Bias-free estimation of information content in temporally sparse neuronal activity

Applying information theoretic measures to neuronal activity data enables the quantification of neuronal encoding quality. However, when the sample size is limited, a naive estimation of the information content typically contains a systematic overestimation (upward bias), which may lead to misinterpretation of coding characteristics. This bias is exacerbated in Ca2+ imaging because of the temporal sparsity of elevated Ca2+ signals. Here, we introduce methods to correct for the bias in the naive estimation of information content from limited sample sizes and temporally sparse neuronal activity. We demonstrate the higher accuracy of our methods over previous ones, when applied to Ca2+ imaging data recorded from the mouse hippocampus and primary visual cortex, as well as to simulated data with matching tuning properties and firing statistics. Our bias-correction methods allowed an accurate estimation of the information place cells carry about the animal's position (spatial information) and uncovered the spatial resolution of hippocampal coding. Furthermore, using our methods, we found that cells with higher peak firing rates carry higher spatial information per spike and exposed differences between distinct hippocampal subfields in the long-term evolution of the spatial code. These results could be masked by the bias when applying the commonly used naive calculation of information content. Thus, a bias-free estimation of information content can uncover otherwise overlooked properties of the neural code.

Automated summary

Applying information theoretic measures to neuronal activity data can quantify the quality of neuronal encoding. However, there is typically an upward bias in the naive estimation of information content due to limited sample size, especially in Ca2+ imaging. This study introduces methods to correct for this bias and demonstrates their higher accuracy compared to previous methods. The bias-correction methods allow for accurate estimation of information content and uncover overlooked properties of neural coding.