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The intersection set of Bayesian and nonparametric statistics was almost empty until about 1973, but now is growing at a healthy rate. This chapter, for the {\it Highly Structured Stochastic Systems} book (Oxford University Press, 2003)…
This paper introduces a novel approach to statistics and data analysis, departing from the conventional assumption of data residing in Euclidean space to consider a Riemannian Manifold. The challenge lies in the absence of vector space…
This paper proposes a new paradigm and computational framework for identification of correspondences between sub-structures of distinct composite systems. For this, we define and investigate a variant of traditional data clustering, termed…
Data-driven methods play an increasingly important role in discovering geometric, structural, and semantic relationships between 3D shapes in collections, and applying this analysis to support intelligent modeling, editing, and…
A response to a letter to the editor by Schilling regarding Bartroff, Lorden, and Wang ("Optimal and fast confidence intervals for hypergeometric successes" 2022, arXiv:2109.05624)
Most real systems consist of a large number of interacting, multi-typed components, while most contemporary researches model them as homogeneous networks, without distinguishing different types of objects and links in the networks.…
This is a review of the book "Mixed Effects Models and Extensions in Ecology with R" by Zuur, Ieno, Walker, Saveliev and Smith (2009, Springer). I was asked to review this book for The American Statistician in 2010. After I wrote the…
Graphical models are commonly used to represent conditional dependence relationships between variables. There are multiple methods available for exploring them from high-dimensional data, but almost all of them rely on the assumption that…
Persistent Homology is a powerful tool in Topological Data Analysis (TDA) to capture topological properties of data succinctly at different spatial resolutions. For graphical data, shape, and structure of the neighborhood of individual data…
Since the introduction of network psychometrics, several connections to statistical models in "classical" psychometrics (i.e., IRT, SEM, GLM) as well as to approaches from other research fields have been established. In this paper, these…
Academic citation graphs represent citation relationships between publications across the full range of academic fields. Top cited papers typically reveal future trends in their corresponding domains which is of importance to both…
Big data features not only large volumes of data but also data with complicated structures. Complexity imposes unique challenges in big data analytics. Meeker and Hong (2014, Quality Engineering, pp. 102-116) provided an extensive…
This article carries out a large dimensional analysis of standard regularized discriminant analysis classifiers designed on the assumption that data arise from a Gaussian mixture model with different means and covariances. The analysis…
Performing machine learning on structured data is complicated by the fact that such data does not have vectorial form. Therefore, multiple approaches have emerged to construct vectorial representations of structured data, from kernel and…
Information visualization is essential in making sense out of large data sets. Often, high-dimensional data are visualized as a collection of points in 2-dimensional space through dimensionality reduction techniques. However, these…
In this paper, we analyze the nature and distribution of structured data on the Web. Web-scale information extraction, or the problem of creating structured tables using extraction from the entire web, is gathering lots of research…
In the evolving domains of Machine Learning and Data Analytics, existing dataset characterization methods such as statistical, structural, and model-based analyses often fail to deliver the deep understanding and insights essential for…
We carry out a thorough bibliometric analysis of recent publications in mathematics based on the database Web of Science. The individual relations between various features and the citations are provided, and the importance of the features…
This is the rejoinder for discussion of "Multinomial Inverse Regression for Text Analysis", Journal of the American Statistical Association 108, 2013.
New insights into the combinatorial structure of the Mandelbrot set are given by `Correspondence' and `Translation' Principles both conjectured and partially proved by E. Lau and D. Schleicher. We provide complete proofs of these principles…