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For a large class of regularized models, leave-one-out cross-validation can be efficiently estimated with an approximate leave-one-out formula (ALO). We consider the problem of adjusting hyperparameters so as to optimize ALO. We derive…
We propose a data-analytic method for detecting cellwise outliers. Given a robust covariance matrix, outlying cells (entries) in a row are found by the cellHandler technique which combines lasso regression with a stepwise application of…
We develop methodology for valid inference after variable selection in logistic regression when the responses are partially observed, that is, when one observes a set of error-prone testing outcomes instead of the true values of the…
We consider the least-square linear regression problem with regularization by the $\ell^1$-norm, a problem usually referred to as the Lasso. In this paper, we first present a detailed asymptotic analysis of model consistency of the Lasso in…
In recent decades, multilevel regression and poststratification (MRP) has surged in popularity for population inference. However, the validity of the estimates can depend on details of the model, and there is currently little research on…
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…
Nonparametric methods are widely applicable to statistical inference problems, since they rely on a few modeling assumptions. In this context, the fresh look advocated here permeates benefits from variable selection and compressive…
Model uncertainty is pervasive in real world analysis situations and is an often-neglected issue in applied statistics. However, standard approaches to the research process do not address the inherent uncertainty in model building and,…
Cross-Validation (CV) is the default choice for evaluating the performance of machine learning models. Despite its wide usage, their statistical benefits have remained half-understood, especially in challenging nonparametric regimes. In…
The high-dimensional linear model $y = X \beta^0 + \epsilon$ is considered and the focus is put on the problem of recovering the support $S^0$ of the sparse vector $\beta^0.$ We introduce Lasso-Zero, a new $\ell_1$-based estimator whose…
When selecting a classification algorithm to be applied to a particular problem, one has to simultaneously select the best algorithm for that dataset \emph{and} the best set of hyperparameters for the chosen model. The usual approach is to…
Much theoretical and applied work has been devoted to high-dimensional regression with clean data. However, we often face corrupted data in many applications where missing data and measurement errors cannot be ignored. Loh and Wainwright…
Lasso and other regularization procedures are attractive methods for variable selection, subject to a proper choice of shrinkage parameter. Given a set of potential subsets produced by a regularization algorithm, a consistent model…
We investigate a robust penalized logistic regression algorithm based on a minimum distance criterion. Influential outliers are often associated with the explosion of parameter vector estimates, but in the context of standard logistic…
We consider a problem of linear model selection in the presence of both continuous and categorical predictors. Feasible models consist of subsets of numerical variables and partitions of levels of factors. A new algorithm called delete or…
The tuning parameter selection strategy for penalized estimation is crucial to identify a model that is both interpretable and predictive. However, popular strategies (e.g., minimizing average squared prediction error via cross-validation)…
In this paper, we study problem of estimating a sparse regression vector with correct support in the presence of outlier samples. The inconsistency of lasso-type methods is well known in this scenario. We propose a combinatorial version of…
Many penalized maximum likelihood estimators correspond to posterior mode estimators under specific prior distributions. Appropriateness of a particular class of penalty functions can therefore be interpreted as the appropriateness of a…
We consider the linear regression problem, where the number $p$ of covariates is possibly larger than the number $n$ of observations $(x_{i},y_{i})_{i\leq i \leq n}$, under sparsity assumptions. On the one hand, several methods have been…
Recursive partitioning approaches producing tree-like models are a long standing staple of predictive modeling, in the last decade mostly as ``sub-learners'' within state of the art ensemble methods like Boosting and Random Forest. However,…