A common goodness-of-fit framework for neural population models using marked point process time-rescaling

A critical component of any statistical modeling procedure is the ability to assess the goodness-of-fit between a model and observed data. For spike train models of individual neurons, many goodness-of-fit measures rely on the time-rescaling theorem and assess model quality using rescaled spike times. Recently, there has been increasing interest in statistical models that describe the simultaneous spiking activity of neuron populations, either in a single brain region or across brain regions. Classically, such models have used spike sorted data to describe relationships between the identified neurons, but more recently clusterless modeling methods have been used to describe population activity using a single model. Here we develop a generalization of the time-rescaling theorem that enables comprehensive goodness-of-fit analysis for either of these classes of population models. We use the theory of marked point processes to model population spiking activity, and show that under the correct model, each spike can be rescaled individually to generate a uniformly distributed set of events in time and the space of spike marks. After rescaling, multiple well-established goodness-of-fit procedures and statistical tests are available. We demonstrate the application of these methods both to simulated data and real population spiking in rat hippocampus. We have made the MATLAB and Python code used for the analyses in this paper publicly available through our Github repository at https://github.com/Eden-Kramer-Lab/popTRT.This work was supported by grants from the NIH (MH105174, NS094288) and the Simons Foundation (542971). (MH105174 - NIH; NS094288 - NIH; 542971 - Simons Foundation)Published versio

Contributions to statistical analysis methods for neural spiking activity

With the technical advances in neuroscience experiments in the past few decades, we have seen a massive expansion in our ability to record neural activity. These advances enable neuroscientists to analyze more complex neural coding and communication properties, and at the same time, raise new challenges for analyzing neural spiking data, which keeps growing in scale, dimension, and complexity. This thesis proposes several new statistical methods that advance statistical analysis approaches for neural spiking data, including sequential Monte Carlo (SMC) methods for efficient estimation of neural dynamics from membrane potential threshold crossings, state-space models using multimodal observation processes, and goodness-of-fit analysis methods for neural marked point process models. In a first project, we derive a set of iterative formulas that enable us to simulate trajectories from stochastic, dynamic neural spiking models that are consistent with a set of spike time observations. We develop a SMC method to simultaneously estimate the parameters of the model and the unobserved dynamic variables from spike train data. We investigate the performance of this approach on a leaky integrate-and-fire model. In another project, we define a semi-latent state-space model to estimate information related to the phenomenon of hippocampal replay. Replay is a recently discovered phenomenon where patterns of hippocampal spiking activity that typically occur during exploration of an environment are reactivated when an animal is at rest. This reactivation is accompanied by high frequency oscillations in hippocampal local field potentials. However, methods to define replay mathematically remain undeveloped. In this project, we construct a novel state-space model that enables us to identify whether replay is occurring, and if so to estimate the movement trajectories consistent with the observed neural activity, and to categorize the content of each event. The state-space model integrates information from the spiking activity from the hippocampal population, the rhythms in the local field potential, and the rat's movement behavior. Finally, we develop a new, general time-rescaling theorem for marked point processes, and use this to develop a general goodness-of-fit framework for neural population spiking models. We investigate this approach through simulation and a real data application

Advances in point process modeling: feature selection, goodness-of-fit and novel applications

The research contained in this thesis extends multivariate marked point process modeling methods for neuroscience, generalizes goodness-of-fit techniques for the class of marked point processes, and introduces the use of a general history-dependent point process model to the domain of sleep apnea. Our first project involves further development of a modeling tool for spiking data from neural populations using the theory of marked point processes. This marked point process model uses features of spike waveforms as marks in order to estimate a state variable of interest. We examine the informational content of geometric features as well as principal components of the waveforms at hippocampal place cell activity by comparing decoding accuracies of a rat's position along a track. We determined that there was additional information available beyond that contained in traditional geometric features used for decoding in practice. The expanded use of this marked point process model in neuroscience necessitates corresponding goodness-of-fit protocols for the marked case. In our second project, we develop a generalized time-rescaling method for marked point processes that produces uniformly distributed spikes under a proper model. Once rescaled, the ground process then behaves as a Poisson process and can be analyzed using traditional point process goodness-of-fit methods. We demonstrate the method's ability to detect quality and manner of fit through both simulation and real neural data analysis. In the final project, we introduce history-dependent point process modeling as a superior method for characterizing severe sleep apnea over the current clinical standard known as the apnea-hypopnea index (AHI). We analyze model fits using combinations of both clinical covariates and event observations themselves through functions of history. Ultimately, apnea onset times were consistently estimated with significantly higher accuracy when history was incorporated alongside sleep stage. We present this method to the clinical audience as a means to gain detailed information on patterns of apnea and to provide more customized diagnoses and treatment prescriptions. These separate yet complementary projects extend existing point process modeling methods and further demonstrate their value in the neurosciences, sleep sciences, and beyond

