Point process filters have been applied successfully to decode neural signals and track neural dynamics. Traditionally these methods assume that multiunit spiking activity has already been correctly spike-sorted. As a result, these methods are not appropriate for situations where sorting cannot be performed with high precision, such as real-time decoding for brain-computer interfaces. Because the unsupervised spike-sorting problem remains unsolved, we took an alternative approach that takes advantage of recent insights into clusterless decoding. Here we present a new point process decoding algorithm that does not require multiunit signals to be sorted into individual units. We use the theory of marked point processes to construct a function that characterizes the relationship between a covariate of interest (in this case, the location of a rat on a track) and features of the spike waveforms. In our example, we use tetrode recordings, and the marks represent a four-dimensional vector of the maximum amplitudes of the spike waveform on each of the four electrodes. In general, the marks may represent any features of the spike waveform. We then use Bayes’s rule to estimate spatial location from hippocampal neural activity. We validate our approach with a simulation study and experimental data recorded in the hippocampus of a rat moving through a linear environment. Our decoding algorithm accurately reconstructs the rat’s position from unsorted multiunit spiking activity. We then compare the quality of our decoding algorithm to that of a traditional spike-sorting and decoding algorithm. Our analyses show that the proposed decoding algorithm performs equivalent to or better than algorithms based on sorted single-unit activity. These results provide a path toward accurate real-time decoding of spiking patterns that could be used to carry out content-specific manipulations of population activity in hippocampus or elsewhere in the brain.

Large data sets arising from neurophysiological experiments are frequently observed with repeating temporal patterns. Our ability to decode these patterns is dependent on the development of methods to assess whether the patterns are significant or occurring by chance. Given a hypothesized sequence within these data, we derive probability formulas to allow assessment of the likelihood of recurrence occurring by chance. We illustrate our approach using data from hippocampal neurons from awake, behaving rats.

Neural receptive fields are dynamic in that with experience, neurons change their spiking responses to relevant stimuli. To understand how neural systems adapt the irrepresentations of biological information, analyses of receptive field plasticity from experimental measurements are crucial. Adaptive signal processing, the well-established engineering discipline for characterizing the temporal evolution of system parameters, suggests a framework for studying the plasticity of receptive fields. We use the Bayes' rule Chapman-Kolmogorov paradigm with a linear state equation and point process observation models to derive adaptive filters appropriate for estimation from neural spike trains. We derive point process filter analogues of the Kalman filter, recursive least squares, and steepest-descent algorithms and describe the properties of these new fil-ters. We illustrate our algorithms in two simulated data examples. The first is a study of slow and rapid evolution of spatial receptive fields in hippocampal neurons. The second is an adaptive decoding study in which a signal is decoded from ensemble neural spiking activity as the recep-tive fields of the neurons in the ensemble evolve. Our results provide a paradigm for adaptive estimation for point process observations and suggest a practical approach for constructing filtering algorithms to track neural receptive field dynamics on a millisecond timescale.

Neural spike train decoding algorithms and techniques to compute Shan-non mutual information are important methods for analyzing how neural systems represent biological signals. Decoding algorithms are also one of several strategies being used to design controls for brain-machine inter-faces. Developing optimal strategies to desig n decoding algorithms and compute mutual information are therefore important problems in com-putational neuroscience. We present a general recursive filter decoding algorithm based on a point process model of individual neuron spiking activity and a linear stochastic state-space model of the biological signal. We derive from the algorithm new instantaneous estimates of the en-tropy, entropy rate, and the mutual information between the signal and the ensemble spiking activity. We assess the accuracy of the algorithm by computing, along with the decoding error, the true coverage probabil-ity of the approximate 0.95 confidence regions for the individual signal estimates. We illustrate the new algorithm by reanalyzing the position and ensemble neural spiking activity of CA1 hippocampal neurons from two rats foraging in an open circular environment. We compare the per-formance of this algorithm with a linear filter constructed by the widely used reverse correlation method. The median decoding error for Animal 1 (2) during 10 minutes of open foraging was 5.9 (5.5) cm, the median entropy was 6.9 (7.0) bits, the median information was 9.4 (9.4) bits, and the true coverage probability for 0.95 confidence regions was 0.67 (0.75) using 34 (32) neurons. These findings improve significantly on our pre-vious results and suggest an integrated approach to dynamically reading neural codes, measuring their properties, and quantifying the accuracy with which encoded information is extracted.

Measuring agreement between a statistical model and a spike train data series, that is, evaluating goodness of fit, is crucial for establishing the model's validity prior to using it to make inferences about a particular neural system. Assessing goodness-of-fit is a challenging problem for point process neural spike train models, especially for histogram-based models such as perstimulus time histograms (PSTH) and rate functions estimated by spike train smoothing. The time-rescaling theorem is a well-known result in probability theory, which states that any point process with an integrable conditional intensity function may be transformed into a Poisson process with unit rate. We describe how the theorem may be used to develop goodness-of-fit tests for both parametric and histogram-based point process models of neural spike trains. We apply these tests in two examples: a comparison of PSTH, inhomogeneous Poisson, and inhomogeneous Markov interval models of neural spike trains from the supplementary eye field of a macque monkey and a comparison of temporal and spatial smoothers, inhomogeneous Poisson, inhomogeneous gamma, and inhomogeneous inverse gaussian models of rat hippocampal place cell spiking activity. To help make the logic behind the time-rescaling theorem more accessible to researchers in neuroscience, we present a proof using only elementary probability theory arguments.We also show how the theorem may be used to simulate a general point process model of a spike train. Our paradigm makes it possible to compare parametric and histogram-based neural spike train models directly. These results suggest that the time-rescaling theorem can be a valuable tool for neural spike train data analysis.