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Percept and the single neuron

Adrien Wohrer, Christian K Machens

2013
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Nature Neuroscience
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volume 16 | number 2 | february 2013 nature neuroscience n e w s a n d v i e w s is the following: a neuron's choice probability depends on the sum over all of its firing rate covariances with other neurons, C kj , weighted by their respective readout weights, β j : where α is a normalization factor. This formula (which is only approximate; the authors also supply an exact version) provides the longsought relationship between choice probabilities and readout weights in the presence of noise
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... elations (Fig. 1c) . It essentially relies on the matrix product Cb, which is simply the trialto-trial covariance between neural activities r k and percept P in the standard model. Although it has been intuitively clear that CP measures something along these lines, Haefner et al. 2 now give mathematical grounding to this intuition. Obtaining the readout weights β k may seem straightforward now: we need to solve equation (1) by inverting the covariance matrix, C. Unfortunately, that is impossible: because experimenters record from only selected ensembles of neurons for a finite number of trials, the covariance matrix cannot be fully determined. It is known only through samples of its elements C kj , and with finite accuracy. How, then, are we to concretely exploit the beauty of the CP formula? Haefner et al. 2 provide two insights into this question. The first insight-probably the more useful in practice-exploits the concept of optimality. Ideally, the organism should choose the readout weights b optimally, to maximize the vector of sensitivity, or signal-to-noise ratio (SNR), of percept P. This optimal choice, Fisher's linear discriminant, is well known from the statistical literature and relies on the inverse of covariance matrix C. As a result, when the optimal readout weight vector b (opt) is used, matrix C is eliminated from equation (1). Better, the exact expressions of b (opt) and (1)

doi:10.1038/nn.3314
pmid:23354380
fatcat:222dac7xqjhs7ho4rq2dyrzeby