Chernoff Information between Gaussian Trees

12/28/2017
by   Binglin Li, et al.
0

In this paper, we aim to provide a systematic study of the relationship between Chernoff information and topological, as well as algebraic properties of the corresponding Gaussian tree graphs for the underlying graphical testing problems. We first show the relationship between Chernoff information and generalized eigenvalues of the associated covariance matrices. It is then proved that Chernoff information between two Gaussian trees sharing certain local subtree structures can be transformed into that of two smaller trees. Under our proposed grafting operations, bottleneck Gaussian trees, namely, Gaussian trees connected by one such operation, can thus be simplified into two 3-node Gaussian trees, whose topologies and edge weights are subject to the specifics of the operation. Thereafter, we provide a thorough study about how Chernoff information changes when small differences are accumulated into bigger ones via concatenated grafting operations. It is shown that the two Gaussian trees connected by more than one grafting operation may not have bigger Chernoff information than that of one grafting operation unless these grafting operations are separate and independent. At the end, we propose an optimal linear dimensional reduction method related to generalized eigenvalues.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

12/28/2017

Topological and Algebraic Properties of Chernoff Information between Gaussian Graphs

In this paper, we want to find out the determining factors of Chernoff i...
06/28/2019

Generating Normal Networks via Leaf Insertion and Nearest Neighbor Interchange

Galled trees are studied as a recombination model in theoretic populatio...
07/10/2019

About Fibonacci trees. II – generalized Fibonacci trees

In this second paper, we look at the following question: are the propert...
03/17/2019

On the Spectrum of Finite, Rooted Homogeneous Trees

In this paper we study the adjacency spectrum of families of finite root...
12/04/2020

On C^0-persistent homology and trees

The study of the topology of the superlevel sets of stochastic processes...
01/03/2019

Mergeable Dictionaries With Shifts

We revisit the mergeable dictionaries with shift problem, where the goal...
04/25/2020

Automated Abstraction of Operation Processes from Unstructured Text for Simulation Modeling

Abstraction of operation processes is a fundamental step for simulation ...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.