On Information Metrics for Spatial Coding

Abstract

The hippocampal formation is involved in navigation, and its neuronal activity exhibits a variety of spatial correlates (e.g., place cells, grid cells). The quantification of the information encoded by spikes has been standard procedure to identify which cells have spatial correlates. For place cells, most of the established metrics derive from Shannon's mutual information (Shannon, 1948), and convey information rate in bits/s or bits/spike (Skaggs et al., 1993, 1996). Despite their widespread use, the performance of these metrics in relation to the original mutual information metric has never been investigated. In this work, using simulated and real data, we find that the current information metrics correlate less with the accuracy of spatial decoding than the original mutual information metric. We also find that the top informative cells may differ among metrics, and show a surrogate-based normalization that yields comparable spatial information estimates. Since different information metrics may identify different neuronal populations, we discuss current and alternative definitions of spatially informative cells, which affect the metric choice.

Dynamic control of hippocampal spatial coding resolution by local visual cues

“…Accordingly, spatial information (in bit/spike), a measure independent of place fields’ detection (Skaggs et al, 1993) was very low in the track without objects (0.06 ± 0.01 bit/spike, n = 48 place cells) and significantly higher in the presence of objects (0.25 ± 0.02 bit/spike, n = 193 place cells; Z = −5.67, p<10 −7 , two-tailed WRS test; Figure 1K). Similar results were obtained with a different method to estimate spatial information content based on the original mutual information metric with a normalization to correct possible bias due to differences in basal firing rates between conditions (Souza et al, 2018) (ØT: 1.67 ± 0.21, n = 48 place cells; OT: 5.62 ± 0.29, n = 193 place cells; Z = −7.57, p<10 −13 , two-tailed WRS test). The effects of objects on spatial coding resolution were also observed when comparisons were performed across recording sessions (Figure 1—figure supplement 2 and Supplementary file 2).…”

“…As another measure of spatial information, we computed the Mutual Information using the following formula:MI=∑i=1N∑j=14pi,jlog2|pi,jpi.pjwhere N is the total number of spatial bins, p i is the occupancy probability of the animal in the i-th spatial bin, p j is the probability to obtain a firing rate amongst one of four non overlapping quartiles of firing rates and p i,j is the joint probability of the animal to be in the i-th spatial bin with a firing rate in the j-th quartile. The Mutual Information was then normalized with a surrogate-based distribution to correct possible bias due to basal firing rate (Souza et al, 2018).…”

A Probabilistic Framework for Decoding Behavior From in vivo Calcium Imaging Data

“…Note that in our case we consider only two levels of activity j (active versus inactive). The MI index is a practical way of sorting neurons by the amount of information they encode ( Supplementary Figure 1), and it was previously found that although related, MI is more reliable and scalable than other spatial information metrics (Souza et al, 2018). In our example, cell #4 displays 0.21 bits of information while considering only trajectories to the right ( Figure 1J).…”

Conjunctive spatial and idiothetic codes are topographically organized in the GABAergic cells of the lateral septum

“…3f). Using an information-theoretic framework [48][49][50] , we computed the mutual information (MI) between calcium activity and spatial location for each cell and expressed the results in bits 47 . To circumvent the inherent issue of sparse sampling in 15min long recordings, we computed the mean MI and confidence interval using 30 bootstrap samples (50% data sampling per sample, Fig.…”