Measuring Directed Functional Connectivity Using Non-Parametric Directionality Analysis : Validation and Comparison with Non-Parametric Granger Causality

BACKGROUND: 'Non-parametric directionality' (NPD) is a novel method for estimation of directed functional connectivity (dFC) in neural data. The method has previously been verified in its ability to recover causal interactions in simulated spiking networks in Halliday et al. (2015). METHODS: This work presents a validation of NPD in continuous neural recordings (e.g. local field potentials). Specifically, we use autoregressive models to simulate time delayed correlations between neural signals. We then test for the accurate recovery of networks in the face of several confounds typically encountered in empirical data. We examine the effects of NPD under varying: a) signal-to-noise ratios, b) asymmetries in signal strength, c) instantaneous mixing, d) common drive, e) data length, and f) parallel/convergent signal routing. We also apply NPD to data from a patient who underwent simultaneous magnetoencephalography and deep brain recording. RESULTS: We demonstrate that NPD can accurately recover directed functional connectivity from simulations with known patterns of connectivity. The performance of the NPD measure is compared with non-parametric estimators of Granger causality (NPG), a well-established methodology for model-free estimation of dFC. A series of simulations investigating synthetically imposed confounds demonstrate that NPD provides estimates of connectivity that are equivalent to NPG, albeit with an increased sensitivity to data length. However, we provide evidence that: i) NPD is less sensitive than NPG to degradation by noise; ii) NPD is more robust to the generation of false positive identification of connectivity resulting from SNR asymmetries; iii) NPD is more robust to corruption via moderate amounts of instantaneous signal mixing. CONCLUSIONS: The results in this paper highlight that to be practically applied to neural data, connectivity metrics should not only be accurate in their recovery of causal networks but also resistant to the confounding effects often encountered in experimental recordings of multimodal data. Taken together, these findings position NPD at the state-of-the-art with respect to the estimation of directed functional connectivity in neuroimaging

Low-frequency oscillatory correlates of auditory predictive processing in cortical-subcortical networks: a MEG-study

Emerging evidence supports the role of neural oscillations as a mechanism for predictive information processing across large-scale networks. However, the oscillatory signatures underlying auditory mismatch detection and information flow between brain regions remain unclear. To address this issue, we examined the contribution of oscillatory activity at theta/alpha-bands (4–8/8–13 Hz) and assessed directed connectivity in magnetoencephalographic data while 17 human participants were presented with sound sequences containing predictable repetitions and order manipulations that elicited prediction-error responses. We characterized the spectro-temporal properties of neural generators using a minimum-norm approach and assessed directed connectivity using Granger Causality analysis. Mismatching sequences elicited increased theta power and phase-locking in auditory, hippocampal and prefrontal cortices, suggesting that theta-band oscillations underlie prediction-error generation in cortical-subcortical networks. Furthermore, enhanced feedforward theta/alpha-band connectivity was observed in auditory-prefrontal networks during mismatching sequences, while increased feedback connectivity in the alpha-band was observed between hippocampus and auditory regions during predictable sounds. Our findings highlight the involvement of hippocampal theta/alpha-band oscillations towards auditory prediction-error generation and suggest a spectral dissociation between inter-areal feedforward vs. feedback signalling, thus providing novel insights into the oscillatory mechanisms underlying auditory predictive processing

The Agnostic Structure of Data Science Methods

In this paper we want to discuss the changing role of mathematics in science, as a way to discuss some methodological trends at work in big data science. More specifically, we will show how the role of mathematics has dramatically changed from its more classical approach. Classically, any application of mathematical techniques requires a previous understanding of the phenomena, and of the mutual relations among the relevant data; modern data analysis appeals, instead, to mathematics in order to identify possible invariants uniquely attached to the specific questions we may ask about the phenomena of interest. In other terms, the new paradigm for the application of mathematics does not require any understanding of the phenomenon, but rather relies on mathematics to organize data in such a way as to reveal possible invariants that may or may not provide further understanding of the phenomenon per se, but that nevertheless provide an answer to the relevant question

