1,587 research outputs found
Topological and Algebraic Properties of Chernoff Information between Gaussian Graphs
In this paper, we want to find out the determining factors of Chernoff
information in distinguishing a set of Gaussian graphs. We find that Chernoff
information of two Gaussian graphs can be determined by the generalized
eigenvalues of their covariance matrices. We find that the unit generalized
eigenvalue doesn't affect Chernoff information and its corresponding dimension
doesn't provide information for classification purpose. In addition, we can
provide a partial ordering using Chernoff information between a series of
Gaussian trees connected by independent grafting operations. With the
relationship between generalized eigenvalues and Chernoff information, we can
do optimal linear dimension reduction with least loss of information for
classification.Comment: Submitted to Allerton2018, and this version contains proofs of the
propositions in the pape
Approximations of Shannon Mutual Information for Discrete Variables with Applications to Neural Population Coding
Although Shannon mutual information has been widely used, its effective
calculation is often difficult for many practical problems, including those in
neural population coding. Asymptotic formulas based on Fisher information
sometimes provide accurate approximations to the mutual information but this
approach is restricted to continuous variables because the calculation of
Fisher information requires derivatives with respect to the encoded variables.
In this paper, we consider information-theoretic bounds and approximations of
the mutual information based on Kullback--Leibler divergence and R\'{e}nyi
divergence. We propose several information metrics to approximate Shannon
mutual information in the context of neural population coding. While our
asymptotic formulas all work for discrete variables, one of them has consistent
performance and high accuracy regardless of whether the encoded variables are
discrete or continuous. We performed numerical simulations and confirmed that
our approximation formulas were highly accurate for approximating the mutual
information between the stimuli and the responses of a large neural population.
These approximation formulas may potentially bring convenience to the
applications of information theory to many practical and theoretical problems.Comment: 31 pages, 6 figure
Distributed Detection over Random Networks: Large Deviations Performance Analysis
We study the large deviations performance, i.e., the exponential decay rate
of the error probability, of distributed detection algorithms over random
networks. At each time step each sensor: 1) averages its decision variable
with the neighbors' decision variables; and 2) accounts on-the-fly for its new
observation. We show that distributed detection exhibits a "phase change"
behavior. When the rate of network information flow (the speed of averaging) is
above a threshold, then distributed detection is asymptotically equivalent to
the optimal centralized detection, i.e., the exponential decay rate of the
error probability for distributed detection equals the Chernoff information.
When the rate of information flow is below a threshold, distributed detection
achieves only a fraction of the Chernoff information rate; we quantify this
achievable rate as a function of the network rate of information flow.
Simulation examples demonstrate our theoretical findings on the behavior of
distributed detection over random networks.Comment: 30 pages, journal, submitted on December 3rd, 201
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