Rescaling, thinning or complementing? On goodness-of-fit procedures for point process models and Generalized Linear Models

Generalized Linear Models (GLMs) are an increasingly popular framework for modeling neural spike trains. They have been linked to the theory of stochastic point processes and researchers have used this relation to assess goodness-of-fit using methods from point-process theory, e.g. the time-rescaling theorem. However, high neural firing rates or coarse discretization lead to a breakdown of the assumptions necessary for this connection. Here, we show how goodness-of-fit tests from point-process theory can still be applied to GLMs by constructing equivalent surrogate point processes out of time-series observations. Furthermore, two additional tests based on thinning and complementing point processes are introduced. They augment the instruments available for checking model adequacy of point processes as well as discretized models.Comment: 9 pages, to appear in NIPS 2010 (Neural Information Processing Systems), corrected missing referenc

Extraction of Network Topology From Multi-Electrode Recordings: Is there a Small-World Effect?

The simultaneous recording of the activity of many neurons poses challenges for multivariate data analysis. Here, we propose a general scheme of reconstruction of the functional network from spike train recordings. Effective, causal interactions are estimated by fitting generalized linear models on the neural responses, incorporating effects of the neurons’ self-history, of input from other neurons in the recorded network and of modulation by an external stimulus. The coupling terms arising from synaptic input can be transformed by thresholding into a binary connectivity matrix which is directed. Each link between two neurons represents a causal influence from one neuron to the other, given the observation of all other neurons from the population. The resulting graph is analyzed with respect to small-world and scale-free properties using quantitative measures for directed networks. Such graph-theoretic analyses have been performed on many complex dynamic networks, including the connectivity structure between different brain areas. Only few studies have attempted to look at the structure of cortical neural networks on the level of individual neurons. Here, using multi-electrode recordings from the visual system of the awake monkey, we find that cortical networks lack scale-free behavior, but show a small, but significant small-world structure. Assuming a simple distance-dependent probabilistic wiring between neurons, we find that this connectivity structure can account for all of the networks’ observed small-world ness. Moreover, for multi-electrode recordings the sampling of neurons is not uniform across the population. We show that the small-world-ness obtained by such a localized sub-sampling overestimates the strength of the true small-world structure of the network. This bias is likely to be present in all previous experiments based on multi-electrode recordings

Establishing a Statistical Link between Network Oscillations and Neural Synchrony

Pairs of active neurons frequently fire action potentials or “spikes” nearly synchronously (i.e., within 5 ms of each other). This spike synchrony may occur by chance, based solely on the neurons’ fluctuating firing patterns, or it may occur too frequently to be explicable by chance alone. When spike synchrony above chances levels is present, it may subserve computation for a specific cognitive process, or it could be an irrelevant byproduct of such computation. Either way, spike synchrony is a feature of neural data that should be explained. A point process regression framework has been developed previously for this purpose, using generalized linear models (GLMs). In this framework, the observed number of synchronous spikes is compared to the number predicted by chance under varying assumptions about the factors that affect each of the individual neuron’s firing-rate functions. An important possible source of spike synchrony is network-wide oscillations, which may provide an essential mechanism of network information flow. To establish the statistical link between spike synchrony and network-wide oscillations, we have integrated oscillatory field potentials into our point process regression framework. We first extended a previously-published model of spike-field association and showed that we could recover phase relationships between oscillatory field potentials and firing rates. We then used this new framework to demonstrate the statistical relationship between oscillatory field potentials and spike synchrony in: 1) simulated neurons, 2) in vitro recordings of hippocampal CA1 pyramidal cells, and 3) in vivo recordings of neocortical V4 neurons. Our results provide a rigorous method for establishing a statistical link between network oscillations and neural synchrony

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

Informační procesy v neuronech

Neurony spolu komunikují pomocí posloupností akčních potenciálů. Celý tento proces může být popsán detailními biochemickými modely membrány a iontových kanálů na neuronu nebo jednoduššími fenomenologickými mo- dely (typickým představitelem jsou tzv. "integrate-and-fire" modely) nebo případně ještě více abstraktními modely sledu akčních potenciálů bez při- hlédnutí k dynamice membrány neuronu. Vybrali jsme konkrétní variantu stochastického "leaky integrate-and-fire" modelu a porovnali jí s aktivitou biologického neuronu (nitrobuněčný zá- znam pořízený in-vivo). Provedli jsme statistický odhad parametrů modelu a na základě počítačových simulací úspěšně srovnali modelovaný záznam se záznamem z reálného neuronu. Při abstraktnější úrovni popisu je sled akčních potenciálů analyzován pouze jako množina bodových událostí v čase a základní otázka zní, jakým způsobem je vnější podnět kódován v zaznamenané posloupnosti akčních po- tenciálů. Bylo navrženo mnoho odlišných kódů pro řešení rozmanitých úloh v neuronových sítích. My jsme se zaměřili na otevřený problém neuronál- ního kódu v úloze prostorového slyšení u savců. V současnosti je zvažováno několik teorií vysvětlujících experimentální nálezy. V naší práci navrhujeme specifickou variantu modelu založeného na frekvenčním kódu. Zkonstruovaný neuronový obvod,...Neurons communicate by action potentials. This process can be described by very detailed biochemical models of neuronal membrane and its channels, or by simpler phenomenological models of membrane potential (integrate-and- fire models) or even by very abstract models when only time of spikes are considered. We took one particular description - stochastic leaky integrate-and-fire model - and compared it with recorded in-vivo intracellular activity of the neuron. We estimated parameters of this model, compared how the model simulation corresponds with a real neuron. It can be concluded that the data are generally consistent with the model. At a more abstract level of description, the spike trains are analyzed without considering exact membrane voltage and one asks how the external stimulus is encoded in the spike train emitted by neurons. There are many neuronal codes described in literature and we focused on the open problem of neural code responsible for spatial hearing in mammals. Several theories explaining the experimental findings have been proposed and we suggest a specific variant of so called slope-encoding model. Neuronal circuit mimick- ing auditory pathway up to the first binaural neuron was constructed and experimental results were reproduced. Finally, we estimated the minimal number of such...First Faculty of Medicine1. lékařská fakult

