Semialgebraic Statistics and Latent Tree Models

ISBN-13: 9780367377496 / Angielski / Miękka / 2019 / 245 str.

Piotr Zwiernik

Opis

This book explains how to analyze statistical models with hidden (latent) variables. It takes a systematic, geometric approach to studying the semialgebraic structure of latent tree models. The first part of the book introduces key concepts in algebraic statistics, focusing on methods that are helpful in the study of models with hidden variables. The second part illustrates important examples of tree models with hidden variables. The author develops the important concepts of L-cumulants and links latent tree models and various tree spaces.

Spis treści

Introduction. Semialgebraic statistics: Algebraic and analytic geometry. Algebraic statistical models. Tensors, moments, and combinatorics. Latent tree graphical models: Phylogenetic trees and their models. The local geometry. The global geometry. Gaussian latent tree models.

O autorze

Piotr Zwiernik is a Marie Skłodowska-Curie International Fellow in the Department of Mathematics at the University of Genoa. His research interests include statistical inference, graphical models with hidden variables, algebraic statistics, singular learning theory, time series analysis, and symbolic methods. He received a PhD in statistics from the University of Warwick.