Analyzing an organism’s sensors using Maximum Entropy models with bias, variance, and confusion matrices

Abstract Biological organisms have sensors that communicate information about the environment. Analyzing how well these biological sensors function has usually been done with mutual information between the sensor signal and the environment, but that can be computationally intractable and summarize something quite complex with just a single number. We suggest that alternatively, one may profitably analyze these biosensors using bias and variance or confusion matrices, depending on the kind of environment. Stimulus-dependent Maximum Entropy models are used to develop estimators of the environmental state given the sensor state, and these estimators in turn are then used to calculate either the bias and variance of the estimator or confusion matrices. We focus on several examples to understand the utility of non-information-based analyses: ligand-receptor binding models spanning genetic regulation to neuronal communication to bacterial chemotaxis, and spin-glass Ising models for neural activity in cultured neurons. These new computationally-efficient analyses add insight to existing analyses based on mutual information; in particular, mutual information estimates give one number to characterize responses to all environmental inputs, and this analysis method characterizes how sensors respond to each environmental input. Categorical analyses, meanwhile, indicate the presence of memory without much prediction in confusion matrix elements in cultured neural networks, adding to previous understanding from mutual information estimates. Author summary All living organisms use external stimuli to navigate their environment via their sensors. Because encoding information costs energy, organisms retain only a fraction of the information received from their sensors, ideally information that maximizes their ability to remember past environmental states or predict future ones, key functions that support survival. To better understand how well sensor systems absorb stimulus information, we used stimulus-dependent Maximum Entropy (MaxEnt) models with maximum likelihood estimation and typical statistical metrics, such as confusion matrices or bias and variance. This approach provides two primary benefits over previous approaches: it is more computationally efficient, and it provides a more information-rich picture on how sensors interact with stimulus. Competing Interest Statement The authors have declared no competing interest.