Related papers: Sparsity considerations for dependent observations
In the context of undirected Gaussian graphical models, we introduce three estimators based on elastic net penalty for the underlying dependence graph. Our goal is to estimate the sparse precision matrix, from which to retrieve both the…
A reciprocal LASSO (rLASSO) regularization employs a decreasing penalty function as opposed to conventional penalization approaches that use increasing penalties on the coefficients, leading to stronger parsimony and superior model…
Due to its low computational cost, Lasso is an attractive regularization method for high-dimensional statistical settings. In this paper, we consider multivariate counting processes depending on an unknown function parameter to be estimated…
Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. While naturally cast as a combinatorial optimization problem, variable or feature selection admits a convex relaxation through the…
We consider a general statistical estimation problem wherein binary labels across different observations are not independent conditioned on their feature vectors, but dependent, capturing settings where e.g. these observations are collected…
We tackle the problem of recovering an unknown signal observed in an ill-posed inverse problem framework. More precisely, we study a procedure commonly used in numerical analysis or image deblurring: minimizing an empirical loss function…
In the context of multiple regression model, suppose that the vector parameter of interest \beta is subjected to lie in the subspace hypothesis H\beta = h, where this restriction is based on either additional information or prior knowledge.…
Penalized likelihood approaches are widely used for high-dimensional regression. Although many methods have been proposed and the associated theory is now well-developed, the relative efficacy of different approaches in finite-sample…
Many recent developments in the high-dimensional statistical time series literature have centered around time-dependent applications that can be adapted to regularized least squares. Of particular interest is the lasso, which both serves to…
This paper proposes a theory for $\ell_1$-norm penalized high-dimensional $M$-estimators, with nonconvex risk and unrestricted domain. Under high-level conditions, the estimators are shown to attain the rate of convergence…
We introduce the localized Lasso, which is suited for learning models that are both interpretable and have a high predictive power in problems with high dimensionality $d$ and small sample size $n$. More specifically, we consider a function…
For data with high-dimensional covariates but small to moderate sample sizes, the analysis of single datasets often generates unsatisfactory results. The integrative analysis of multiple independent datasets provides an effective way of…
We propose a novel $\ell_1+\ell_2$-penalty, which we refer to as the Generalized Elastic Net, for regression problems where the feature vectors are indexed by vertices of a given graph and the true signal is believed to be smooth or…
The paper introduces a new estimation method for the standard linear regression model. The procedure is not driven by the optimisation of any objective function rather, it is a simple weighted average of slopes from observation pairs. The…
For high-dimensional sparse parameter estimation problems, Log-Sum Penalty (LSP) regularization effectively reduces the sampling sizes in practice. However, it still lacks theoretical analysis to support the experience from previous…
Gaussian graphical models are recently used in economics to obtain networks of dependence among agents. A widely-used estimator is the Graphical Lasso (GLASSO), which amounts to a maximum likelihood estimation regularized using the…
This paper carries out sparse-penalized deep neural networks predictors for learning weakly dependent processes, with a broad class of loss functions. We deal with a general framework that includes, regression estimation, classification,…
We consider high-dimensional generalized linear models with Lipschitz loss functions, and prove a nonasymptotic oracle inequality for the empirical risk minimizer with Lasso penalty. The penalty is based on the coefficients in the linear…
Sparse regularization such as $\ell_1$ regularization is a quite powerful and widely used strategy for high dimensional learning problems. The effectiveness of sparse regularization has been supported practically and theoretically by…
Causal effect estimation is a critical task in statistical learning that aims to find the causal effect on subjects by identifying causal links between a number of predictor (or, explanatory) variables and the outcome of a treatment. In a…