The Equivalence of Information-Theoretic and Likelihood-Based Methods for Neural Dimensionality Reduction
Fig 8
Estimation of high-dimensional subspaces using a nonlinearity parametrized with cylindrical basis functions (CBFs).
(A) Eight most informative filters for an example complex cell, estimated with iSTAC (top row) and cbf-LNP (bottom row). For the cbf-LNP model, the nonlinearity was parametrized with three first-order CBFs for the output of each filter (see Methods). (B) Estimated 1D nonlinearity along each filter axis, for the filters shown in (A). Note that third and fourth iSTAC filters are suppressive while third and fourth cbf-LNP filter are excitatory. (C) Cross-validated single-spike information for iSTAC, cbf-LNP, and rbf-LNP, as a function of the number of filters, averaged over a population of 16 neurons (selected from [29] for having ≥ 8 informative filters). The cbf-LNP estimate outperformed iSTAC in all cases, while rbf-LNP yielded a slight further increase for the first four dimensions. (D) Computation time for the numerical optimization of the cbf-LNP likelihood for up to 8 filters. Even for 30 minutes of data and 8 filters, optimisation took about 4 hours. (E) Average number of excitatory filters as a function of total number of filters, for each method. (F) Information gain from excitatory filters, for each method, averaged across neurons. Each point represents the average amount of information gained from adding an excitatory filter, as a function of the number of filters.