAIF) to scale up the computation of LASSO solutions. SAIF does not require a solution from a heavier penalty parameter as in sequential screening or updating the full model for each…
In high-dimensional linear regression, the goal pursued here is to estimate an unknown regression function using linear combinations of a suitable set of covariates. One of the key assumptions for the success of any statistical procedure in…
Sparsity-inducing penalties are useful tools for variable selection and they are also effective for regression settings where the data are functions. We consider the problem of selecting not only variables but also decision boundaries in…
Clustering high-dimensional data often requires some form of dimensionality reduction, where clustered variables are separated from "noise-looking" variables. We cast this problem as finding a low-dimensional projection of the data which is…
Many regression and classification procedures fit a parameterized function $f(x;w)$ of predictor variables $x$ to data $\{x_{i},y_{i}\}_1^N$ based on some loss criterion $L(y,f)$. Often, regularization is applied to improve accuracy by…
In machine learning, training data often capture the behaviour of multiple subgroups of some underlying human population. This behaviour can often be modelled as observations of an unknown dynamical system with an unobserved state. When the…
Many conventional statistical procedures are extremely sensitive to seemingly minor deviations from modeling assumptions. This problem is exacerbated in modern high-dimensional settings, where the problem dimension can grow with and…
The lasso is a popular method to induce shrinkage and sparsity in the solution vector (coefficients) of regression problems, particularly when there are many predictors relative to the number of observations. Solving the lasso in this…
This paper provides a statistical analysis of high-dimensional batch Reinforcement Learning (RL) using sparse linear function approximation. When there is a large number of candidate features, our result sheds light on the fact that…
Submodular functions are discrete analogs of convex functions, which have applications in various fields, including machine learning and computer vision. However, in large-scale applications, solving Submodular Function Minimization (SFM)…
In this paper, we propose a way to combine two acceleration techniques for the $\ell\_{1}$-regularized least squares problem: safe screening tests, which allow to eliminate useless dictionary atoms; and the use of fast structured…
Sure screening technique has been considered as a powerful tool to handle the ultrahigh dimensional variable selection problems, where the dimensionality p and the sample size n can satisfy the NP dimensionality log p=O(n^a) for some a>0…
A new sparse semiparametric model is proposed, which incorporates the influence of two functional random variables in a scalar response in a flexible and interpretable manner. One of the functional covariates is included through a…
Regularization is often used in high-dimensional regression settings to generate a sparse model, which can save tremendous computing resources and identify predictors that are most strongly associated with the response. When the predictors…
In genomic analysis, biomarker discovery, image recognition, and other systems involving machine learning, input variables can often be organized into different groups by their source or semantic category. Eliminating some groups of…
Typical dimension reduction techniques for nonoverlapping sparse optimization involve screening or sieving strategies based on a dual certificate derived from the first-order optimality condition, approximating the gradients or exploiting…
Spreading the information over all coefficients of a representation is a desirable property in many applications such as digital communication or machine learning. This so-called antisparse representation can be obtained by solving a convex…
The goal of predictive sparse coding is to learn a representation of examples as sparse linear combinations of elements from a dictionary, such that a learned hypothesis linear in the new representation performs well on a predictive task.…
To find efficient screening methods for high dimensional linear regression models, this paper studies the relationship between model fitting and screening performance. Under a sparsity assumption, we show that a subset that includes the…
We examine the linear regression problem in a challenging high-dimensional setting with correlated predictors where the vector of coefficients can vary from sparse to dense. In this setting, we propose a combination of probabilistic…