Tensor Analysis and Fusion of Multimodal Brain Images

Current high-throughput data acquisition technologies probe dynamical systems with different imaging modalities, generating massive data sets at different spatial and temporal resolutions posing challenging problems in multimodal data fusion. A case in point is the attempt to parse out the brain structures and networks that underpin human cognitive processes by analysis of different neuroimaging modalities (functional MRI, EEG, NIRS etc.). We emphasize that the multimodal, multi-scale nature of neuroimaging data is well reflected by a multi-way (tensor) structure where the underlying processes can be summarized by a relatively small number of components or "atoms". We introduce Markov-Penrose diagrams - an integration of Bayesian DAG and tensor network notation in order to analyze these models. These diagrams not only clarify matrix and tensor EEG and fMRI time/frequency analysis and inverse problems, but also help understand multimodal fusion via Multiway Partial Least Squares and Coupled Matrix-Tensor Factorization. We show here, for the first time, that Granger causal analysis of brain networks is a tensor regression problem, thus allowing the atomic decomposition of brain networks. Analysis of EEG and fMRI recordings shows the potential of the methods and suggests their use in other scientific domains.Comment: 23 pages, 15 figures, submitted to Proceedings of the IEE

Disentangling causal webs in the brain using functional Magnetic Resonance Imaging: A review of current approaches

In the past two decades, functional Magnetic Resonance Imaging has been used to relate neuronal network activity to cognitive processing and behaviour. Recently this approach has been augmented by algorithms that allow us to infer causal links between component populations of neuronal networks. Multiple inference procedures have been proposed to approach this research question but so far, each method has limitations when it comes to establishing whole-brain connectivity patterns. In this work, we discuss eight ways to infer causality in fMRI research: Bayesian Nets, Dynamical Causal Modelling, Granger Causality, Likelihood Ratios, LiNGAM, Patel's Tau, Structural Equation Modelling, and Transfer Entropy. We finish with formulating some recommendations for the future directions in this area

Learning Temporal Dependence from Time-Series Data with Latent Variables

We consider the setting where a collection of time series, modeled as random processes, evolve in a causal manner, and one is interested in learning the graph governing the relationships of these processes. A special case of wide interest and applicability is the setting where the noise is Gaussian and relationships are Markov and linear. We study this setting with two additional features: firstly, each random process has a hidden (latent) state, which we use to model the internal memory possessed by the variables (similar to hidden Markov models). Secondly, each variable can depend on its latent memory state through a random lag (rather than a fixed lag), thus modeling memory recall with differing lags at distinct times. Under this setting, we develop an estimator and prove that under a genericity assumption, the parameters of the model can be learned consistently. We also propose a practical adaption of this estimator, which demonstrates significant performance gains in both synthetic and real-world datasets

Joint estimation of multiple related biological networks

Graphical models are widely used to make inferences concerning interplay in multivariate systems. In many applications, data are collected from multiple related but nonidentical units whose underlying networks may differ but are likely to share features. Here we present a hierarchical Bayesian formulation for joint estimation of multiple networks in this nonidentically distributed setting. The approach is general: given a suitable class of graphical models, it uses an exchangeability assumption on networks to provide a corresponding joint formulation. Motivated by emerging experimental designs in molecular biology, we focus on time-course data with interventions, using dynamic Bayesian networks as the graphical models. We introduce a computationally efficient, deterministic algorithm for exact joint inference in this setting. We provide an upper bound on the gains that joint estimation offers relative to separate estimation for each network and empirical results that support and extend the theory, including an extensive simulation study and an application to proteomic data from human cancer cell lines. Finally, we describe approximations that are still more computationally efficient than the exact algorithm and that also demonstrate good empirical performance.Comment: Published in at http://dx.doi.org/10.1214/14-AOAS761 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Causal Discovery from Temporal Data: An Overview and New Perspectives

Temporal data, representing chronological observations of complex systems, has always been a typical data structure that can be widely generated by many domains, such as industry, medicine and finance. Analyzing this type of data is extremely valuable for various applications. Thus, different temporal data analysis tasks, eg, classification, clustering and prediction, have been proposed in the past decades. Among them, causal discovery, learning the causal relations from temporal data, is considered an interesting yet critical task and has attracted much research attention. Existing casual discovery works can be divided into two highly correlated categories according to whether the temporal data is calibrated, ie, multivariate time series casual discovery, and event sequence casual discovery. However, most previous surveys are only focused on the time series casual discovery and ignore the second category. In this paper, we specify the correlation between the two categories and provide a systematical overview of existing solutions. Furthermore, we provide public datasets, evaluation metrics and new perspectives for temporal data casual discovery.Comment: 52 pages, 6 figure