Related papers: Group selection and shrinkage: Structured sparsity…

We study counterfactual regression, which aims to map input features to outcomes under hypothetical scenarios that differ from those observed in the data. This is particularly useful for decision-making when adapting to sudden shifts in…

The parameters of a neural network are naturally organized in groups, some of which might not contribute to its overall performance. To prune out unimportant groups of parameters, we can include some non-differentiable penalty to the…

We present a framework to define a large class of neural networks for which, by construction, training by gradient flow provably reaches arbitrarily low loss when the number of parameters grows. Distinct from the fixed-space global…

Network modeling of high-dimensional time series data is a key learning task due to its widespread use in a number of application areas, including macroeconomics, finance and neuroscience. While the problem of sparse modeling based on…

This paper studies the sparse identification problem of unknown sparse parameter vectors in stochastic dynamic systems. Firstly, a novel sparse identification algorithm is proposed, which can generate sparse estimates based on least squares…

We study the problem of estimating multiple linear regression equations for the purpose of both prediction and variable selection. Following recent work on multi-task learning Argyriou et al. [2008], we assume that the regression vectors…

Balancing predictive power and interpretability has long been a challenging research area, particularly in powerful yet complex models like neural networks, where nonlinearity obstructs direct interpretation. This paper introduces a novel…

We introduce and study the Group Square-Root Lasso (GSRL) method for estimation in high dimensional sparse regression models with group structure. The new estimator minimizes the square root of the residual sum of squares plus a penalty…

Semiparametric regression offers a flexible framework for modeling non-linear relationships between a response and covariates. A prime example are generalized additive models where splines (say) are used to approximate non-linear functional…

We consider estimation in a sparse additive regression model with the design points on a regular lattice. We establish the minimax convergence rates over Sobolev classes and propose a Fourier-based rate-optimal estimator which is adaptive…

We consider semi-supervised binary classification for applications in which data points are naturally grouped (e.g., survey responses grouped by state) and the labeled data is biased (e.g., survey respondents are not representative of the…

Nowadays an increasing amount of data is available and we have to deal with models in high dimension (number of covariates much larger than the sample size). Under sparsity assumption it is reasonable to hope that we can make a good…

Selective inference methods are developed for group lasso estimators for use with a wide class of distributions and loss functions. The method includes the use of exponential family distributions, as well as quasi-likelihood modeling for…

We study the problem of variable selection in convex nonparametric least squares (CNLS). Whereas the least absolute shrinkage and selection operator (Lasso) is a popular technique for least squares, its variable selection performance is…

This paper aims to front with dimensionality reduction in regression setting when the predictors are a mixture of functional variable and high-dimensional vector. A flexible model, combining both sparse linear ideas together with…

Modern technologies are generating ever-increasing amounts of data. Making use of these data requires methods that are both statistically sound and computationally efficient. Typically, the statistical and computational aspects are treated…

Additive regression provides an extension of linear regression by modeling the signal of a response as a sum of functions of covariates of relatively low complexity. We study penalized estimation in high-dimensional nonparametric additive…

While adaptive sensing has provided improved rates of convergence in sparse regression and classification, results in nonparametric regression have so far been restricted to quite specific classes of functions. In this paper, we describe an…

Stacking regressions is an ensemble technique that forms linear combinations of different regression estimators to enhance predictive accuracy. The conventional approach uses cross-validation data to generate predictions from the…

We study the problem of multivariate regression where the data are naturally grouped, and a regression matrix is to be estimated for each group. We propose an approach in which a dictionary of low rank parameter matrices is estimated across…