Assessment of synchrony in multiple neural spike trains using loglinear point process models

Neural spike trains, which are sequences of very brief jumps in voltage across the cell membrane, were one of the motivating applications for the development of point process methodology. Early work required the assumption of stationarity, but contemporary experiments often use time-varying stimuli and produce time-varying neural responses. More recently, many statistical methods have been developed for nonstationary neural point process data. There has also been much interest in identifying synchrony, meaning events across two or more neurons that are nearly simultaneous at the time scale of the recordings. A natural statistical approach is to discretize time, using short time bins, and to introduce loglinear models for dependency among neurons, but previous use of loglinear modeling technology has assumed stationarity. We introduce a succinct yet powerful class of time-varying loglinear models by (a) allowing individual-neuron effects (main effects) to involve time-varying intensities; (b) also allowing the individual-neuron effects to involve autocovariation effects (history effects) due to past spiking, (c) assuming excess synchrony effects (interaction effects) do not depend on history, and (d) assuming all effects vary smoothly across time.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS429 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Extrinsic and Intrinsic Control of Integrative Processes in Neural Systems

At the simplest dynamical level, neurons can be understood as integrators. That is, neurons accumulate excitation from afferent neurons until, eventually, a threshold is reached and they produce a spike. Here, we consider the control of integrative processes in neural circuits in two contexts. First, we consider the problem of extrinsic neurocontrol, or modulating the spiking activity of neural circuits using stimulation, as is desired in a wide range of neural engineering applications. From a control-theoretic standpoint, such a problem presents several interesting nuances, including discontinuity in the dynamics due to the spiking process, and the technological limitations associated with underactuation (i.e., many neurons controlled by the same stimulation input). We consider these factors in a canonical problem of selective spiking, wherein a particular integrative neuron is controlled to a spike, while other neurons remain below threshold. This problem is solved in an optimal control framework, wherein several new geometric phenomena associated with the aforementioned nuances are revealed. Further, in an effort to enable scaling to large populations, we develop relaxations and alternative approaches, including the use of statistical models within the control design framework. Following this treatment of extrinsic control, we turn attention to a scientifically-driven question pertaining to intrinsic control, i.e., how neurons in the brain may themselves be controlling higher-level perceptual processes. We specifically postulate that neural activity is decoded, or “read-out” in terms of a drift-diffusion process, so that spiking activity drives a latent state towards a detection/perception threshold. Under this premise, we optimize the neural spiking trajectories according to several empirical cost functions and show that the optimal responses are physiologically plausible. In this vein, we also examine the nature of \u27optimal evidence\u27 for the general class of threshold-based integrative decision problems

Algorithms and inference for simultaneous-event multivariate point-process, with applications to neural data

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 115-118).The formulation of multivariate point-process (MPP) models based on the Jacod likelihood does not allow for simultaneous occurrence of events at an arbitrarily small time resolution. In this thesis, we introduce two versatile representations of a simultaneous event multivariate point-process (SEMPP) model to correct this important limitation. The first one maps an SEMPP into a higher-dimensional multivariate point-process with no simultaneities, and is accordingly termed the disjoint representation. The second one is a marked point-process representation of an SEMPP, which leads to new thinning and time-rescaling algorithms for simulating an SEMPP stochastic process. Starting from the likelihood of a discrete-time form of the disjoint representation, we present derivations of the continuous likelihoods of the disjoint and MkPP representations of SEMPPs. For static inference, we propose a parametrization of the likelihood of the disjoint representation in discrete-time which gives a multinomial generalized linear model (mGLM) algorithm for model fitting. For dynamic inference, we derive generalizations of point-process adaptive filters. The MPP time-rescaling theorem can be used to assess model goodness-of-fit. We illustrate the features of our SEMPP model by simulating SEMPP data and by analyzing neural spiking activity from pairs of simultaneously-recorded rat thalamic neurons stimulated by periodic whisker deflections. The SEMPP model demonstrates a strong effect of whisker motion on simultaneous spiking activity at the one millisecond time scale. Together, the MkPP representation of the SEMPP model, the mGLM and the MPP time-rescaling theorem offer a theoretically sound, practical tool for measuring joint spiking propensity in a neuronal ensemble.by Demba Ba.Ph.D