Related papers: Group Model Selection Using Marginal Correlations:…
We present a new optimization method for the group selection problem in linear regression. In this problem, predictors are assumed to have a natural group structure and the goal is to select a small set of groups that best fits the…
The effort to understand network systems in increasing detail has resulted in a diversity of methods designed to extract their large-scale structure from data. Unfortunately, many of these methods yield diverging descriptions of the same…
When multitudes of features can plausibly be associated with a response, both privacy considerations and model parsimony suggest grouping them to increase the predictive power of a regression model. Specifically, the identification of…
In regression problems where covariates can be naturally grouped, the group Lasso is an attractive method for variable selection since it respects the grouping structure in the data. We study the selection and estimation properties of the…
Grouping structures arise naturally in many statistical modeling problems. Several methods have been proposed for variable selection that respect grouping structure in variables. Examples include the group LASSO and several concave group…
Motivation: Gene selection has become a common task in most gene expression studies. The objective of such research is often to identify the smallest possible set of genes that can still achieve good predictive performance. The problem of…
In many application areas, predictive models are used to support or make important decisions. There is increasing awareness that these models may contain spurious or otherwise undesirable correlations. Such correlations may arise from a…
Group-based sparsity models are proven instrumental in linear regression problems for recovering signals from much fewer measurements than standard compressive sensing. The main promise of these models is the recovery of "interpretable"…
The estimation problem in a high regression model with structured sparsity is investigated. An algorithm using a two steps block thresholding procedure called GR-LOL is provided. Convergence rates are produced: they depend on simple…
Learning invariant representations is an important requirement when training machine learning models that are driven by spurious correlations in the datasets. These spurious correlations, between input samples and the target labels, wrongly…
Background: Selecting feature genes to predict phenotypes is one of the typical tasks in analyzing genomics data. Though many general-purpose algorithms were developed for prediction, dealing with highly correlated genes in the prediction…
Generative models typically sample outputs independently, and recent inference-time guidance and scaling algorithms focus on improving the quality of individual samples. However, in real-world applications, users are often presented with a…
In clinical trials and other applications, we often see regions of the feature space that appear to exhibit interesting behaviour, but it is unclear whether these observed phenomena are reflected at the population level. Focusing on a…
The paper considers variable selection in linear regression models where the number of covariates is possibly much larger than the number of observations. High dimensionality of the data brings in many complications, such as (possibly…
Variable selection for models including interactions between explanatory variables often needs to obey certain hierarchical constraints. The weak or strong structural hierarchy requires that the existence of an interaction term implies at…
Important objectives in cancer research are the prediction of a patient's risk based on molecular measurements such as gene expression data and the identification of new prognostic biomarkers (e.g. genes). In clinical practice, this is…
High-dimensional group inference is an essential part of statistical methods for analysing complex data sets, including hierarchical testing, tests of interaction, detection of heterogeneous treatment effects and inference for local…
Traditionally, the least squares regression is mainly concerned with studying the effects of individual predictor variables, but strongly correlated variables generate multicollinearity which makes it difficult to study their effects.…
Gaussian graphical model is a graphical representation of the dependence structure for a Gaussian random vector. It is recognized as a powerful tool in different applied fields such as bioinformatics, error-control codes, speech language,…
It is in general challenging to provide confidence intervals for individual variables in high-dimensional regression without making strict or unverifiable assumptions on the design matrix. We show here that a "group-bound" confidence…