Multivariate Multiscale Analysis of Neural Spike Trains

This dissertation introduces new methodologies for the analysis of neural spike trains. Biological properties of the nervous system, and how they are reflected in neural data, can motivate specific analytic tools. Some of these biological aspects motivate multiscale frameworks, which allow for simultaneous modelling of the local and global behaviour of neurons. Chapter 1 provides the preliminary background on the biology of the nervous system and details the concept of information and randomness in the analysis of the neural spike trains. It also provides the reader with a thorough literature review on the current statistical models in the analysis of neural spike trains. The material presented in the next six chapters (2-7) have been the focus of three papers, which have either already been published or are being prepared for publication. It is demonstrated in Chapters 2 and 3 that the multiscale complexity penalized likelihood method, introduced in Kolaczyk and Nowak (2004), is a powerful model in the simultaneous modelling of spike trains with biological properties from different time scales. To detect the periodic spiking activities of neurons, two periodic models from the literature, Bickel et al. (2007, 2008); Shao and Li (2011), were combined and modified in a multiscale penalized likelihood model. The contributions of these chapters are (1) employinh a powerful visualization tool, inter-spike interval (ISI) plot, (2) combining the multiscale method of Kolaczyk and Nowak (2004) with the periodic models ofBickel et al. (2007, 2008) and Shao and Li (2011), to introduce the so-called additive and multiplicative models for the intensity function of neural spike trains and introducing a cross-validation scheme to estimate their tuning parameters, (3) providing the numerical bootstrap confidence bands for the multiscale estimate of the intensity function, and (4) studying the effect of time-scale on the statistical properties of spike counts. Motivated by neural integration phenomena, as well as the adjustments for the neural refractory period, Chapters 4 and 5 study the Skellam process and introduce the Skellam Process with Resetting (SPR). Introducing SPR and its application in the analysis of neural spike trains is one of the major contributions of this dissertation. This stochastic process is biologically plausible, and unlike the Poisson process, it does not suffer from limited dependency structure. It also has multivariate generalizations for the simultaneous analysis of multiple spike trains. A computationally efficient recursive algorithm for the estimation of the parameters of SPR is introduced in Chapter 5. Except for the literature review at the beginning of Chapter 4, the rest of the material within these two chapters is original. The specific contributions of Chapters 4 and 5 are (1) introducing the Skellam Process with Resetting as a statistical tool to analyze neural spike trains and studying its properties, including all theorems and lemmas provided in Chapter 4, (2) the two fairly standard definitions of the Skellam process (homogeneous and inhomogeneous) and the proof of their equivalency, (3) deriving the likelihood function based on the observable data (spike trains) and developing a computationally efficient recursive algorithm for parameter estimation, and (4) studying the effect of time scales on the SPR model. The challenging problem of multivariate analysis of the neural spike trains is addressed in Chapter 6. As far as we know, the multivariate models which are available in the literature suffer from limited dependency structures. In particular, modelling negative correlation among spike trains is a challenging problem. To address this issue, the multivariate Skellam distribution, as well as the multivariate Skellam process, which both have flexible dependency structures, are developed. Chapter 5 also introduces a multivariate version of Skellam Process with Resetting (MSPR), and a so-called profile-moment likelihood estimation of its parameters. This chapter generalizes the results of Chapter 4 and 5, and therefore, except for the brief literature review provided at the beginning of the chapter, the remainder of the material is original work. In particular, the contributions of this chapter are (1) introducing multivariate Skellam distribution, (2) introducing two definitions of the Multivariate Skellam process in both homogeneous and inhomogeneous cases and proving their equivalence, (3) introducing Multivariate Skellam Process with Resetting (MSPR) to simultaneously model spike trains from an ensemble of neurons, and (4) utilizing the so-called profile-moment likelihood method to compute estimates of the parameters of MSPR. The discussion of the developed methodologies as well as the ``next steps'' are outlined in Chapter 7