scholarly journals Introduction to Computational Algebraic Statistics

Author(s):  
Satoshi Aoki
Keyword(s):  
2011 ◽  
Vol 20 (1) ◽  
pp. 25-33 ◽  
Author(s):  
Winfried Bruns ◽  
Raymond Hemmecke ◽  
Bogdan Ichim ◽  
Matthias Köppe ◽  
Christof Söger

2010 ◽  
Vol 1 (1) ◽  
Author(s):  
Journal Of Algebraic Statistics

Just as it has been continually happening in the world of mathematical sciences, the group of mathematical scientists led by (for example) Professor Eyup Cetin and his colleagues (who are responsible for the remarkably successful journal, The European Journal of Pure and Applied Mathematics ) have apparently broken the boundaries between pure and applied mathematics by establishing a new journal, the Journal of Algebraic Statistics . I am sure that both the mathematical as well as statistical communities at large will heartily welcome such an interesting and potentially useful addition to the list of broad-based journals in the mathematical sciences.I do sincerely wish the Journal of Algebraic Statistics every success in its endeavor to attract and publish high-quality papers which are aimed essentially and substantially at significantly bridging the gaps between the various areas within the disciplines of the mathematical and statistical sciences.Hari M. Srivastava, University of Victoria , Canada* * *The present moment seems a very appropriate one to launch a new journal on algebraic statistics. In fact many fields of mathematics are considering with interest concrete applications of well developed theories towards the solution of problems coming from everyday science and technology. This applies in particular to certain branches of algebraic geometry.I wish to the new journal a good success.Fabrizio Catanese, University of Bayreuth, Germany* * *Algebraic Statistics is a rapidly growing discipline, and presents many opportunities for research and applications. The newly launched Journal of Algebraic Statistics will bring together researchers working on problems in this area and as such is highly welcome.I congratulate the Editors for bringing it out and wish them and the journal success.Arjun K. Gupta, Bowling Green State University, USA* * *Many people think that Algebra and Statistics have really nothing in common, except some applications of Linear Algebra to Statistics. This is far away from the truth. A main purpose of this new journal is to uncover the numerous connections between these fields, and hence to advance both Statistics and Algebra.Many of these connections were not intended in the beginning and came as pleasant surprises. The applications go in both directions and bring new ideas and method from one area to the other.I want to congratulate the founders and Editors-in-Chief of this new journal for establishing it and for promoting the study of this fascinating interplay.Günter Pilz, Johannes Kepler University, Austria* * *Modern Algebra is central to all fields of mathematics, and impacts engineering fields such as coding theory and cryptography. Likewise, Statistics touches on all aspects of modern science. The intersection of these two fields, Algebraic Statistics, is becoming important in a number of application areas in the form of random walks on groups, random matrix theory, multivariate statistical analysis, geometric probability, and topological analysis of large data sets.Though efforts in these different areas have been published over the past half century in a variety of venues, having one place to go where readers interested in the theory and application of both Algebra and Statistics will enable significant advances by providing a hub from which connections to the broader literature can be more easily made. The Journal of Algebraic Statistics has the potential to be such a forum, and I look forward to the success of this new journal.Gregory S. Chirikjian, Johns Hopkins University, USA* * *I would like to congratulate the editorial team for the inaugural issue of the Journal of Algebraic Statistics .Algebraic Statistics is the emerging new field focused on the applications of algebraic geometry and its computational tools in the study of statistical models. Algebraic Statistics is built around the observation that many statistical models are (semi)-algebraic sets. The study of the geometry and equations of these algebraic sets can be useful for making statistical inferences, thus the areas of interest include categorical data analysis, experimental design, graphical models, maximum likelihood estimation, and Bayesian methods.Also some work shows applications of Algebraic Statistics to problems in computational biology. Nearly all statistical models for discrete random variables fall into the category above, and many models for continuous random variables can be treated this way as well. Thus, it is likely that these algebraic statistical techniques will be useful in many more areas of computational and mathematical biology such as systems biology, evolutionary biology, functional genomics, bioinformatics, and epidemiology.Algebraic Statistics is an exciting field and attracts many younger researchers. Thus I wish for theJournal of Algebraic Statistics to be very successful.Ruriko Yoshida, University of Kentucky, USA


2014 ◽  
Vol 5 (1) ◽  
Author(s):  
Alexander Schönhuth

The generic identication problem is to decide whether a stochastic process (Xt) is ahidden Markov process and if yes to infer its parameters for all but a subset of parametrizationsthat form a lower-dimensional subvariety in parameter space. Partial answers so far availabledepend on extra assumptions on the processes, which are usually centered around stationarity.Here we present a general solution for binary-valued hidden Markov processes. Our approach isrooted in algebraic statistics hence it is geometric in nature. We nd that the algebraic varietiesassociated with the probability distributions of binary-valued hidden Markov processes are zerosets of determinantal equations which draws a connection to well-studied objects from algebra. Asa consequence, our solution allows for algorithmic implementation based on elementary (linear)algebraic routines.


2012 ◽  
Vol 12 (3&4) ◽  
pp. 346-354
Author(s):  
Joseph M. Landsburg ◽  
Yang Qi ◽  
Ke Ye

We answer a question of L. Grasedyck that arose in quantum information theory, showing that the limit of tensors in a space of tensor network states need not be a tensor network state. We also give geometric descriptions of spaces of tensor networks states corresponding to trees and loops. Grasedyck's question has a surprising connection to the area of Geometric Complexity Theory, in that the result is equivalent to the statement that the boundary of the Mulmuley-Sohoni type variety associated to matrix multiplication is strictly larger than the projections of matrix multiplication (and re-expressions of matrix multiplication and its projections after changes of bases). Tensor Network States are also related to graphical models in algebraic statistics.


2019 ◽  
Vol 10 (1) ◽  
pp. 30-50
Author(s):  
Thi Mui Pham ◽  
Maria Kateri

Tools of algebraic statistics combined with MCMC algorithms have been used in contingency table analysis for model selection and model fit testing of log-linear models. However, this approach has not been considered so far for association models, which are special log-linear models for tables with ordinal classification variables. The simplest association model for two-way tables, the uniform (U) association model, has just one parameter more than the independence model and is applicable when both classification variables are ordinal. Less parsimonious are the row (R) and column (C) effect association models, appropriate when at least one of the classification variables is ordinal. Association models have been extended for multidimensional contingency tables as well. Here, we adjust algebraic methods for association models analysis and investigate their eligibility, focusing mainly on two-way tables. They are implemented in the statistical software R and illustrated on real data tables. Finally the algebraic model fit and selection procedure is assessed and compared to the asymptotic approach in terms of a simulation study.


2020 ◽  
Vol 2020 (20) ◽  
pp. 6699-6712
Author(s):  
Jose Israel Rodriguez ◽  
Botong Wang

Abstract We give a numerical algorithm computing Euler obstruction functions using maximum likelihood degrees. The maximum likelihood degree is a well-studied property of a variety in algebraic statistics and computational algebraic geometry. In this article we use this degree to give a new way to compute Euler obstruction functions. We define the maximum likelihood obstruction function and show how it coincides with the Euler obstruction function. With this insight, we are able to bring new tools of computational algebraic geometry to study Euler obstruction functions.


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