Related papers: Sparse Linear Models and Two-Stage Estimation in H…
In this work, we obtain sufficient conditions for the "stability" of our recently proposed algorithms, Least Squares Compressive Sensing residual (LS-CS) and modified-CS, for recursively reconstructing sparse signal sequences from noisy…
We show that two polynomial time methods, a Lasso estimator with adaptively chosen tuning parameter and a Slope estimator, adaptively achieve the exact minimax prediction and $\ell_2$ estimation rate $(s/n)\log (p/s)$ in high-dimensional…
Recently, deep neural networks have been found to nearly interpolate training data but still generalize well in various applications. To help understand such a phenomenon, it has been of interest to analyze the ridge estimator and its…
This article is motivated by the objective of providing a new analytically tractable and fully frequentist framework to characterize and implement regression trees while also allowing a multivariate (potentially high dimensional) response.…
This paper studies the distributed adaptiveestimation problems for stochastic large regression modelswith an infinite number of parameters. By constructing a re-cursive local cost function, we propose a novel distributedrecursive least…
The least absolute shrinkage and selection operator (Lasso) is a popular method for high-dimensional statistics. However, it is known that the Lasso often has estimation bias and prediction error. To address such disadvantages, many…
We examine the rate of convergence of the Lasso estimator of lower dimensional components of the high-dimensional parameter. Under bounds on the $\ell_1$-norm on the worst possible sub-direction these rates are of order $\sqrt {|J| \log p /…
This paper discusses asymptotic distributions of various estimators of the underlying parameters in some regression models with long memory (LM) Gaussian design and nonparametric heteroscedastic LM moving average errors. In the simple…
In this paper, we present several estimators of the diagonal elements of the inverse of the covariance matrix, called precision matrix, of a sample of iid random vectors. The focus is on high dimensional vectors having a sparse precision…
Supervised learning by extreme learning machines resp. neural networks with random weights is studied under a non-stationary spatial-temporal sampling design which especially addresses settings where an autonomous object moving in a…
Estimating linear, mean-square continuous functionals is a pivotal challenge in statistics. In high-dimensional contexts, this estimation is often performed under the assumption of exact model sparsity, meaning that only a small number of…
We study sparse principal component analysis for high dimensional vector autoregressive time series under a doubly asymptotic framework, which allows the dimension $d$ to scale with the series length $T$. We treat the transition matrix of…
This paper studies the statistical properties of the group Lasso estimator for high dimensional sparse quantile regression models where the number of explanatory variables (or the number of groups of explanatory variables) is possibly much…
An important problem in space-time adaptive detection is the estimation of the large p-by-p interference covariance matrix from training signals. When the number of training signals n is greater than 2p, existing estimators are generally…
We consider the problem of estimating the parameters of a Gaussian or binary distribution in such a way that the resulting undirected graphical model is sparse. Our approach is to solve a maximum likelihood problem with an added l_1-norm…
We study various constraints and conditions on the true coefficient vector and on the design matrix to establish non-asymptotic oracle inequalities for the prediction error, estimation accuracy and variable selection for the Lasso estimator…
In this paper, we apply shrinkage strategies to estimate regression coefficients efficiently for the high-dimensional multiple regression model, where the number of samples is smaller than the number of predictors. We assume in the sparse…
Two-stage hierarchical models have been widely used in small area estimation to produce indirect estimates of areal means. When the areas are treated exchangeably and the model parameters are assumed to be the same over all areas, we might…
Existing theory of momentum assumes that gradients arrive at every parameter at a roughly constant rate, an assumption violated in practice by heavy-tailed data distributions and modern architectures. We theoretically analyze the dynamics…
High-dimensional prediction typically comprises two steps: variable selection and subsequent least-squares refitting on the selected variables. However, the standard variable selection procedures, such as the lasso, hinge on tuning…