Figure 3. Results of Computer Simulation I.

Performance comparison between an ideal version of Implementation 1 (use of auxiliary RVs, results shown in green) and an ideal version of implementations that satisfy the NCC (results shown in blue) for probabilistic inference in the Bayesian network of Fig. 1B (“explaining away”. Evidence (see (1)) is entered for the RVs and , and the marginal probability is estimated. A) Target values of for and are shown in black, results from sampling for from a network of spiking neurons are shown in green and blue. Panels C) and D) show the temporal evolution of the Kullback-Leibler divergence between the resulting estimates through neural sampling and the correct posterior , averaged over 10 trials for in C) and for in D). The green and blue areas around the green and blue curves represent the unbiased value of the standard deviation. The estimated marginal posterior is calculated for each time point from the samples (number of spikes) from the beginning of the simulation (or from for the second inference query with ). Panels A, C, D show that both approaches yield correct probabilistic inference through neural sampling, but the approach via satisfying the NCC converges about 10 times faster. B) The firing rates of principal neuron (solid line) and of the principal neuron (dashed line) in the approach via satisfying the NCC, estimated with a sliding window (alpha kernel ). In this experiment the evidence was switched after 3 s (red vertical line) from to . The “explaining away”effect is clearly visible from the complementary evolution of the firing rates of the neurons and .