False discovery rate regression: an application to neural synchrony detection in primary visual cortex

Many approaches for multiple testing begin with the assumption that all tests in a given study should be combined into a global false-discovery-rate analysis. But this may be inappropriate for many of today's large-scale screening problems, where auxiliary information about each test is often available, and where a combined analysis can lead to poorly calibrated error rates within different subsets of the experiment. To address this issue, we introduce an approach called false-discovery-rate regression that directly uses this auxiliary information to inform the outcome of each test. The method can be motivated by a two-groups model in which covariates are allowed to influence the local false discovery rate, or equivalently, the posterior probability that a given observation is a signal. This poses many subtle issues at the interface between inference and computation, and we investigate several variations of the overall approach. Simulation evidence suggests that: (1) when covariate effects are present, FDR regression improves power for a fixed false-discovery rate; and (2) when covariate effects are absent, the method is robust, in the sense that it does not lead to inflated error rates. We apply the method to neural recordings from primary visual cortex. The goal is to detect pairs of neurons that exhibit fine-time-scale interactions, in the sense that they fire together more often than expected due to chance. Our method detects roughly 50% more synchronous pairs versus a standard FDR-controlling analysis. The companion R package FDRreg implements all methods described in the paper

A Semiparametric Bayesian Model for Detecting Synchrony Among Multiple Neurons

We propose a scalable semiparametric Bayesian model to capture dependencies among multiple neurons by detecting their co-firing (possibly with some lag time) patterns over time. After discretizing time so there is at most one spike at each interval, the resulting sequence of 1's (spike) and 0's (silence) for each neuron is modeled using the logistic function of a continuous latent variable with a Gaussian process prior. For multiple neurons, the corresponding marginal distributions are coupled to their joint probability distribution using a parametric copula model. The advantages of our approach are as follows: the nonparametric component (i.e., the Gaussian process model) provides a flexible framework for modeling the underlying firing rates; the parametric component (i.e., the copula model) allows us to make inference regarding both contemporaneous and lagged relationships among neurons; using the copula model, we construct multivariate probabilistic models by separating the modeling of univariate marginal distributions from the modeling of dependence structure among variables; our method is easy to implement using a computationally efficient sampling algorithm that can be easily extended to high dimensional problems. Using simulated data, we show that our approach could correctly capture temporal dependencies in firing rates and identify synchronous neurons. We also apply our model to spike train data obtained from prefrontal cortical areas in rat's brain

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

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

Discriminación de estados mentales mediante la extracción de patrones espaciales bajo restricciones de no estacionariedad e independencia de sujeto