Constraining the function of CA1 in associative memory models of the hippocampus

Institute for Adaptive and Neural ComputationCA1 is the main source of afferents from the hippocampus, but the function of CA1 and its perforant path (PP) input remains unclear. In this thesis, Marr’s model of the hippocampus is used to investigate previously hypothesized functions, and also to investigate some of Marr’s unexplored theoretical ideas. The last part of the thesis explains the excitatory responses to PP activity in vivo, despite inhibitory responses in vitro. Quantitative support for the idea of CA1 as a relay of information from CA3 to the neocortex and subiculum is provided by constraining Marr’s model to experimental data. Using the same approach, the much smaller capacity of the PP input by comparison implies it is not a one-shot learning network. In turn, it is argued that the entorhinal-CA1 connections cannot operate as a short-term memory network through reverberating activity. The PP input to CA1 has been hypothesized to control the activity of CA1 pyramidal cells. Marr suggested an algorithm for self-organising the output activity during pattern storage. Analytic calculations show a greater capacity for self-organised patterns than random patterns for low connectivities and high loads, confirmed in simulations over a broader parameter range. This superior performance is maintained in the absence of complex thresholding mechanisms, normally required to maintain performance levels in the sparsely connected networks. These results provide computational motivation for CA3 to establish patterns of CA1 activity without involvement from the PP input. The recent report of CA1 place cell activity with CA3 lesioned (Brun et al., 2002. Science, 296(5576):2243-6) is investigated using an integrate-and-fire neuron model of the entorhinal-CA1 network. CA1 place field activity is learnt, despite a completely inhibitory response to the stimulation of entorhinal afferents. In the model, this is achieved using N-methyl-D-asparate receptors to mediate a significant proportion of the excitatory response. Place field learning occurs over a broad parameter space. It is proposed that differences between similar contexts are slowly learnt in the PP and as a result are amplified in CA1. This would provide improved spatial memory in similar but different contexts

Multiuser detection employing recurrent neural networks for DS-CDMA systems.

Thesis (M.Sc.Eng.)-University of KwaZulu-Natal, 2006.Over the last decade, access to personal wireless communication networks has evolved to a point of necessity. Attached to the phenomenal growth of the telecommunications industry in recent times is an escalating demand for higher data rates and efficient spectrum utilization. This demand is fuelling the advancement of third generation (3G), as well as future, wireless networks. Current 3G technologies are adding a dimension of mobility to services that have become an integral part of modem everyday life. Wideband code division multiple access (WCDMA) is the standardized multiple access scheme for 3G Universal Mobile Telecommunication System (UMTS). As an air interface solution, CDMA has received considerable interest over the past two decades and a great deal of current research is concerned with improving the application of CDMA in 3G systems. A factoring component of CDMA is multiuser detection (MUD), which is aimed at enhancing system capacity and performance, by optimally demodulating multiple interfering signals that overlap in time and frequency. This is a major research problem in multipoint-to-point communications. Due to the complexity associated with optimal maximum likelihood detection, many different sub-optimal solutions have been proposed. This focus of this dissertation is the application of neural networks for MUD, in a direct sequence CDMA (DS-CDMA) system. Specifically, it explores how the Hopfield recurrent neural network (RNN) can be employed to give yet another suboptimal solution to the optimization problem of MUD. There is great scope for neural networks in fields encompassing communications. This is primarily attributed to their non-linearity, adaptivity and key function as data classifiers. In the context of optimum multiuser detection, neural networks have been successfully employed to solve similar combinatorial optimization problems. The concepts of CDMA and MUD are discussed. The use of a vector-valued transmission model for DS-CDMA is illustrated, and common linear sub-optimal MUD schemes, as well as the maximum likelihood criterion, are reviewed. The performance of these sub-optimal MUD schemes is demonstrated. The Hopfield neural network (HNN) for combinatorial optimization is discussed. Basic concepts and techniques related to the field of statistical mechanics are introduced and it is shown how they may be employed to analyze neural classification. Stochastic techniques are considered in the context of improving the performance of the HNN. A neural-based receiver, which employs a stochastic HNN and a simulated annealing technique, is proposed. Its performance is analyzed in a communication channel that is affected by additive white Gaussian noise (AWGN) by way of simulation. The performance of the proposed scheme is compared to that of the single-user matched filter, linear decorrelating and minimum mean-square error detectors, as well as the classical HNN and the stochastic Hopfield network (SHN) detectors. Concluding, the feasibility of neural networks (in this case the HNN) for MUD in a DS-CDMA system is explored by quantifying the relative performance of the proposed model using simulation results and in view of implementation issues

