Related papers: Discussion: One-step sparse estimates in nonconcav…
We propose sequential Monte Carlo based algorithms for maximum likelihood estimation of the static parameters in hidden Markov models with an intractable likelihood using ideas from approximate Bayesian computation. The static parameter…
The horseshoe prior is known to possess many desirable properties for Bayesian estimation of sparse parameter vectors, yet its density function lacks an analytic form. As such, it is challenging to find a closed-form solution for the…
This paper studies sparse density estimation via $\ell_1$ penalization (SPADES). We focus on estimation in high-dimensional mixture models and nonparametric adaptive density estimation. We show, respectively, that SPADES can recover, with…
Sparse learning is a very important tool for mining useful information and patterns from high dimensional data. Non-convex non-smooth regularized learning problems play essential roles in sparse learning, and have drawn extensive attentions…
Penalized likelihood methods are fundamental to ultra-high dimensional variable selection. How high dimensionality such methods can handle remains largely unknown. In this paper, we show that in the context of generalized linear models,…
In this paper we study nonconvex penalization using Bernstein functions whose first-order derivatives are completely monotone. The Bernstein function can induce a class of nonconvex penalty functions for high-dimensional sparse estimation…
This paper is concerned with the selection and estimation of fixed and random effects in linear mixed effects models. We propose a class of nonconcave penalized profile likelihood methods for selecting and estimating important fixed…
Suppose there are two unknown parameters, each parameter is the solution to an estimating equation, and the estimating equation of one parameter depends on the other parameter. The parameters can be jointly estimated by "stacking" their…
We study the heavy hitters and related sparse recovery problems in the low-failure probability regime. This regime is not well-understood, and has only been studied for non-adaptive schemes. The main previous work is one on sparse recovery…
We propose an algorithm which predicts each subsequent time step relative to the previous timestep of intractable short rate model (when adjusted for drift and overall distribution of previous percentile result) and show that the method…
The rapid growth of online network platforms generates large-scale network data and it poses great challenges for statistical analysis using the spatial autoregression (SAR) model. In this work, we develop a novel distributed estimation and…
Despite its prevalence in statistical datasets, heteroscedasticity (non-constant sample variances) has been largely ignored in the high-dimensional statistics literature. Recently, studies have shown that the Lasso can accommodate…
In a recent work (arXiv:0910.2517), for nonlinear models with sparse underlying linear structures, we studied the error bounds of $\ell_0$-regularized estimation. In this note, we show that $\ell_1$-regularized estimation in some important…
We propose an empirical likelihood ratio test for nonparametric model selection, where the competing models may be nested, nonnested, overlapping, misspecified, or correctly specified. It compares the squared prediction errors of models…
We consider a resampling scheme for parameters estimates in nonlinear regression models. We provide an estimation procedure which recycles, via random weighting, the relevant parameters estimates to construct consistent estimates of the…
Consider the communication-constrained problem of nonparametric function estimation, in which each distributed terminal holds multiple i.i.d. samples. Under certain regularity assumptions, we characterize the minimax optimal rates for all…
Causal models are important tools to understand complex phenomena and predict the outcome of controlled experiments, also known as interventions. In this work, we present statistical rates of estimation for linear cyclic causal models under…
We consider nonconvex constrained optimization problems and propose a new approach to the convergence analysis based on penalty functions. We make use of classical penalty functions in an unconventional way, in that penalty functions only…
This paper focuses on stochastic proximal gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer and convex constraints. To the best of our knowledge we present the first non-asymptotic…
Sparse regression models are increasingly prevalent due to their ease of interpretability and superior out-of-sample performance. However, the exact model of sparse regression with an $\ell_0$ constraint restricting the support of the…