Neuronal Spike Train Analysis in Likelihood Space

Conventional methods for spike train analysis are predominantly based on the rate function. Additionally, many experiments have utilized a temporal coding mechanism. Several techniques have been used for analyzing these two sources of information separately, but using both sources in a single framework remains a challenging problem. Here, an innovative technique is proposed for spike train analysis that considers both rate and temporal information.Point process modeling approach is used to estimate the stimulus conditional distribution, based on observation of repeated trials. The extended Kalman filter is applied for estimation of the parameters in a parametric model. The marked point process strategy is used in order to extend this model from a single neuron to an entire neuronal population. Each spike train is transformed into a binary vector and then projected from the observation space onto the likelihood space. This projection generates a newly structured space that integrates temporal and rate information, thus improving performance of distribution-based classifiers. In this space, the stimulus-specific information is used as a distance metric between two stimuli. To illustrate the advantages of the proposed technique, spiking activity of inferior temporal cortex neurons in the macaque monkey are analyzed in both the observation and likelihood spaces. Based on goodness-of-fit, performance of the estimation method is demonstrated and the results are subsequently compared with the firing rate-based framework.From both rate and temporal information integration and improvement in the neural discrimination of stimuli, it may be concluded that the likelihood space generates a more accurate representation of stimulus space. Further, an understanding of the neuronal mechanism devoted to visual object categorization may be addressed in this framework as well

Bayesian decoding of tactile afferents responsible for sensorimotor control

In daily activities, humans manipulate objects and do so with great precision. Empirical studies have demonstrated that signals encoded by mechanoreceptors facilitate the precise object manipulation in humans, however, little is known about the underlying mechanisms. Models used in literature to analyze tactile afferent data range from advanced—for example some models account for skin tissue properties—to simple regression fit. These models, however, do not systematically account for factors that influence tactile afferent activity. For instance, it is not yet clear whether the first derivative of force influences the observed tactile afferent spike train patterns. In this study, I use the technique of microneurography—with the help of Dr. Birznieks—to record tactile afferent data from humans. I then implement spike sorting algorithms to identify spike occurrences that pertain to a single cell. For further analyses of the resulting spike trains, I use a Bayesian decoding framework to investigate tactile afferent mechanisms that are responsible for sensorimotor control in humans. The Bayesian decoding framework I implement is a two stage process where in a first stage (encoding model) the relationships between the administered stimuli and the recorded tactile afferent signals is established, and a second stage uses results based on the first stage to make predictions. The goal of encoding model is to increase our understanding of the mechanisms that underlie dexterous object manipulation and, from an engineering perspective, guide the design of algorithms for inferring stimulus from previously unseen tactile afferent data, a process referred to as decoding. Specifically, the objective of the study was to devise quantitative methods that would provide insight into some mechanisms that underlie touch, as well as provide strategies through which real-time biomedical devices can be realized. Tactile afferent data from eight subjects (18 - 30 years) with no known form of neurological disorders were recorded by inserting a needle electrode in the median nerve at the wrist. I was involved in designing experimental protocols, designing mechanisms that were put in place for safety measures, designing and building electronic components as needed, experimental setup, subject recruitment, and data acquisition. Dr. Ingvars Birznieks (performed the actual microneurography procedure by inserting a needle electrode into the nerve and identifying afferent types) and Dr. Heba Khamis provided assistance with the data acquisition and experimental design. The study took place at Neuroscience Research Australia (NeuRA). Once the data were acquired, I analyzed the data recorded from slowly adapting type I tactile afferents (SA-I). The initial stages of data analysis involved writing software routines to spike sort the data (identify action potential waveforms that pertain to individual cells). I analyzed SA-I tactile afferents because they were more numerous (it was difficult to target other types of afferents during experiments). In addition, SA-I tactile afferents respond during both the dynamic and the static phase of a force stimulus. Since they respond during both the dynamic and static phases of the force stimulus, it seemed reasonable to hypothesize that SA-I’s alone could provide sufficient information for predicting the force profile, given spike data. In the first stage, I used an inhomogeneous Poisson process encoding model through which I assessed the relative importance of aspects of the stimuli to observed spike data. In addition I estimated the likelihood for SA-I data given the inhomogeneous Poisson model, which was used during the second stage. The likelihood is formulated by deriving the joint distribution of the data, as a function of the model parameters with the data fixed. In the second stage, I used a recursive nonlinear Bayesian filter to reconstruct the force profile, given the SA-I spike patterns. Moreover, the decoding method implemented in this thesis is feasible for real-time applications such as interfacing with prostheses because it can be realized with readily available electronic components. I also implemented a renewal point process encoding model—as a generalization of the Poisson process encoding model—which can account for some history dependence properties of neural data. I discovered that under my encoding model, the relative contributions of the force and its derivative are 1.26 and 1.02, respectively. This suggests that the force derivative contributes significantly to the spiking behavior of SA-I tactile afferents. This is a novel contribution because it provides a quantitative result to the long standing question of whether the force derivative contributes towards SA-I tactile afferent spiking behavior. As a result, I incorporated the first derivative of force, along with the force, in the encoding models I implemented in this thesis. The decoding model shows that SA-I fibers provide sufficient information for an approximation of the force profile. Furthermore, including fast adapting tactile afferents would provide better information about the first moment of contact and last moment of contact, and thus improved decoding results. Finally I show that a renewal point process encoding model captures interspike time and stimulus features better than an inhomogeneous Poisson point process encoding model. This is useful because it is now possible to generate synthetic data with statistical structure that is similar to real SA-I data: This would enable further investigations of mechanisms that underlie SA-I tactile afferents

