We present a variational Bayesian (VB) approach for the state and parameter inference of a state-space model with point-process observations, a physiologically plausible model for signal processing of spike data. We also give the derivation of a variational smoother, as well as an efficient online filtering algorithm, which can also be used to track changes in physiological parameters. The methods are assessed on simulated data, and results are compared to expectation-maximization, as well as Monte Carlo estimation techniques, in order to evaluate the accuracy of the proposed approach. The VB filter is further assessed on a data set of taste-response neural cells, showing that the proposed approach can effectively capture dynamical changes in neural responses in real time.
"This arises from the fact that parameter β appears in the likelihood only via the product β c x k , and the term α multiplies a binary stimulus that is nonzero only at sparse points in time. This makes α and β difficult to estimate, as Smith and Brown (2003) and Zammit Mangion et al. (2011) noted. In practice, we fix β c and σ 2 ε to ensure a strong, identifiable model, as with previous work. "
[Show abstract][Hide abstract] ABSTRACT: This letter considers how a number of modern Markov chain Monte Carlo (MCMC) methods can be applied for parameter estimation and inference in state-space models with point process observations. We quantified the efficiencies of these MCMC methods on synthetic data, and our results suggest that the Reimannian manifold Hamiltonian Monte Carlo method offers the best performance. We further compared such a method with a previously tested variational Bayes method on two experimental data sets. Results indicate similar performance on the large data sets and superior performance on small ones. The work offers an extensive suite of MCMC algorithms evaluated on an important class of models for physiological signal analysis.
[Show abstract][Hide abstract] ABSTRACT: Latent linear dynamical systems with generalised-linear observation models arise in a variety of applications, for instance when modelling the spiking activ-ity of populations of neurons. Here, we show how spectral learning methods (usually called subspace identification in this context) for linear systems with linear-Gaussian observations can be extended to estimate the parameters of a generalised-linear dynamical system model despite a non-linear and non-Gaussian observation process. We use this approach to obtain estimates of parameters for a dynamical model of neural population data, where the observed spike-counts are Poisson-distributed with log-rates determined by the latent dynamical process, possibly driven by external inputs. We show that the extended subspace identifica-tion algorithm is consistent and accurately recovers the correct parameters on large simulated data sets with a single calculation, avoiding the costly iterative compu-tation of approximate expectation-maximisation (EM). Even on smaller data sets, it provides an effective initialisation for EM, avoiding local optima and speeding convergence. These benefits are shown to extend to real neural data.
[Show abstract][Hide abstract] ABSTRACT: 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.
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