Hybrid Statistical Estimation of Mutual Information and its Application to Information Flow

TL;DR

This paper introduces a hybrid statistical estimation technique for mutual information and entropy that combines precise and approximate analyses, optimizing sample sizes and leveraging prior knowledge to efficiently analyze complex systems.

Contribution

It presents a novel hybrid method that integrates different analysis precisions and dynamically optimizes sampling, improving efficiency in estimating information-theoretic measures.

Findings

Outperforms existing methods in quantifying information leakage

Reduces sample sizes using prior knowledge and abstraction techniques

Demonstrates effectiveness through case studies

Abstract

Analysis of a probabilistic system often requires to learn the joint probability distribution of its random variables. The computation of the exact distribution is usually an exhaustive precise analysis on all executions of the system. To avoid the high computational cost of such an exhaustive search, statistical analysis has been studied to efficiently obtain approximate estimates by analyzing only a small but representative subset of the system's behavior. In this paper we propose a hybrid statistical estimation method that combines precise and statistical analyses to estimate mutual information, Shannon entropy, and conditional entropy, together with their confidence intervals. We show how to combine the analyses on different components of a discrete system with different accuracy to obtain an estimate for the whole system. The new method performs weighted statistical analysis with different sample sizes over different components and dynamically finds their optimal sample sizes. Moreover, it can reduce sample sizes by using prior knowledge about systems and a new abstraction-then-sampling technique based on qualitative analysis. To apply the method to the source code of a system, we show how to decompose the code into components and to determine the analysis method for each component by overviewing the implementation of those techniques in the HyLeak tool. We demonstrate with case studies that the new method outperforms the state of the art in quantifying information leakage.