Intrinsic gain modulation and adaptive neural coding

In many cases, the computation of a neural system can be reduced to a receptive field, or a set of linear filters, and a thresholding function, or gain curve, which determines the firing probability; this is known as a linear/nonlinear model. In some forms of sensory adaptation, these linear filters and gain curve adjust very rapidly to changes in the variance of a randomly varying driving input. An apparently similar but previously unrelated issue is the observation of gain control by background noise in cortical neurons: the slope of the firing rate vs current (f-I) curve changes with the variance of background random input. Here, we show a direct correspondence between these two observations by relating variance-dependent changes in the gain of f-I curves to characteristics of the changing empirical linear/nonlinear model obtained by sampling. In the case that the underlying system is fixed, we derive relationships relating the change of the gain with respect to both mean and variance with the receptive fields derived from reverse correlation on a white noise stimulus. Using two conductance-based model neurons that display distinct gain modulation properties through a simple change in parameters, we show that coding properties of both these models quantitatively satisfy the predicted relationships. Our results describe how both variance-dependent gain modulation and adaptive neural computation result from intrinsic nonlinearity.Comment: 24 pages, 4 figures, 1 supporting informatio

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

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

Point process modeling as a framework to dissociate intrinsic and extrinsic components in neural systems

Understanding the factors shaping neuronal spiking is a central problem in neuroscience. Neurons may have complicated sensitivity and, often, are embedded in dynamic networks whose ongoing activity may influence their likelihood of spiking. One approach to characterizing neuronal spiking is the point process generalized linear model (GLM), which decomposes spike probability into explicit factors. This model represents a higher level of abstraction than biophysical models, such as Hodgkin-Huxley, but benefits from principled approaches for estimation and validation. Here we address how to infer factors affecting neuronal spiking in different types of neural systems. We first extend the point process GLM, most commonly used to analyze single neurons, to model population-level voltage discharges recorded during human seizures. Both GLMs and descriptive measures reveal rhythmic bursting and directional wave propagation. However, we show that GLM estimates account for covariance between these features in a way that pairwise measures do not. Failure to account for this covariance leads to confounded results. We interpret the GLM results to speculate the mechanisms of seizure and suggest new therapies. The second chapter highlights flexibility of the GLM. We use this single framework to analyze enhancement, a statistical phenomenon, in three distinct systems. Here we define the enhancement score, a simple measure of shared information between spike factors in a GLM. We demonstrate how to estimate the score, including confidence intervals, using simulated data. In real data, we find that enhancement occurs prominently during human seizure, while redundancy tends to occur in mouse auditory networks. We discuss implications for physiology, particularly during seizure. In the third part of this thesis, we apply point process modeling to spike trains recorded from single units in vitro under external stimulation. We re-parameterize models in a low-dimensional and physically interpretable way; namely, we represent their effects in principal component space. We show that this approach successfully separates the neurons observed in vitro into different classes consistent with their gene expression profiles. Taken together, this work contributes a statistical framework for analyzing neuronal spike trains and demonstrates how it can be applied to create new insights into clinical and experimental data sets