Supervised estimation of Granger-based causality between time series

Brain effective connectivity aims to detect causal interactions between distinct brain units and it is typically studied through the analysis of direct measurements of the neural activity, e.g., magneto/electroencephalography (M/EEG) signals. The literature on methods for causal inference is vast. It includes model-based methods in which a generative model of the data is assumed and model-free methods that directly infer causality from the probability distribution of the underlying stochastic process. Here, we firstly focus on the model-based methods developed from the Granger criterion of causality, which assumes the autoregressive model of the data. Secondly, we introduce a new perspective, that looks at the problem in a way that is typical of the machine learning literature. Then, we formulate the problem of causality detection as a supervised learning task, by proposing a classification-based approach. A classifier is trained to identify causal interactions between time series for the chosen model and by means of a proposed feature space. In this paper, we are interested in comparing this classification-based approach with the standard Geweke measure of causality in the time domain, through simulation study. Thus, we customized our approach to the case of a MAR model and designed a feature space which contains causality measures based on the idea of precedence and predictability in time. Two variations of the supervised method are proposed and compared to a standard Granger causal analysis method. The results of the simulations show that the supervised method outperforms the standard approach, in particular it is more robust to noise. As evidence of the efficacy of the proposed method, we report the details of our submission to the causality detection competition of Biomag2014, where the proposed method reached the 2nd place. Moreover, as empirical application, we applied the supervised approach on a dataset of neural recordings of rats obtaining an important reduction in the false positive rate

Classification-based prediction of effective connectivity between timeseries with a realistic cortical network model

Effective connectivity measures the pattern of causal interactions between brain regions. Traditionally, these patterns of causality are inferred from brain recordings using either non-parametric, i.e., model-free, or parametric, i.e., model-based, approaches. The latter approaches, when based on biophysically plausible models, have the advantage that they may facilitate the interpretation of causality in terms of underlying neural mechanisms. Recent biophysically plausible neural network models of recurrent microcircuits have shown the ability to reproduce well the characteristics of real neural activity and can be applied to model interacting cortical circuits. Unfortunately, however, it is challenging to invert these models in order to estimate effective connectivity from observed data. Here, we propose to use a classification-based method to approximate the result of such complex model inversion. The classifier predicts the pattern of causal interactions given a multivariate timeseries as input. The classifier is trained on a large number of pairs of multivariate timeseries and the respective pattern of causal interactions, which are generated by simulation from the neural network model. In simulated experiments, we show that the proposed method is much more accurate in detecting the causal structure of timeseries than current best practice methods. Additionally, we present further results to characterize the validity of the neural network model and the ability of the classifier to adapt to the generative model of the data

Ottimizzazione di algoritmi di deconvoluzione applicati alla DSC-MRI

La quantificazione dell’emodinamica cerebrale risulta particolarmente importante nello studio di patologie come neoplasie cerebrali, sclerosi multipla, ischemie e infarti. La DSC-MRI è una delle tecniche di imaging funzionale che ne permettono la stima. Prevede l’iniezione di un agente di contrasto non radioattivo, il Gadolinio, e la successiva acquisizione di immagini MR. L’emodinamica è quantificata stimando la funzione residuo che permette di ottenere: il flusso cerebrale ematico (CBF), il volume cerebrale ematico (CBV) e il tempo medio di transito (MTT). Fondamentale a tal proposito è la risoluzione dell’operazione di deconvoluzione. Con questo lavoro sono state approfondite e ottimizzate due tecniche di deconvoluzione non lineari e modello indipendenti la Nonlinear Stochastic Regularization (NSR) e la Stable Spline (SS) con l’obiettivo di renderle applicabili in DSC-MRIope

Ottimizzazione di algoritmi di deconvoluzione applicati alla DSC-MRI

La quantificazione dell’emodinamica cerebrale risulta particolarmente importante nello studio di patologie come neoplasie cerebrali, sclerosi multipla, ischemie e infarti. La DSC-MRI è una delle tecniche di imaging funzionale che ne permettono la stima. Prevede l’iniezione di un agente di contrasto non radioattivo, il Gadolinio, e la successiva acquisizione di immagini MR. L’emodinamica è quantificata stimando la funzione residuo che permette di ottenere: il flusso cerebrale ematico (CBF), il volume cerebrale ematico (CBV) e il tempo medio di transito (MTT). Fondamentale a tal proposito è la risoluzione dell’operazione di deconvoluzione. Con questo lavoro sono state approfondite e ottimizzate due tecniche di deconvoluzione non lineari e modello indipendenti la Nonlinear Stochastic Regularization (NSR) e la Stable Spline (SS) con l’obiettivo di renderle applicabili in DSC-MR

