Particle-filtering approaches for nonlinear Bayesian decoding of neuronal spike trains

The number of neurons that can be simultaneously recorded doubles every seven years. This ever increasing number of recorded neurons opens up the possibility to address new questions and extract higher dimensional stimuli from the recordings. Modeling neural spike trains as point processes, this task of extracting dynamical signals from spike trains is commonly set in the context of nonlinear filtering theory. Particle filter methods relying on importance weights are generic algorithms that solve the filtering task numerically, but exhibit a serious drawback when the problem dimensionality is high: they are known to suffer from the 'curse of dimensionality' (COD), i.e. the number of particles required for a certain performance scales exponentially with the observable dimensions. Here, we first briefly review the theory on filtering with point process observations in continuous time. Based on this theory, we investigate both analytically and numerically the reason for the COD of weighted particle filtering approaches: Similarly to particle filtering with continuous-time observations, the COD with point-process observations is due to the decay of effective number of particles, an effect that is stronger when the number of observable dimensions increases. Given the success of unweighted particle filtering approaches in overcoming the COD for continuous- time observations, we introduce an unweighted particle filter for point-process observations, the spike-based Neural Particle Filter (sNPF), and show that it exhibits a similar favorable scaling as the number of dimensions grows. Further, we derive rules for the parameters of the sNPF from a maximum likelihood approach learning. We finally employ a simple decoding task to illustrate the capabilities of the sNPF and to highlight one possible future application of our inference and learning algorithm

Neural decoding with visual attention using sequential Monte Carlo for leaky integrate-and-fire neurons

How the brain makes sense of a complicated environment is an important question, and a first step is to be able to reconstruct the stimulus that give rise to an observed brain response. Neural coding relates neurobiological observations to external stimuli using computational methods. Encoding refers to how a stimulus affects the neuronal output, and entails constructing a neural model and parameter estimation. Decoding refers to reconstruction of the stimulus that led to a given neuronal output. Existing decoding methods rarely explain neuronal responses to complicated stimuli in a principled way. Here we perform neural decoding for a mixture of multiple stimuli using the leaky integrate-and-fire model describing neural spike trains, under the visual attention hypothesis of probability mixing in which the neuron only attends to a single stimulus at any given time. We assume either a parallel or serial processing visual search mechanism when decoding multiple simultaneous neurons. We consider one or multiple stochastic stimuli following Ornstein-Uhlenbeck processes, and dynamic neuronal attention that switches following discrete Markov processes. To decode stimuli in such situations, we develop various sequential Monte Carlo particle methods in different settings. The likelihood of the observed spike trains is obtained through the first-passage time probabilities obtained by solving the Fokker-Planck equations. We show that the stochastic stimuli can be successfully decoded by sequential Monte Carlo, and different particle methods perform differently considering the number of observed spike trains, the number of stimuli, model complexity, etc. The proposed novel decoding methods, which analyze the neural data through psychological visual attention theories, provide new perspectives to understand the brain

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

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

Neurons with stereotyped and rapid responses provide a reference frame for relative temporal coding in primate auditory cortex

The precise timing of spikes of cortical neurons relative to stimulus onset carries substantial sensory information. To access this information the sensory systems would need to maintain an internal temporal reference that reflects the precise stimulus timing. Whether and how sensory systems implement such reference frames to decode time-dependent responses, however, remains debated. Studying the encoding of naturalistic sounds in primate (Macaca mulatta) auditory cortex we here investigate potential intrinsic references for decoding temporally precise information. Within the population of recorded neurons, we found one subset responding with stereotyped fast latencies that varied little across trials or stimuli, while the remaining neurons had stimulus-modulated responses with longer and variable latencies. Computational analysis demonstrated that the neurons with stereotyped short latencies constitute an effective temporal reference for relative coding. Using the response onset of a simultaneously recorded stereotyped neuron allowed decoding most of the stimulus information carried by onset latencies and the full spike train of stimulus-modulated neurons. Computational modeling showed that few tens of such stereotyped reference neurons suffice to recover nearly all information that would be available when decoding the same responses relative to the actual stimulus onset. These findings reveal an explicit neural signature of an intrinsic reference for decoding temporal response patterns in the auditory cortex of alert animals. Furthermore, they highlight a role for apparently unselective neurons as an early saliency signal that provides a temporal reference for extracting stimulus information from other neurons