graficas, tablasEvaluation of brain dynamics elicited by motor imagery (MI) tasks can contribute to clinical and learning applications. In this work, we propose four specific improvements for brain motor intention response analysis based on EEG recordings by considering the nonstationarity, nonlinearity of brain signals, inter- and intra-subject variability, aimed to provide physiological interpretability and the distintiveness between subjects neural response. Firstly, to build up the subject-level feature framework, a common representational space, is proposed that encodes the electrode (spatial) contribution, evolving through time and frequency domains. Three feature extraction methods were compared, providing insight into the possible limitations. Secondly, we present an Entropy-based method, termed \textit{VQEnt}, for estimation of ERD/S using quantized stochastic patterns as a symbolic space, aiming to improve their discriminability and physiological interpretability. The proposed method builds the probabilistic priors by assessing the Gaussian similarity between the input measured data and their reduced vector-quantized representation. The validating results of a bi-class imagine task database (left and right hand) prove that \textit{VQEnt} holds symbols that encode several neighboring samples, providing similar or even better accuracy than the other baseline sample-based algorithms of Entropy estimation. Besides, the performed ERD/S time-series are close enough to the trajectories extracted by the variational percentage of EEG signal power and fulfill the physiological MI paradigm. In BCI literate individuals, the \textit{VQEnt} estimator presents the most accurate outcomes at a lower amount of electrodes placed in the sensorimotor cortex so that reduced channel set directly involved with the MI paradigm is enough to discriminate between tasks, providing an accuracy similar to the performed by the whole electrode set. Thirdly, multi-subject analysis is to make inferences on the group/population level about the properties of MI brain activity. However, intrinsic neurophysiological variability of neural dynamics poses a challenge for devising efficient MI systems. Here, we develop a \textit{time-frequency} model for estimating the spatial relevance of common neural activity across subjects employing an introduced statistical thresholding rule. In deriving multi-subject spatial maps, we present a comparative analysis of three feature extraction methods: \textit{Common Spatial Patterns}, \textit{Functional Connectivity}, and \textit{Event-Related De/Synchronization}. In terms of interpretability, we evaluate the effectiveness in gathering MI data from collective populations by introducing two assumptions: \textit{i}) Non-linear assessment of the similarity between multi-subject data originating the subject-level dynamics; \textit{ii}) Assessment of time-varying brain network responses according to the ranking of individual accuracy performed in distinguishing distinct motor imagery tasks (left-hand versus right-hand). The obtained validation results indicate that the estimated collective dynamics differently reflect the flow of sensorimotor cortex activation, providing new insights into the evolution of MI responses. Lastly, we develop a data-driven estimator, termed {Deep Regression Network} (DRN), which jointly extracts and performs the regression analysis in order to assess the efficiency of the individual brain networks in practicing MI tasks. The proposed double-stage estimator initially learns a pool of deep patterns, extracted from the input data, in order to feed a neural regression model, allowing for infering the distinctiveness between subject assemblies having similar variability. The results, which were obtained on real-world MI data, prove that the DRN estimator fosters pre-training neural desynchronization and initial training synchronization to predict the bi-class accuracy response, thus providing a better understanding of the Brain--Computer Interface inefficiency of subjects. (Texto tomado de la fuente)La evaluación de la dinámica cerebral provocada por las tareas de imaginación motora (\textit{Motor Imagery - MI}) puede contribuir al desarrollo de aplicaciones clínicas y de aprendizaje. En este trabajo, se proponen cuatro mejoras específicas para el an\'lisis de la respuesta de la intención motora cerebral basada en registros de Electroencefalografía (EEG) al considerar la no estacionariedad, la no linealidad de las se\tilde{n}ales cerebrales y la variabilidad inter e intrasujeto, con el objetivo de proporcionar interpretabilidad fisiológica y la discriminación entre la respuesta neuronal de los sujetos. En primer lugar, para construir el marco de características a nivel de sujeto, se propone un espacio de representación común que codifica la contribución del electrodo (espacial) y como esta evoluciona a través de los dominios de tiempo y frecuencia. Tres métodos de extracción de características fueron comparados, proporcionando información sobre las posibles limitaciones. En segundo lugar, se presenta un método basado en Entropía, denominado \textit{VQEnt}, para la estimación de la desincronización relacionada a eventos (\textit{Event-Related De-Synchronization - ERD/S}) utilizando patrones estocásticos cuantificados en un espacio simbólico, con el objetivo de mejorar su discriminabilidad e interpretabilidad fisiol\'gica. El método propuesto construye los antecedentes probabilísticos mediante la evaluación de la similitud gaussiana entre los datos medidos de entrada y su representación cuantificada vectorial reducida. Los resultados de validación en una base de datos de tareas de imaginación bi-clase (mano izquierda y mano derecha) prueban que \textit{VQEnt} contiene símbolos que codifican varias muestras vecinas, proporcionando una precisión similar o incluso mejor que los otros algoritmos basados en estimación de entropía de referencia. Además, las series temporales de ERD/S calculadas son lo suficientemente cercanas a las trayectorias extraídas por el porcentaje de variación de la potencia de la señal EEG y cumplen con el paradigma fisiológico de MI. En individuos alfabetizados en BCI, el estimador \textit{VQEnt} presenta los resultados precisos con una menor cantidad de electrodos colocados en la corteza sensoriomotora, de modo que el conjunto reducido de canales directamente involucrados con el paradigma MI es suficiente para discriminar entre tareas. En tercer lugar, el análisis multisujeto consiste en hacer inferencias a nivel de grupo/población sobre las propiedades de la actividad cerebral de la imaginación motora. Sin embargo, la variabilidad neurofisiológica intrínseca de la dinámica neuronal plantea un desafío para el diseño de sistemas MI eficientes. En este sentido, se presenta un modelo de \textit{tiempo-frecuencia} para estimar la relevancia espacial de la actividad neuronal común entre sujetos empleando una regla de umbral estadística que deriva en mapas espaciales de múltiples sujetos. Se presenta un análisis comparativo de tres métodos de extracción de características: \textit{Patrones espaciales comunes}, \textit{Conectividad funcional} y \textit{De-sincronización relacionada con eventos}. En términos de interpretabilidad, evaluamos la efectividad en la recopilación de datos de MI para multisujetos mediante la introducción de dos suposiciones: \textit{i}) Evaluación no lineal de la similitud entre los datos de múltiples sujetos que originan la dinámica a nivel de sujeto; \textit{ii}) Evaluación de las respuestas de la red cerebral que varían en el tiempo de acuerdo con la clasificación de la precisión individual realizada al distinguir distintas tareas de imaginación motora (mano izquierda versus mano derecha). Los resultados de validación obtenidos indican que la dinámica colectiva estimada refleja de manera diferente el flujo de activación de la corteza sensoriomotora, lo que proporciona nuevos conocimientos sobre la evolución de las respuestas de MI. Por último, se muestra un estimador denominado {Red de regresión profunda} (\textit{Deep Regression Network - DRN}), que extrae y realiza conjuntamente un análisis de regresión para evaluar la eficiencia de las redes cerebrales individuales, de cada sujeto, en la práctica de tareas de MI. El estimador de doble etapa propuesto inicialmente aprende un conjunto de patrones profundos, extraídos de los datos de entrada, para alimentar un modelo de regresión neuronal, lo que permite inferir la distinción entre conjuntos de sujetos que tienen una variabilidad similar. Los resultados, que se obtuvieron con datos MI del mundo real, demuestran que el estimador DRN usa la desincronización neuronal previa al entrenamiento y la sincronización del entrenamiento inicial para predecir la respuesta de precisión bi-clase, proporcionando así una mejor comprensión de la ineficiencia de la respuesta de MI de los sujetos en las Interfaces Cerebro-Computador.DoctoradoDoctor en IngenieríaReconocimiento de PatronesEléctrica, Electrónica, Automatización Y Telecomunicaciones.Sede Manizale

