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Stimulus encoding fidelity and uniqueness with scaled additive noise (i.e. additive noise with response variance multiplicatively related to the response mean).

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posted on 08.02.2017 by Johannes Burge, Priyank Jaini

The original stimuli are represented as points in a three dimensional space (bigger red and blue dots, one stimulus from each of two levels of the latent variable). The original stimuli are then projected into a standard (i.e. orthogonal) basis {e1,e2} that spans the same subspace as two (possibly non-orthogonal) filters {f1,f2}. The uncertainty ellipse represents uncertainty about the encoded stimulus given the filter responses. The size and orientation of each uncertainty ellipse is determined by the stimulus (dot), the filter response noise, and the correlation between the filters. A-F Unlike with constant additive noise, stimulus encoding with scaled additive noise is unique (up to a sign flip) regardless of whether the filters are orthogonal. Filters that are somewhat anti-correlated yield uncertainty ellipses that are oriented approximately with lines radiating from the origin.