Using ROC analysis (1ms timescale, 10-fold cross-validated ), we find that spikes are predicted with an area-under-the-curve (AUC) of 0.71:0.01 for Model 1, while Model 2 yields 0.72:0.01, 0.74:0.01, and 0.77:0.01 as the input amplitude increases from 0.5 a, to 1.00 a, to 1.5 a.

As with the detection of connections, here we define a weight change as detectable if modeling the effects 191”ng and bpre¢>g around a known change-point t’ results in a cross-validated log likelihood ratio >0 when compared to a model with a single coupling effect bpre for all observations.

The regularization hyper-parameter is optimized by maximizing cross-validated log-likeli-hood, and no regularization is performed on the baseline or post-spike history terms.

Using ROC analysis we find that cross-validated area-under-the-curve increases from 0.72:0.01 when 5% of the inputs are observed to 0.98:0.01 in the model that includes all (100%) inputs (Fig.

An important concept in functional connectivity analysis is whether or not an input is “de-tectable.” One approach is to define an input as detectable if the effect bpre, from the model in Eq.1, results in a cross-validated log likelihood ratio >0 when compared to the nested model with bpre = 0.

Here we base “detection time” on the minimum amount of recorded data (averaged over blocks length T) needed to satisfy the cross-validated LLR criterion.

In deciding whether a connection is present or not, it may be useful to compare the assumptions of the cross-validated log likelihood ratio and the un-cross-validated, explicit likelihood-ratio test.

B) Model accuracy: Receiver operating characteristic (ROC) curves for the example cell and area under the curve (AUC) for all cells from A. Curves show the cross-validated false positive rate (FPR) vs true positive rate (TPR) for spike detection in 1ms bins.

We then performed a cross-validated evaluation to establish which of the four regularized estimators was most efficient for representing the population activity of dense groups of neurons in mouse primary visual corteX recorded with high-speed 3D random-access two-photon imaging of calcium signals.

Therefore, showing that a more constrained model has better cross-validated performance than a more compleX model does not necessarily support the conclusion that it reveals a better representation of dependencies in the data.

To demonstrate that estimator rankings were robust to deviations from Gaussian models, we repeated the same cross-validated evaluation using pairwise Ising models to generate the data.

This simulation study demonstrated that cross-validated evaluation of regularized estimators of the covariance matrices of population activity can discriminate between structures of dependencies in the population.