Predicting a noisy signal: the costs and benefits of time averaging as a noise mitigation strategy

TL;DR

This paper investigates how cells can optimally predict noisy, time-varying signals under resource constraints by extending the information bottleneck method, revealing a trade-off between noise reduction and dynamical accuracy.

Contribution

It introduces an extended information bottleneck framework for signal prediction with compression constraints, deriving the optimal kernel and analyzing the impact of resource limitations.

Findings

Optimal integration kernel reduces to Wiener filter without constraints

Existence of an optimal integration time balancing noise and dynamical error

Push-pull network behavior aligns with theoretical predictions under noise and compression

Abstract

One major challenge for living cells is the measurement and prediction of signals corrupted by noise. In general, cells need to make decisions based on their compressed representation of noisy, time-varying signals. Strategies for signal noise mitigation are often tackled using Wiener filtering theory, but this theory cannot account for systems that have limited resources and hence must compress the signal. To study how accurately linear systems can predict noisy, time-varying signals in the presence of a compression constraint, we extend the information bottleneck method. We show that the optimal integration kernel reduces to the Wiener filter in the absence of a compression constraint. This kernel combines a delta function at short times and an exponential function that decays on a timescale that sets the integration time. Moreover, there exists an optimal integration time, which arises from a trade-off between time averaging signal noise and dynamical error. As the level of compression is increased, time averaging becomes harder, and as a result the optimal integration time decreases and the delta peak increases. We compare the behaviour of the optimal system with that of a canonical motif in cell signalling, the push-pull network, finding that the system reacts to signal noise and compression in a similar way.