Detecting Brain Effective Connectivity with Supervised and Bayesian Methods

The study of causality has drawn the attention of researchers from many different fields for centuries. In particular, nowadays causal inference is a central question in neuroscience and an entire body of research, called brain effective connectivity, is devoted to detecting causal interactions between distinct brain areas. Brain effective connectivity is typically studied by the statistical analysis of direct measurements of the neural activity. The main purpose of this work is on methods for studying time series causality. More in details, we focus on a well-establish criterion of causality: the Granger criterion, which is based on the concepts of temporal precedence and predictability. Firstly, we consider the standard parametric implementation of the Granger criterion that is based on the multivariate autoregressive model, where we face the problem of model identification. For this purpose, we present a new Bayesian method for linear model identification and we explore its capability of modeling the sparsity structure of the signals. As a second contribution, we look at the causal inference through the lens of machine learning and we propose an approach based on the concept of learning from examples. Thus, given a set of signals, their causal interactions are estimated by a classifier that is trained on a synthetic dataset generated by a parametric model. This approach, that we call supervised parametric approach, is implemented by adopting the Granger criterion of causality and compared with the standard parametric measure of Granger causality. Moreover, the roles of the feature space and the generative model of the training set are investigated through a simulation study. Additionally, we show an example of application on rat neural recordings. Finally, we focus on the bias introduced by parametric methods when applied in a real context, i.e. the inability of having a fully realistic generative model. For this purpose, we analyze how the supervised parametric approach can help in making the inference more application-dependent, by exploiting a physiologically plausible generative model

Supervised Estimation of Granger-Based Causality between Time Series

Brain effective connectivity aims to detect causal interactions between distinct brain units and it is typically studied through the analysis of direct measurements of the neural activity, e.g., magneto/electroencephalography (M/EEG) signals. The literature on methods for causal inference is vast. It includes model-based methods in which a generative model of the data is assumed and model-free methods that directly infer causality from the probability distribution of the underlying stochastic process. Here, we firstly focus on the model-based methods developed from the Granger criterion of causality, which assumes the autoregressive model of the data. Secondly, we introduce a new perspective, that looks at the problem in a way that is typical of the machine learning literature. Then, we formulate the problem of causality detection as a supervised learning task, by proposing a classification-based approach. A classifier is trained to identify causal interactions between time series for the chosen model and by means of a proposed feature space. In this paper, we are interested in comparing this classification-based approach with the standard Geweke measure of causality in the time domain, through simulation study. Thus, we customized our approach to the case of a MAR model and designed a feature space which contains causality measures based on the idea of precedence and predictability in time. Two variations of the supervised method are proposed and compared to a standard Granger causal analysis method. The results of the simulations show that the supervised method outperforms the standard approach, in particular it is more robust to noise. As evidence of the efficacy of the proposed method, we report the details of our submission to the causality detection competition of Biomag2014, where the proposed method reached the 2nd place. Moreover, as empirical application, we applied the supervised approach on a dataset of neural recordings of rats obtaining an important reduction in the false positive rate

Classification-Based Prediction of Effective Connectivity Between Timeseries With a Realistic Cortical Network Model

Effective connectivity measures the pattern of causal interactions between brain regions. Traditionally, these patterns of causality are inferred from brain recordings using either non-parametric, i.e., model-free, or parametric, i.e., model-based, approaches. The latter approaches, when based on biophysically plausible models, have the advantage that they may facilitate the interpretation of causality in terms of underlying neural mechanisms. Recent biophysically plausible neural network models of recurrent microcircuits have shown the ability to reproduce well the characteristics of real neural activity and can be applied to model interacting cortical circuits. Unfortunately, however, it is challenging to invert these models in order to estimate effective connectivity from observed data. Here, we propose to use a classification-based method to approximate the result of such complex model inversion. The classifier predicts the pattern of causal interactions given a multivariate timeseries as input. The classifier is trained on a large number of pairs of multivariate timeseries and the respective pattern of causal interactions, which are generated by simulation from the neural network model. In simulated experiments, we show that the proposed method is much more accurate in detecting the causal structure of timeseries than current best practice methods. Additionally, we present further results to characterize the validity of the neural network model and the ability of the classifier to adapt to the generative model of the data

The kernel two-sample test vs. brain decoding

Assessing whether the patterns of brain activity systematically differ when the subject is presented with different sets of stimuli is called 'brain decoding'. The most common solution to this problem is based on testing whether a classifier can accurately predict the type of stimulus from brain data. In this work we present a novel approach to the brain decoding problem which does not require any classifier. The proposed method is based on a high-dimensional two-sample test recently proposed in the machine learning literature. The test tries to determine whether the set of brain recordings related to one kind of stimulus, i.e. the first sample, and the ones related to the other kind of stimulus, i.e. the second sample, are drawn from the same probability distribution or not. In this work we illustrate the advantages of this novel approach together with experimental evidence of its efficacy on magneto encephalographic (MEG) data from a Face, House and Body discrimination task. © 2013 IEEE