Localist representation can improve efficiency for detection and counting

Almost all representations have both distributed and localist aspects, depending upon what properties of the data are being considered. With noisy data, features represented in a localist way can be detected very efficiently, and in binary representations they can be counted more efficiently than those represented in a distributed way. Brains operate in noisy environments, so the localist representation of behaviourally important events is advantageous, and fits what has been found experimentally. Distributed representations require more neurons to perform as efficiently, but they do have greater versatility

Graph quilting: graphical model selection from partially observed covariances

We investigate the problem of conditional dependence graph estimation when several pairs of nodes have no joint observation. For these pairs even the simplest metric of covariability, the sample covariance, is unavailable. This problem arises, for instance, in calcium imaging recordings where the activities of a large population of neurons are typically observed by recording from smaller subsets of cells at once, and several pairs of cells are never recorded simultaneously. With no additional assumption, the unavailability of parts of the covariance matrix translates into the unidentifiability of the precision matrix that, in the Gaussian graphical model setting, specifies the graph. Recovering a conditional dependence graph in such settings is fundamentally an extremely hard challenge, because it requires to infer conditional dependences between network nodes with no empirical evidence of their covariability. We call this challenge the "graph quilting problem". We demonstrate that, under mild conditions, it is possible to correctly identify not only the edges connecting the observed pairs of nodes, but also a superset of those connecting the variables that are never observed jointly. We propose an $\ell_1$ regularized graph estimator based on a partially observed sample covariance matrix and establish its rates of convergence in high-dimensions. We finally present a simulation study and the analysis of calcium imaging data of ten thousand neurons in mouse visual cortex.Comment: 6 figure