Causal inference and forescasting methods for climate data nalysis

To advance time series forecasting we need to progress on multiple fronts. In this thesis, we develop algorithms to identify causal relations which allow to identify the driving processes containing useful information for the prediction of the process of interest. Complementing this, machine learning algorithms allow to exploit such information to build data-driven forecast models, and to correct the prediction of dynamical models. The identification from time series analysis of reliable indicators of causal relationships, is essential for many disciplines. Main challenges are distinguishing correlation from causality and discriminating between direct and indirect interactions. Over the years, many methods for data-driven causal inference have been proposed; however, their success largely depends on the characteristics of the system under investigation. Often, their data requirements, computational cost or number of parameters, limit their applicability. In this thesis, we propose a computationally efficient measure for causality testing, with the goal of overcoming the limitations of information-theoretic measures, due their high computational cost. The proposed metric is useful when causality networks need to be inferred from the analysis of a large number of relatively short time series. It can also be very useful for the selection of the inputs for the machine learning algorithms; in fact, it allows to identify those processes which contain useful information for the prediction of a given process. This is particularly useful for systems composed of a large number of processes, whose interactions are poorly understood. On the other hand, the socioeconomic impact of weather extremes draws the attention of researchers to the development of novel methodologies to make more accurate weather predictions. The Madden-Julian Oscillation (MJO), which is the dominant mode of variability in the tropical atmosphere on sub-seasonal time scales, is particularly important because it can promote or enhance extreme events in both, the tropics and the extratropics. Currently, the prediction skill of MJO is receiving a lot of attention, and in this thesis we take two machine learning approaches; first we use machine learning as a stand-alone technique to analyze observed data, showing that two artificial neural networks, a feed-forward neural network and a recurrent neural network, allow a competitive prediction, yet not exceeding the skill of the state-of-art dynamical models. Then, we combine dynamical models with machine learning, which allows to improve the predictions of the best dynamical model. In particular, machine learning allows to improve the prediction of the MJO intensity and geographical localizationPara avanzar en el pronóstico de series temporales, es necesario avanzar en múltiples frentes. En esta tesis, desarrollamos algoritmos para descubrir relaciones causales que identifican los procesos que actúan como fuentes de información y pueden ayudar a mejorar la predicción del proceso de interés. Por otro lado, los algoritmos de aprendizaje automático permiten explotar dicha información para mejorar la predicción de los modelos dinámicos. La identificación de relaciones de causalidad a partir de series temporales es esencial en muchas disciplinas. Los desafíos en este ámbito son distinguir la correlación de la causalidad, así como diferenciar entre las interacciones directas e indirectas. A lo largo de los años se han propuesto numerosos métodos de inferencia causal basados en la observación de datos. No obstante, su éxito depende de las características del sistema a investigar. A menudo, el coste computacional o el número de parámetros limitan su aplicabilidad. En esta tesis se propone una medida computacionalmente eficiente para el testeo de causalidad. La métrica que se propone resulta util cuando es necesario inferir causalidad a partir de análisis de un gran número de series temporales relativamente cortas. También puede resultar muy útil en la selección de entradas en los algoritmos de aprendizaje automático. De hecho, permite identificar aquellos procesos que contienen información útil en la predicción de cierto proceso dado. Por otro lado, el impacto socioeconómico de fenómenos meteorológicos extremos requiere el desarrollo de nuevas metodologías con el objetivo de obtener predicciones meteorológicas más precisas. La Oscilación de Madden-Julian (MJO) es el modo dominante de variabilidad en la atmósfera tropical en escalas temporales subestacionales, y puede promover o aumentar eventos extremos tanto en el trópico como el extratrópico. Actualmente, la prediccion de la MJO genera mucho interés. Por esta razon, en esta tesis se han escogido dos metodologías diferentes de aprendizaje automático. Primero, se han utilizado dos redes neuronales artificiales para analizar datos observacionales, una red neuronal feed-forward y una red neuronal recurrente. Se muestra que esto permite una predicción competitiva, pero sin superar la capacidad de los modelos dinámicos actuales. Por este motivo, en un segundo estudio se han combinado modelos dinámicos con aprendizaje automático, que permiten mejorar las predicciones del mejor modelo dinámico. En particular, el aprendizaje automático permite mejorar la predicción de la intensidad de MJO y su localización geográficaPostprint (published version