Related papers: Geometric Data Analysis, From Correspondence Analy…
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…
This article critically assesses the utility of the classical statistical technique of Canonical Correlation Analysis (CCA) for studying spatial associations and proposes a new approach to enhance it. Unlike bivariate correlation analysis,…
A structural genetic model incorporating a modern understanding of the genome and common practice in genome-wide association studies is derived mathematically. The model shows the Haldane map distance as a direct consequence of the…
The paper by Alfons, Croux and Gelper (2013), Sparse least trimmed squares regression for analyzing high-dimensional large data sets, considered a combination of least trimmed squares (LTS) and lasso penalty for robust and sparse…
In this paper, we provide an overview of the research conducted in the context of structural systems since the latest survey by Dion et al. in 2003. We systematically consider all the papers that cite this survey as well as the seminal work…
Despite of various similar features, Functional Data Analysis and High-Dimensional Data Analysis are two major fields in Statistics that grew up recently almost independently one from each other. The aim of this paper is to propose a survey…
We give a corrected version of Corollary 3.33 in: H. Flenner, S. Kaliman, and M. Zaidenberg, Birational transformations of weighted graphs. Affine algebraic geometry. Osaka Univ. Press, 2007, 107-147.
We introduce and study methods for inferring and learning from correspondences among neurons. The approach enables alignment of data from distinct multiunit studies of nervous systems. We show that the methods for inferring correspondences…
Bases, mappings, projections and metrics, natural for Neural network training, are introduced. Graph-theoretical interpretation is offered. Non-Gaussianity naturally emerges, even in relatively simple datasets. Training statistics,…
We examine data-processing of Markov chains through the lens of information geometry. We first establish a theory of congruent Markov morphisms within the framework of stochastic matrices. Specifically, we introduce and justify the concept…
Discussion of "Treelets--An adaptive multi-Scale basis for sparse unordered data" [arXiv:0707.0481]
Discussion on ``Regression by Composition'' by Farewell, Daniel, Stensrud, and Huitfeldt
A graphical model is a statistical model that is associated to a graph whose nodes correspond to variables of interest. The edges of the graph reflect allowed conditional dependencies among the variables. Graphical models admit…
The development of theories and techniques for big data analytics offers tremendous flexibility for investigating large-scale events and patterns that emerge over space and time. In this research, we utilize a unique open-access dataset…
An informal introduction to some new geometric partial differential equations motivated by string theories is provided. Some of these equations are also interesting from the point of view of non-K\"ahler geometry and the theory of…
In this paper, we explore the use of the diffusion geometry framework for the fusion of geometric and photometric information in local and global shape descriptors. Our construction is based on the definition of a diffusion process on the…
Neural representations of 3D data have been widely adopted across various applications, particularly in recent work leveraging coordinate-based networks to model scalar or vector fields. However, these approaches face inherent challenges,…
This is a reply to Johansen's comment on `Are Financial Crashes Predictable?', by L. Laloux, M. Potters, R. Cont, J.P. Aguilar, J.P. Bouchaud, Europhys. Lett. 45, p. 1 (1999).
This letter presente a comment on the paper Prediction of Kidney Function from Biopsy Images using Convolutional Neural Networks by Ledbetter et al. (2017)
Evaluating the quality of learned representations without relying on a downstream task remains one of the challenges in representation learning. In this work, we present Geometric Component Analysis (GeomCA) algorithm that evaluates…