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

MEG Decoding Across Subjects

Brain decoding is a data analysis paradigm for neuroimaging experiments that is based on predicting the stimulus presented to the subject from the concurrent brain activity. In order to make inference at the group level, a straightforward but sometimes unsuccessful approach is to train a classifier on the trials of a group of subjects and then to test it on unseen trials from new subjects. The extreme difficulty is related to the structural and functional variability across the subjects. We call this approach "decoding across subjects". In this work, we address the problem of decoding across subjects for magnetoencephalographic (MEG) experiments and we provide the following contributions: first, we formally describe the problem and show that it belongs to a machine learning sub-field called transductive transfer learning (TTL). Second, we propose to use a simple TTL technique that accounts for the differences between train data and test data. Third, we propose the use of ensemble learning, and specifically of stacked generalization, to address the variability across subjects within train data, with the aim of producing more stable classifiers. On a face vs. scramble task MEG dataset of 16 subjects, we compare the standard approach of not modelling the differences across subjects, to the proposed one of combining TTL and ensemble learning. We show that the proposed approach is consistently more accurate than the standard one

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

Comparison of Distances for Supervised Segmentation of White Matter Tractography

Tractograms are mathematical representations of the main paths of axons within the white matter of the brain, from diffusion MRI data. Such representations are in the form of polylines, called streamlines, and one streamline approximates the common path of tens of thousands of axons. The analysis of tractograms is a task of interest in multiple fields, like neurosurgery and neurology. A basic building block of many pipelines of analysis is the definition of a distance function between streamlines. Multiple distance functions have been proposed in the literature, and different authors use different distances, usually without a specific reason other than invoking the "common practice". To this end, in this work we want to test such common practices, in order to obtain factual reasons for choosing one distance over another. For these reasons, in this work we compare many streamline distance functions available in the literature. We focus on the common task of automatic bundle segmentation and we adopt the recent approach of supervised segmentation from expert-based examples. Using the HCP dataset, we compare several distances obtaining guidelines on the choice of which distance function one should use for supervised bundle segmentation

Classification-based tests for neuroimaging data analysis: comparison of best practices

In neuroimaging data analysis, classification algorithms are frequently used to discriminate between two populations of interest, like patients and healthy controls, or between stimuli presented to the subject, like face and house. Usually, the ability of the classifier to discriminate populations is used within a statistical test, in order to evaluate scientific hypotheses. In the literature, different procedures are adopted to carry out such tests, like using permutations, assuming the binomial model or using confidence intervals. Moreover multiple choices are made by practitioners when implementing those tests, like the actual classification algorithm or the use of a resampling scheme. In this work we analyze those procedures and some of those choices with respect to their effect on the Type I (false discovery) and Type II (sensitivity) errors. With a simulation study, we compare the different procedures and show the impact in practice. The final aim is to characterize the best practices and give more insight for their use

Alignment of Tractograms As Graph Matching

The white matter pathways of the brain can be reconstructed as 3D polylines, called streamlines, through the analysis of diffusion magnetic resonance imaging (dMRI) data. The whole set of streamlines is called tractogram and represents the structural connectome of the brain. In multiple applications, like group-analysis, segmentation, or atlasing, tractograms of different subjects need to be aligned. Typically, this is done with registration methods, that transform the tractograms in order to increase their similarity. In contrast with transformation-based registration methods, in this work we propose the concept of tractogram correspondence, whose aim is to find which streamline of one tractogram corresponds to which streamline in another tractogram, i.e., a map from one tractogram to another. As a further contribution, we propose to use the relational information of each streamline, i.e., its distances from the other streamlines in its own tractogram, as the building block to define the optimal correspondence. We provide an operational procedure to find the optimal correspondence through a combinatorial optimization problem and we discuss its similarity to the graph matching problem. In this work, we propose to represent tractograms as graphs and we adopt a recent inexact sub-graph matching algorithm to approximate the solution of the tractogram correspondence problem. On tractograms generated from the Human Connectome Project dataset, we report experimental evidence that tractogram correspondence, implemented as graph matching, provides much better alignment than affine registration and comparable if not better results than non-linear registration of volumes

Anatomically-Informed Multiple Linear Assignment Problems for White Matter Bundle Segmentation

Segmenting white matter bundles from human tractograms is a task of interest for several applications. Current methods for bundle segmentation consider either only prior knowledge about the relative anatomical position of a bundle, or only its geometrical properties. Our aim is to improve the results of segmentation by proposing a method that takes into account information about both the underlying anatomy and the geometry of bundles at the same time. To achieve this goal, we extend a state-of-the-art example-based method based on the Linear Assignment Problem (LAP) by including prior anatomical information within the optimization process. The proposed method shows a significant improvement with respect to the original method, in particular on small bundles