Mismatched Decoding in the Brain

Abstract

"How is information decoded in the brain?" is one of the most difficult and important questions in neuroscience. We have developed a general framework for investigating to what extent the decoding process in the brain can be simplified. First, we hierarchically constructed simplified probabilistic models of neural responses that ignore more than Kth-order correlations using the maximum entropy principle. We then computed how much information is lost when information is decoded using these simplified probabilistic models (i.e., "mismatched decoders"). To evaluate the information obtained by mismatched decoders, we introduced an information theoretic quantity, I*, which was derived by extending the mutual information in terms of communication rate across a channel. We showed that I* provides consistent results with the minimum mean-square error as well as the mutual information, and demonstrated that a previously proposed measure quantifying the importance of correlations in decoding substantially deviates from I* when many cells are analyzed. We then applied this proposed framework to spike data for vertebrate retina using short natural scene movies of 100 ms duration as a set of stimuli and computing the information contained in neural activities. Although significant correlations were observed in population activities of ganglion cells, information loss was negligibly small even if all orders of correlation were ignored in decoding. We also found that, if we inappropriately assumed stationarity for long durations in the information analysis of dynamically changing stimuli, such as natural scene movies, correlations appear to carry a large proportion of total information regardless of their actual importance.

Shifted encoding strategy in retinal luminance adaptation: from firing rate to neural correlation

“…Nirenberg and Latham proposed such a measure, the Kullback-Leibler divergence between true encoding model [i.e., p(r|s)] and a mismatched one that neglects neuronal correlation (Nirenberg et al 2001). Recently, a measure called I*, which is directly linked to the decoding error of a maximum likelihood inference based on a mismatched model (Oizumi et al 2010;Wu et al 2001), was applied to analyze neural data. There is a standing debate over which measure better quantifies the stimulus information conveyed by neural correlation (Latham and Nirenberg 2005;Schneidman et al 2003).…”

“…Some studies suggested that the firing rates of neurons conveyed the majority of the stimulus information, and that the contribution of neural correlation could be largely neglected (Meytlis et al 2012;Nirenberg et al 2001;Oizumi et al 2010), whereas others suggested that neural correlation played an indispensable role in neural computation (Dan et al 1998; …”

Millisecond encoding precision of auditory cortex neurons

“…S2A). It is important to note that this shuffling procedure does not alter the statistical dimensionality (number of time bins N) of the data and allows investigating different effective temporal precisions without changing the absolute length of the time window T. The latter is important because the associated biases of the information estimate are kept constant (38) and because it avoids spurious scaling of the information values by changing the considered time window T: Direct information estimates increase rapidly with decreasing window T because the use of short windows can underestimate the redundancy of the information carried by spikes in adjacent response windows when these windows become too short (41,42). Note that this shuffling procedure is equivalent to decreasing the spiking precision by randomly jittering spike times within the window T with a jitter taken from a uniform distribution.…”

Information-theoretic methods for studying population codes

“…It can be shown (Oizumi et al, 2009(Oizumi et al, , 2010 thatÎ k ≤ I(S; R) and that I LB−k equals I (β) k for β = 1. SinceÎ k is the maximum over β of I (β) k , it follows that I k ≥ I LB−k , confirming that I LB−k is a lower bound.…”

“…The computation of the precise amount of information decodable by taking into account correlations up to order k,Î k has not been used in neuroscience until very recently (Oizumi et al, 2009(Oizumi et al, , 2010. Its sampling properties and the best procedures to estimate it from a limited amount of data are still largely unexplored.…”