Related papers: A Note on High Dimensional Linear Regression with …
Considering the flexibility and applicability of Bayesian modeling, in this work we revise the main characteristics of two hierarchical models in a regression setting. We study the full probabilistic structure of the models along with the…
We study the problem of high-dimensional variable selection via some two-step procedures. First we show that given some good initial estimator which is $\ell_{\infty}$-consistent but not necessarily variable selection consistent, we can…
Interactions between pieces of information (entities) play a substantial role in the way an individual acts on them: adoption of a product, the spread of news, strategy choice, etc. However, the underlying interaction mechanisms are often…
Hierarchical Bayesian methods enable information sharing across multiple related regression problems. While standard practice is to model regression parameters (effects) as (1) exchangeable across datasets and (2) correlated to differing…
In this work we address the problem of approximating high-dimensional data with a low-dimensional representation. We make the following contributions. We propose an inverse regression method which exchanges the roles of input and response,…
Large-scale Hierarchical Classification (HC) involves datasets consisting of thousands of classes and millions of training instances with high-dimensional features posing several big data challenges. Feature selection that aims to select…
This paper studies a linear model for multidimensional panel data of three or more dimensions with unobserved interactive fixed-effects. The main estimator uses a Neyman-orthogonal approach, and requires two preliminary steps. First, the…
Predict a new response from a covariate is a challenging task in regression, which raises new question since the era of high-dimensional data. In this paper, we are interested in the inverse regression method from a theoretical viewpoint.…
In the era of big data, analysts usually explore various statistical models or machine learning methods for observed data in order to facilitate scientific discoveries or gain predictive power. Whatever data and fitting procedures are…
We study the problem of treatment effect estimation in randomized experiments with high-dimensional covariate information, and show that essentially any risk-consistent regression adjustment can be used to obtain efficient estimates of the…
Penalized regression methods are an attractive tool for high-dimensional data analysis, but their widespread adoption has been hampered by the difficulty of applying inferential tools. In particular, the question "How reliable is the…
Choice designs for the main effects model, broader main effects model and main effects plus specified interaction effects model are discussed in this paper. Universally optimal choice designs are obtained for all of these models using…
We study principal components regression (PCR) in an asymptotic high-dimensional regression setting, where the number of data points is proportional to the dimension. We derive exact limiting formulas for the estimation and prediction…
A common approach to statistical learning with big-data is to randomly split it among $m$ machines and learn the parameter of interest by averaging the $m$ individual estimates. In this paper, focusing on empirical risk minimization, or…
We collect robust proposals given in the field of regression models with heteroscedastic errors. Our motivation stems from the fact that the practitioner frequently faces the confluence of two phenomena in the context of data analysis:…
One of the central issues of several machine learning applications on real data is the choice of the input features. Ideally, the designer should select only the relevant, non-redundant features to preserve the complete information…
High dimensionality comparable to sample size is common in many statistical problems. We examine covariance matrix estimation in the asymptotic framework that the dimensionality $p$ tends to $\infty$ as the sample size $n$ increases.…
We study the emergence of a giant component in a spatial network where the distribution of the metric distances between the nodes is scale-invariant, and the interaction between the nodes has a long-range power-law behavior. The nodes are…
Achieving seamless, human-like interaction remains a key challenge for full-duplex spoken dialogue models (SDMs). Reinforcement learning (RL) has substantially enhanced text- and vision-language models, while well-designed reward signals…
The issue of opinion sharing and formation has received considerable attention in the academic literature, and a few models have been proposed to study this problem. However, existing models are limited to the interactions among nearest…