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Recent advances in multiple single-unit re­cording and optical imaging techniques now routinely enable observation of the activi­ty from tens to hundreds of neurons simulta­neously. The result is high-dimensional mul­tivariate time series which offer an unprece­dented range of possibilities for gaining in­sight into the detailed spatio-temporal neu­ral dynamics underlying cognition. For in­stance, they may pave the way for reliable single-trial analyses, for investigating the role of higher-order correlations in neural coding, the mechanisms of neural ensemble forma­tion, or more generally of transitions among attractor states accompanying cognitive pro­cesses. At the same time, exploiting the infor­mation in these multivariate time series may require more sophisticated statistical meth­ods beyond the commonly employed rep­ertoire. Here we review, using specific ex­perimental examples, some of these meth­ods for visualizing structure in high-dimen­sional data sets, for statistical inference about the apparent structure, for single-trial analy­sis of neural time series, and for reconstruct­ing some of the dynamical properties of neu­ral systems that can only be inferred from si­multaneous recordings.

Statistical approaches for reconstructing neuro-cognitive dynamics from high-dimensional neural recordings