Intersection information and SubPID (Subatomic Partial Information Decomposition)

This package is composed by four parts:

• A MATLAB implementation of the partial information decomposition (PID) for distributions over three random variables using the definitions from Bertschinger, N., Rauh, J., Olbrich, E., Jost, J., and Ay, N. Quantifying unique information.. Entropy 2014, 16(4):2161–2183.
• Two MATLAB implementations of the intersection information I_{II}(S;R;C) that, in perceptual discrimination experiments, quantifies the sensory information in the recorded neural response R that is relevant to behavior. This measure is defined and described in Pica, G., Piasini, E., Safaai, H., Runyan, C.A., Diamond, M.E., Fellin, T., Kayser, C., Harvey, C.D., Panzeri, S., Quantifying how much sensory information in a neural code is relevant for behavior, Advances in neural information processing 2017, 3687-3697. The first implementation, "src/matlab/intersection information.m", evaluates I_{II}(S;R;C) starting from the empirical joint probability distribution p(s,r,c). The second implementation, "src/matlab/intersection information_from_binned_response.m", evaluates I_{II}(S;R;C) starting from vectors containing the stimulus s, the response r, and the choice c, corresponding to each trial. Here, the response is discretized into equipopulated bins for a conservative estimate of I_{II}(S;R;C).
• A MATLAB numerical implementation of the subatomic partial information decomposition proposed in Pica, G., Piasini, E., Chicharro, D., and Panzeri, S. Invariant Components of Synergy, Redundancy, and Unique Information Among Three Variables.. Entropy 2017, 19, 451, doi:10.3390/e19090451.