A hierarchical Bayesian inference model for volatile multivariate exponentially distributed signals

TL;DR

This paper introduces a hierarchical Bayesian model to analyze complex, time-varying brain signals that follow exponential distributions.

Contribution

A novel hierarchical Bayesian inference model for multivariate exponential signals with time-varying rate parameters and interactions.

Findings

The model successfully estimates time-varying rate parameters of multivariate exponential signals.

It captures the underlying correlation structure of volatile exponentially distributed data.

The model provides closed-form update equations for efficient inference.

Abstract

Brain activities often follow an exponential family of distributions. The exponential distribution is the maximum entropy distribution of continuous random variables in the presence of a mean. The memoryless and peakless properties of an exponential distribution impose difficulties for data analysis methods. To estimate the rate parameter of multivariate exponential distribution from a time series of sensory inputs (i.e., observations), we constructed a hierarchical Bayesian inference model based on a variant of general hierarchical Brownian filter (GHBF). To account for the complex interactions among multivariate exponential random variables, the model estimates the second-order interaction of the rate intensity parameter in logarithmic space. Using variational Bayesian scheme, a family of closed-form and analytical update equations are introduced. These update equations also constitute a complete predictive coding framework. The simulation study shows that our model has the ability to evaluate the time-varying rate parameters and the underlying correlation structure of volatile multivariate exponentially distributed signals. The proposed hierarchical Bayesian inference model is of practical utility in analyzing high-dimensional neural activities.

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