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Title: Bias and variance of the Bayesian-mean decoder
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" [1], 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.  more » « less
Award ID(s):
1949418
PAR ID:
10518166
Author(s) / Creator(s):
;
Publisher / Repository:
ACM Digital Library
Date Published:
Journal Name:
Advances in neural information processing systems
Edition / Version:
1
ISSN:
1049-5258
Page Range / eLocation ID:
23793-23805
Format(s):
Medium: X Size: 285KB Other: pdf
Size(s):
285KB
Location:
https://dl.acm.org/doi/10.5555/3540261.3542083
Sponsoring Org:
National Science Foundation
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