Related papers: Topological Techniques in Model Selection
Multitask learning can be effective when features useful in one task are also useful for other tasks, and the group lasso is a standard method for selecting a common subset of features. In this paper, we are interested in a less restrictive…
Leading methods for support recovery in high-dimensional regression, such as Lasso, have been well-studied and their limitations in the context of correlated design have been characterized with precise incoherence conditions. In this work,…
The lasso and related sparsity inducing algorithms have been the target of substantial theoretical and applied research. Correspondingly, many results are known about their behavior for a fixed or optimally chosen tuning parameter specified…
Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and…
Nonconvex penalty methods for sparse modeling in linear regression have been a topic of fervent interest in recent years. Herein, we study a family of nonconvex penalty functions that we call the trimmed Lasso and that offers exact control…
The moment-sum of squares hierarchy by Lasserre has become an established technique for solving polynomial optimization problems. It provides a monotonically increasing series of tight bounds, but has well-known scalability limitations. For…
Categorical predictors are omnipresent in everyday regression practice: in fact, most regression data involve some categorical predictors, and this tendency is increasing in modern applications with more complex structures and larger data…
Mixture models are becoming a popular tool for the clustering and classification of high-dimensional data. In such high dimensional applications, model selection is problematic. The Bayesian information criterion, which is popular in lower…
The Lasso (Least Absolute Shrinkage and Selection Operator) has been a popular technique for simultaneous linear regression estimation and variable selection. In this paper, we propose a new novel approach for robust Lasso that follows the…
We compare alternative computing strategies for solving the constrained lasso problem. As its name suggests, the constrained lasso extends the widely-used lasso to handle linear constraints, which allow the user to incorporate prior…
Statistical power is often a concern for clustered RCTs due to variance inflation from design effects and the high cost of adding study clusters (such as hospitals, schools, or communities). While covariate pre-specification is the…
The automated discovery of constitutive models from data has recently emerged as a promising alternative to the traditional model calibration paradigm. In this work, we present a fully automated framework for constitutive model discovery…
We study the estimation capacity of the generalized Lasso, i.e., least squares minimization combined with a (convex) structural constraint. While Lasso-type estimators were originally designed for noisy linear regression problems, it has…
This paper studies high-dimensional regression models with lasso when data is sampled under multi-way clustering. First, we establish convergence rates for the lasso and post-lasso estimators. Second, we propose a novel inference method…
We consider the problem of model selection and estimation in sparse high dimensional linear regression models with strongly correlated variables. First, we study the theoretical properties of the dual Lasso solution, and we show that joint…
Performance of regularized least-squares estimation in noisy compressed sensing is analyzed in the limit when the dimensions of the measurement matrix grow large. The sensing matrix is considered to be from a class of random ensembles that…
Penalized regression methods, most notably the lasso, are a popular approach to analyzing high-dimensional data. An attractive property of the lasso is that it naturally performs variable selection. An important area of concern, however, is…
Ordinal data are quite common in applied statistics. Although some model selection and regularization techniques for categorical predictors and ordinal response models have been developed over the past few years, less work has been done…
Transfer learning techniques aim to leverage information from multiple related datasets to enhance prediction quality against a target dataset. Such methods have been adopted in the context of high-dimensional sparse regression, and some…
In life sciences, the experts generally use empirical knowledge to recode variables, choose interactions and perform selection by classical approach. The aim of this work is to perform automatic learning algorithm for variables selection…