Related papers: Foundational principles for large scale inference:…
In this paper, we study inference for high-dimensional data characterized by small sample sizes relative to the dimension of the data. In particular, we provide an infinite-dimensional framework to study statistical models that involve…
Many applications benefit from theory relevant to the identification of variables having large correlations or partial correlations in high dimension. Recently there has been progress in the ultra-high dimensional setting when the sample…
Traditional statistical inference considers relatively small data sets and the corresponding theoretical analysis focuses on the asymptotic behavior of a statistical estimator when the number of samples approaches infinity. However, many…
In this paper, we present a novel and effective inference approach to conduct both finite- and large-sample inference for high-dimensional linear regression models. This approach is developed under the so-called repro samples framework, in…
This article presents a novel, general, and effective simulation-inspired approach, called {\it repro samples method}, to conduct statistical inference. The approach studies the performance of artificial samples, referred to as {\it repro…
To model modern large-scale datasets, we need efficient algorithms to infer a set of $P$ unknown model parameters from $N$ noisy measurements. What are fundamental limits on the accuracy of parameter inference, given finite signal-to-noise…
Graphical models have become a very popular tool for representing dependencies within a large set of variables and are key for representing causal structures. We provide results for uniform inference on high-dimensional graphical models…
This chapter presents key concepts and theoretical results for analyzing estimation and inference in high-dimensional models. High-dimensional models are characterized by having a number of unknown parameters that is not vanishingly small…
Discovering valuable insights from data through meaningful associations is a crucial task. However, it becomes challenging when trying to identify representative patterns in quantitative databases, especially with large datasets, as…
In this work, we consider causal inference in various high-dimensional treatment settings, including for single multi-valued treatments and vector treatments with binary or continuous components, when the number of treatments can be…
In real-world data, information is stored in extremely large feature vectors. These variables are typically correlated due to complex interactions involving many features simultaneously. Such correlations qualitatively correspond to…
Quantile regression has been successfully used to study heterogeneous and heavy-tailed data. Varying-coefficient models are frequently used to capture changes in the effect of input variables on the response as a function of an index or…
This article is due to appear in the Handbook of Statistics, Vol. 43, Elsevier/North-Holland, Amsterdam, edited by Arni S. R. Srinivasa Rao and C. R. Rao. In modern day analytics, there is ever growing need to develop statistical models to…
Considering the increasing size of available data, the need for statistical methods that control the finite sample bias is growing. This is mainly due to the frequent settings where the number of variables is large and allowed to increase…
The abundance of models of complex networks and the current insufficient validation standards make it difficult to judge which models are strongly supported by data and which are not. We focus here on likelihood maximization methods for…
We propose a robust inferential procedure for assessing uncertainties of parameter estimation in high-dimensional linear models, where the dimension $p$ can grow exponentially fast with the sample size $n$. Our method combines the…
The increased availability of massive data sets provides a unique opportunity to discover subtle patterns in their distributions, but also imposes overwhelming computational challenges. To fully utilize the information contained in big…
The identification of the dependent components in multiple data sets is a fundamental problem in many practical applications. The challenge in these applications is that often the data sets are high-dimensional with few observations or…
Network datasets appear across a wide range of scientific fields, including biology, physics, and the social sciences. To enable data-driven discoveries from these networks, statistical inference techniques like estimation and hypothesis…
Informatics and technological advancements have triggered generation of huge volume of data with varied complexity in its management and analysis. Big Data analytics is the practice of revealing hidden aspects of such data and making…