The precise diagnostics of complex diseases require to integrate a large amount of information from heterogeneous clinical and biomedical data, whose direct and indirect interdependences are notoriously difficult to assess. To this end, we propose an efficient computational approach to simultaneously compute and assess the significance of multivariate information between any combination of mixed-type (continuous/categorical) variables. The method is then used to uncover direct, indirect and possibly causal relationships between mixed-type data from medical records, by extending a recent machine learning method to reconstruct graphical models beyond simple categorical datasets. The method is shown to outperform existing tools on benchmark mixed-type datasets, before being applied to analyze the medical records of eldery patients with cognitive disorders from La Pitié-Salpêtrière Hospital, Paris. The resulting clinical network visually captures the global interdependences in these medical records and some facets of clinical diagnosis practice, without specific hypothesis nor prior knowledge on any clinically relevant information. In particular, it provides some physiological insights linking the consequence of cerebrovascular accidents to the atrophy of important brain structures associated to cognitive impairment.

We consider constraint-based methods for causal structure learning, such as the PC algorithm or any PC-derived algorithms whose first step consists in pruning a complete graph to obtain an undirected graph skeleton, which is subsequently oriented. All constraint-based methods perform this first step of removing dispensable edges, iteratively, whenever a separating set and corresponding conditional independence can be found. Yet, constraint-based methods lack robustness over sampling noise and are prone to uncover spurious conditional independences in finite datasets. In particular, there is no guarantee that the separating sets identified during the iterative pruning step remain consistent with the final graph. In this paper, we propose a simple modification of PC and PC-derived algorithms so as to ensure that all separating sets identified to remove dispensable edges are consistent with the final graph,thus enhancing the explainability of constraint-basedmethods. It is achieved by repeating the constraint-based causal structure learning scheme, iteratively, while searching for separating sets that are consistent with the graph obtained at the previous iteration. Ensuring the consistency of separating sets can be done at a limited complexity cost, through the use of block-cut tree decomposition of graph skeletons, and is found to increase their validity in terms of actual d-separation. It also significantly improves the sensitivity of constraint-based methods while retaining good overall structure learning performance. Finally and foremost, ensuring sepset consistency improves the interpretability of constraint-based models for real-life applications.

Summary: We present a web server running the MIIC algorithm, a network learning method combining constraint-based and information-theoretic frameworks to reconstruct causal, non-causal or mixed networks from non-perturbative data, without the need for an a priori choice on the class of reconstructed network. Starting from a fully connected network, the algorithm first removes dispensable edges by iteratively subtracting the most significant information contributions from indirect paths between each pair of variables. The remaining edges are then filtered based on their confidence assessment or oriented based on the signature of causality in observational data. MIIC online server can be used for a broad range of biological data, including possible unobserved (latent) variables, from single-cell gene expression data to protein sequence evolution and outperforms or matches state-of-the-art methods for either causal or non-causal network reconstruction. Availability and implementation: MIIC online can be freely accessed at https://miic.curie.fr. Supplementary information: Supplementary data are available at Bioinformatics online.

Learning causal networks from large-scale genomic data remains challenging in absence of time series or controlled perturbation experiments. We report an information- theoretic method which learns a large class of causal or non-causal graphical models from purely observational data, while including the effects of unobserved latent variables, commonly found in many genomic datasets. Starting from a complete graph, the method iteratively removes dispensable edges, by uncovering significant information contributions from indirect paths, and assesses edge-specific confidences from randomization of available data. The remaining edges are then oriented based on the signature of causality in observational data. The approach and associated algorithm, miic, outperform earlier methods on a broad range of benchmark networks. Causal network reconstructions are presented at different biological size and time scales, from gene regulation in single cells to whole genome duplication in tumor development as well as long term evolution of vertebrates. Miic is publicly available at https://github.com/miicTeam/MIIC.