Spurious correlation as an approximation of the mutual information between redundant outputs and an unknown input

Stochastic resonance (SR) is a counterintuitive phenomenon, observed in a wide variety of nonlinear systems, for which the addition of noise of opportune magnitude can improve signal detection. Tuning the noise for maximizing the SR effect is important both for artificial and biological systems. In the case of artificial systems, full exploitation of the SR effect opens the possibility of measuring otherwise unmeasurable signals. In biology, identification of possible SR maximization mechanisms is of great interest for explaining the low-energy high-sensitivity perception capabilities often observed in animals. SR maximization approaches presented in literature use knowledge on the input signal (or stimulus, in the case of living beings), and maximize the mutual information between the input and the output signal. The input signal, however, is unknown in many practical settings. To cope with this problem, this paper introduces an approximation of the input–output mutual information based on the spurious correlation among a set of redundant units. A proof of the approximation, as well as numerical examples of its application are given.