Fig. 2: Multi-timescale & weighted Dynamic Bayesian Networks based estimation of unique dependencies in a sparsely sampled recurrent neuronal network.

a Bayesian Networks for graph representation of dependencies in a multivariate system. b Dynamic Bayesian Networks (DBN) for graph representation of dependencies in multivariate time series data. c Analysis flow for multi-timescale weighted DBN (MTwDBN) graphical model fitting. d Edge weight of MTwDBN graph as a function of connection weight in a 2-population simulated network using the pipeline in c. Error bars indicate 95% confidence interval (n = 100 weighted DAGs). e Spiking activity of 6 subpopulations in a simulated network with recurrent connectivity. Connectivity is visualized in the overlaid schematic. f Directed dependencies (edge in the graph) in the simulated network in e, estimated using MTwDBN fitting. g Summary graph of dependencies across all timescales from f. Solid and dashed lines indicate two different timescales. h F-score (harmonic mean of precision and recall of dependency structure) as a function of % of neural population observed. F-score was estimated for shuffle corrected weighted DAGs (MTwDBN, green), weighted DAGs with a fixed threshold (weightedFT, blue), unweighted DAGs (red), or LASSO regression, an example of regularized regression (RR) models (black). Each point represents the average of five separate runs, except 100% (single run). Error bars indicate standard deviation, some error bars are smaller than symbol size. i DBN decoder accuracy with different sizes of MTwDBN DAGs. Decoders were trained to predict population activities using a subsample of shuffle-corrected edges (see “Methods”). Graph edges for the decoder were sampled from the learned structure either in an unbiased fashion (black) or biased with the edge weights (green). Box indicates lower quartile, median, and upper quartile; whiskers indicate range of data points (n = 100 model seeds). Asterisk (*) indicates significant differences between unbiased and weight biased M-Scores (p < 0.001, two-tailed paired t-test, Bonferroni adjusted). j Schema for estimating modulation of unique dependencies in a network of neural populations, using MTwDBN.