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

A Nonparametric Bayesian Approach to Uncovering Rat Hippocampal Population Codes During Spatial Navigation

Rodent hippocampal population codes represent important spatial information about the environment during navigation. Several computational methods have been developed to uncover the neural representation of spatial topology embedded in rodent hippocampal ensemble spike activity. Here we extend our previous work and propose a nonparametric Bayesian approach to infer rat hippocampal population codes during spatial navigation. To tackle the model selection problem, we leverage a nonparametric Bayesian model. Specifically, to analyze rat hippocampal ensemble spiking activity, we apply a hierarchical Dirichlet process-hidden Markov model (HDP-HMM) using two Bayesian inference methods, one based on Markov chain Monte Carlo (MCMC) and the other based on variational Bayes (VB). We demonstrate the effectiveness of our Bayesian approaches on recordings from a freely-behaving rat navigating in an open field environment. We find that MCMC-based inference with Hamiltonian Monte Carlo (HMC) hyperparameter sampling is flexible and efficient, and outperforms VB and MCMC approaches with hyperparameters set by empirical Bayes

Neural activity classification with machine learning models trained on interspike interval series data

The flow of information through the brain is reflected by the activity patterns of neural cells. Indeed, these firing patterns are widely used as input data to predictive models that relate stimuli and animal behavior to the activity of a population of neurons. However, relatively little attention was paid to single neuron spike trains as predictors of cell or network properties in the brain. In this work, we introduce an approach to neuronal spike train data mining which enables effective classification and clustering of neuron types and network activity states based on single-cell spiking patterns. This approach is centered around applying state-of-the-art time series classification/clustering methods to sequences of interspike intervals recorded from single neurons. We demonstrate good performance of these methods in tasks involving classification of neuron type (e.g. excitatory vs. inhibitory cells) and/or neural circuit activity state (e.g. awake vs. REM sleep vs. nonREM sleep states) on an open-access cortical spiking activity dataset

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

Point process modeling and estimation: advances in the analysis of dynamic neural spiking data

A common interest of scientists in many fields is to understand the relationship between the dynamics of a physical system and the occurrences of discrete events within such physical system. Seismologists study the connection between mechanical vibrations of the Earth and the occurrences of earthquakes so that future earthquakes can be better predicted. Astrophysicists study the association between the oscillating energy of celestial regions and the emission of photons to learn the Universe's various objects and their interactions. Neuroscientists study the link between behavior and the millisecond-timescale spike patterns of neurons to understand higher brain functions. Such relationships can often be formulated within the framework of state-space models with point process observations. The basic idea is that the dynamics of the physical systems are driven by the dynamics of some stochastic state variables and the discrete events we observe in an interval are noisy observations with distributions determined by the state variables. This thesis proposes several new methodological developments that advance the framework of state-space models with point process observations at the intersection of statistics and neuroscience. In particular, we develop new methods 1) to characterize the rhythmic spiking activity using history-dependent structure, 2) to model population spike activity using marked point process models, 3) to allow for real-time decision making, and 4) to take into account the need for dimensionality reduction for high-dimensional state and observation processes. We applied these methods to a novel problem of tracking rhythmic dynamics in the spiking of neurons in the subthalamic nucleus of Parkinson's patients with the goal of optimizing placement of deep brain stimulation electrodes. We developed a decoding algorithm that can make decision in real-time (for example, to stimulate the neurons or not) based on various sources of information present in population spiking data. Lastly, we proposed a general three-step paradigm that allows us to relate behavioral outcomes of various tasks to simultaneously recorded neural activity across multiple brain areas, which is a step towards closed-loop therapies for psychological diseases using real-time neural stimulation. These methods are suitable for real-time implementation for content-based feedback experiments