Individual neurons often produce highly variable responses over nominally identical trials, reflecting a mixture of intrinsic ‘noise’ and systematic changes in the animal's cognitive and behavioral state. Disentangling these sources of variability is of great scientific interest in its own right, but it is also increasingly inescapable as neuroscientists aspire to study more complex and naturalistic animal behaviors. In these settings, behavioral actions never repeat themselves exactly and may rarely do so even approximately. Thus, new statistical methods that extract reliable features of neural activity using few, if any, repeated trials are needed. Accurate statistical modeling in this severely trial-limited regime is challenging, but still possible if simplifying structure in neural data can be exploited. We review recent works that have identified different forms of simplifying structure — including shared gain modulations across neural subpopulations, temporal smoothness in neural firing rates, and correlations in responses across behavioral conditions — and exploited them to reveal novel insights into the trial-by-trial operation of neural circuits.
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