Search

Learning graphical conditional independence structures is an important machine learning problem and a cornerstone of causal discovery. However, the accuracy and execution time of learning algorithms generally struggle to scale to problems with hundreds of highly connected variables -- for instance, recovering brain networks from fMRI data. We introduce the best order score search (BOSS) and grow-shrink trees (GSTs) for learning directed acyclic graphs (DAGs) in this paradigm. BOSS greedily searches over permutations of variables, using GSTs to construct and score DAGs from permutations. GSTs efficiently cache scores to eliminate redundant calculations. BOSS achieves state-of-the-art performance in accuracy and execution time, comparing favorably to a variety of combinatorial and gradient-based learning algorithms under a broad range of conditions. To demonstrate its practicality, we apply BOSS to two sets of resting-state fMRI data: simulated data with pseudo-empirical noise distributions derived from randomized empirical fMRI cortical signals and clinical data from 3T fMRI scans processed into cortical parcels. BOSS is available for use within the TETRAD project which includes Python and R wrappers.

This paper presents an innovative hierarchical meta-modelling approach for predicting the effective elastic properties of stone injected with composite cement grouts containing Carbon NanoTubes (CNTs) for structural rehabilitation purposes. The study first addresses the homogenization of the nano- and micro-scales through numerical representative volume elements. The first numerical model focuses on the cement matrix doped with randomly oriented CNTs, while the second model represents the porous stone with CNT/cement grout filling the pores. However, the computational burden associated with these models poses a significant limitation when analysing large-scale macrostructural elements. To overcome this challenge, a hierarchical meta-modelling approach based on two nested Kriging surrogate models is proposed. This approach offers a fast and accurate alternative to bypass the time-consuming numerical homogenization process. The first surrogate model establishes a connection between the microstructural characteristics of the CNTs and cement and the effective elastic properties of the composite grout. Subsequently, a second meta-model expands over the first one by introducing two additional variables: the elastic modulus of the stone and the porosity, allowing for estimation of the overall elastic properties of CNT/cement/stone composites. The accuracy and efficiency of the proposed hierarchical meta-model is demonstrated through detailed parametric analyses. To showcase its potential for optimizing rehabilitation interventions, the paper is closed with its application to a benchmark case study of a stone column injected with CNT/cement grout.

Standard fMRI connectivity analyses depend on aggregating the time series of individual voxels within regions of interest (ROIs). In certain cases, this spatial aggregation implies a loss of valuable functional and anatomical information about smaller subsets of voxels that drive the ROI level connectivity. We use two recently published graphical search methods to identify subsets of voxels that are highly responsible for the connectivity between larger ROIs. To illustrate the procedure, we apply both methods to longitudinal high-resolution resting state fMRI data from regions in the medial temporal lobe from a single individual. Both methods recovered similar subsets of voxels within larger ROIs of entorhinal cortex and hippocampus subfields that also show spatial consistency across different scanning sessions and across hemispheres. In contrast to standard functional connectivity methods, both algorithms applied here are robust against false positive connections produced by common causes and indirect paths (in contrast to Pearson's correlation) and common effect conditioning (in contrast to partial correlation based approaches). These algorithms allow for identification of subregions of voxels driving the connectivity between regions of interest, recovering valuable anatomical and functional information that is lost when ROIs are aggregated. Both methods are specially suited for voxelwise connectivity research, given their running times and scalability to big data problems.

It is commonplace to encounter heterogeneous or nonstationary data, of which the underlying generating process changes across domains or over time. Such a distribution shift feature presents both challenges and opportunities for causal discovery. In this paper, we develop a framework for causal discovery from such data, called Constraint-based causal Discovery from heterogeneous/NOnstationary Data (CD-NOD), to find causal skeleton and directions and estimate the properties of mechanism changes. First, we propose an enhanced constraint-based procedure to detect variables whose local mechanisms change and recover the skeleton of the causal structure over observed variables. Second, we present a method to determine causal orientations by making use of independent changes in the data distribution implied by the underlying causal model, benefiting from information carried by changing distributions. After learning the causal structure, next, we investigate how to efficiently estimate the "driving force" of the nonstationarity of a causal mechanism. That is, we aim to extract from data a low-dimensional representation of changes. The proposed methods are nonparametric, with no hard restrictions on data distributions and causal mechanisms, and do not rely on window segmentation. Furthermore, we find that data heterogeneity benefits causal structure identification even with particular types of confounders. Finally, we show the connection between heterogeneity/nonstationarity and soft intervention in causal discovery. Experimental results on various synthetic and real-world data sets (task-fMRI and stock market data) are presented to demonstrate the efficacy of the proposed methods.

Autism spectrum disorder (ASD) is one of the major developmental disorders affecting children. Recently, it has been hypothesized that ASD is associated with atypical brain connectivities. A substantial body of researches use Pearson's correlation coefficients, mutual information, or partial correlation to investigate the differences in brain connectivities between ASD and typical controls from functional Magnetic Resonance Imaging (fMRI). However, correlation or partial correlation does not directly reveal causal influences - the information flow - between brain regions. Comparing to correlation, causality pinpoints the key connectivity characteristics and removes redundant features for diagnosis. In this paper, we propose a two-step method for large-scale and cyclic causal discovery from fMRI. It can identify brain causal structures without doing interventional experiments. The learned causal structure, as well as the causal influence strength, provides us the path and effectiveness of information flow. With the recovered causal influence strength as candidate features, we then perform ASD diagnosis by further doing feature selection and classification. We apply our methods to three datasets from Autism Brain Imaging Data Exchange (ABIDE). From experimental results, it shows that with causal connectivities, the diagnostic accuracy largely improves. A closer examination shows that information flows starting from the superior front gyrus to default mode network and posterior areas are largely reduced. Moreover, all enhanced information flows are from posterior to anterior or in local areas. Overall, it shows that long-range influences have a larger proportion of reductions than local ones, while local influences have a larger proportion of increases than long-range ones. By examining the graph properties of brain causal structure, the group of ASD shows reduced small-worldness.