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Jointly efficient encoding and decoding in neural populations
Fig 6
Characterization of optimal solutions as functions of training set size.
In all simulations, N = 12, and 
. Solid curves represent the mean across different initializations, and shaded regions correspond to one standard deviation. The legend in panel A serves as a legend for all panels. (A) Solutions of the ELBO optimization problem as functions of the target rate, for the training set (top) and for the test set (bottom). Top: distortion, 
, and rate, 
(inset), for the training set as a function of the target rate, for different sizes of the training set, colored according to the legend. For smaller training sets, at higher rates the model tends to overfit the data, resulting in a lower training distortion than optimal (red line, large training set, same data as in Fig 4). Bottom: distortion, 
, and rate, 
(inset), for the test set as functions of the target rate, for different sizes of the training set. For smaller training sets, at higher rates the model does not generalize to unseen samples, resulting in a large distortion. (B) Left: Kullback-Leibler divergence between the stimulus and the generative distributions, as a function of 
, for different sizes of the training set. At higher rates, the generative model fits poorly the stimulus distribution. Right: examples of comparisons between stimulus (green line) and generative distribution (red and orange line) at low (top) and high (bottom) rates, for different sizes of the training set, Ntrn = 100 and Ntrn = 2000, colored according to the legend as in panel A. (C) Tuning width, wi, as a function of the location of a preferred stimulus, ci (dots), at low (left) and high (right) rates, for different sizes of the training set, Ntrn = 100 and Ntrn = 1000. The grey curve represents the stimulus distribution, π(x). (D) MSE in the stimulus estimate, obtained as the MAP, as a function of 
, for different sizes of the training set.
doi: https://doi.org/10.1371/journal.pcbi.1012240.g006