A risk profile for information fusion algorithms

TL;DR

This paper introduces a risk profile framework for information fusion algorithms based on nonlinear statistical coupling, balancing robustness and accuracy through a generalized entropy measure, and evaluates a two-parameter fusion method.

Contribution

It develops a novel risk metric using Tsallis entropy generalization to quantify robustness and decisiveness in information fusion algorithms.

Findings

The coupled-surprisal metric effectively assesses robustness and accuracy.

The two-parameter fusion algorithm models correlation and smoothing effects.

The framework provides a trade-off analysis between robustness and decisiveness.

Abstract

E.T. Jaynes, originator of the maximum entropy interpretation of statistical mechanics, emphasized that there is an inevitable trade-off between the conflicting requirements of robustness and accuracy for any inferencing algorithm. This is because robustness requires discarding of information in order to reduce the sensitivity to outliers. The principal of nonlinear statistical coupling, which is an interpretation of the Tsallis entropy generalization, can be used to quantify this trade-off. The coupled-surprisal, -ln_k (p)=-(p^k-1)/k, is a generalization of Shannon surprisal or the logarithmic scoring rule, given a forecast p of a true event by an inferencing algorithm. The coupling parameter k=1-q, where q is the Tsallis entropy index, is the degree of nonlinear coupling between statistical states. Positive (negative) values of nonlinear coupling decrease (increase) the surprisal information metric and thereby biases the risk in favor of decisive (robust) algorithms relative to the Shannon surprisal (k=0). We show that translating the average coupled-surprisal to an effective probability is equivalent to using the generalized mean of the true event probabilities as a scoring rule. The metric is used to assess the robustness, accuracy, and decisiveness of a fusion algorithm. We use a two-parameter fusion algorithm to combine input probabilities from N sources. The generalized mean parameter 'alpha' varies the degree of smoothing and raising to a power N^beta with beta between 0 and 1 provides a model of correlation.