Bias-free estimation of information content in temporally sparse neuronal activity
Fig 3
Correcting the upward bias in naïve SI using the SSR method.
Validation based on data from simulated place cells with similar tuning properties to those observed in the real hippocampal data, corresponding to 20 minutes of free exploration in the linear track. (A) Demonstration of the shuffle reduction (SR) method. Estimated SI as a function of sample duration for the naïve calculation (blue), shuffle (black), SR (red), and the true SI (cyan). (B) Demonstration of the scaled shuffle reduction (SSR) method. Estimated SI as a function of sample duration for the naïve calculation (blue), shuffle (black), SSR (magenta), and the true SI (cyan). The SSR estimation is obtained by assuming a fixed ratio between the bias in the naïve SI (biasn, blue) and the bias in the shuffle SI (biass, black) for two different sample durations, and using this bias ratio to subtract from the naïve SI a scaled version of the shuffle SI. Data in A-B show the mean across 100 cells from one example simulation. (C) Estimated SI (mean ± SEM) as a function of sample duration for the naïve calculation (blue), SR (red), SSR (magenta), and the true SI (cyan). (D) Correction instability (mean ± SEM), defined as the standard deviation of the estimated SI across sample durations, for the naïve calculation, SR, and SSR. SSR is more stable than the naïve calculation (matched-pairs two-sided t-test(8), t = 51.5, p = 2.2·10−11) and SR (matched-pairs two-sided t-test(8), t = 54.5, p = 1.4·10−11). Data in C-D were averaged across N = 9 simulations. Each simulation corresponds to behavioral data from a different mouse and consists of 100 simulated place cells. ***p < 0.001.