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Dear CCN Colleagues,
Please welcome our guest speaker, Dr. Arthur Prat-Carrabin, Columbia University who will be guest speaking for this week's LCV meeting. Title and abstract below!
Title: Bias and variance with efficient coding and Bayesian-mean decoding
Abstract: Perception, in theoretical neuroscience, has been modeled as the encoding of external stimuli into internal signals, which are then decoded. The Bayesian mean is an important decoder, as it is optimal for purposes of both estimation and discrimination. We present widely-applicable approximations to the bias and to the variance of the Bayesian mean, obtained under the minimal and biologically-relevant assumption that the encoding results from a series of independent, though not necessarily identically-distributed, signals. Simulations substantiate the accuracy of our approximations in the small-noise regime. The bias of the Bayesian mean comprises two components: one driven by the prior, and one driven by the precision of the encoding. If the encoding is 'efficient', the two components have opposite effects; their relative strengths are determined by the objective that the encoding optimizes. The experimental literature on perception reports both 'Bayesian' biases directed towards prior expectations, and opposite, 'anti-Bayesian' biases. We show that different tasks are indeed predicted to yield such contradictory biases, under a consistently-optimal encoding-decoding model. Moreover, we recover Wei and Stocker's 'law of human perception', a relation between the bias of the Bayesian mean and the derivative of its variance, and show how the coefficient of proportionality in this law depends on the task at hand. Our results provide a parsimonious theory of optimal perception under constraints, in which encoding and decoding are adapted both to the prior and to the task faced by the observer.
Please be advised the LCV Group meetings will convene in the 3rd Floor Classroom at the Flatiron building (162 5th Avenue) until further notice, as the construction of the new CCN office meeting spaces will continue to be under construction until further notice. Zoom credentials provided in the Google Calendar invite for anyone tuning in remotely.