Self-learning Bayesian Networks in Diagnosis

MRSL: a causal network pruning algorithm based on GWAS summary data

Causal discovery is a powerful tool to disclose underlying structures by analyzing purely observational data. Genetic variants can provide useful complementary information for structure learning. Recently, Mendelian randomization (MR) studies have provided abundant marginal causal relationships of traits. Here, we propose a causal network pruning algorithm MRSL (MR-based structure learning algorithm) based on these marginal causal relationships. MRSL combines the graph theory with multivariable MR to learn the conditional causal structure using only genome-wide association analyses (GWAS) summary statistics. Specifically, MRSL utilizes topological sorting to improve the precision of structure learning. It proposes MR-separation instead of d-separation and three candidates of sufficient separating set for MR-separation. The results of simulations revealed that MRSL had up to 2-fold higher F1 score and 100 times faster computing time than other eight competitive methods. Furthermore, we applied MRSL to 26 biomarkers and 44 International Classification of Diseases 10 (ICD10)-defined diseases using GWAS summary data from UK Biobank. The results cover most of the expected causal links that have biological interpretations and several new links supported by clinical case reports or previous observational literatures.

Mining real-world high dimensional structured data in medicine and its use in decision support. Some different perspectives on unknowns, interdependency, and distinguishability

There are many difficulties in extracting and using knowledge for medical analytic and predictive purposes from Real-World Data, even when the data is already well structured in the manner of a large spreadsheet. Preparative curation and standardization or "normalization" of such data involves a variety of chores but underlying them is an interrelated set of fundamental problems that can in part be dealt with automatically during the datamining and inference processes. These fundamental problems are reviewed here and illustrated and investigated with examples. They concern the treatment of unknowns, the need to avoid independency assumptions, and the appearance of entries that may not be fully distinguished from each other. Unknowns include errors detected as implausible (e.g., out of range) values that are subsequently converted to unknowns. These problems are further impacted by high dimensionality and problems of sparse data that inevitably arise from high-dimensional datamining even if the data is extensive. All these considerations are different aspects of incomplete information, though they also relate to problems that arise if care is not taken to avoid or ameliorate consequences of including the same information twice or more, or if misleading or inconsistent information is combined. This paper addresses these aspects from a slightly different perspective using the Q-UEL language and inference methods based on it by borrowing some ideas from the mathematics of quantum mechanics and information theory. It takes the view that detection and correction of probabilistic elements of knowledge subsequently used in inference need only involve testing and correction so that they satisfy certain extended notions of coherence between probabilities. This is by no means the only possible view, and it is explored here and later compared with a related notion of consistency.

Bidirectional General Graphs for inference. Principles and implications for medicine

Probabilistic inference methods require a more general and realistic description of the world as a Bidirectional General Graph (BGG). While in its original form the Bayes Net (BN) has been promoted as a predictive tool, it is more immediately a way of testing a hypothesis or model about interactions in a system usually considered on a causal basis. Once established, the model can be used in a predictive way, but the problem here is that for a traditional BN the hypotheses or models that can be formed are limited to the Directed Acyclic Graph (DAG) by definition. Three interrelated features are highlighted that represent deficiencies of the DAG which are corrected by conversion to a method based on a BGG: (i) lack of intrinsic representation of coherence by Bayes' rule, (ii) relatedly the need to consider interdependence in parent nodes, and (iii) the need for management of a property called recurrence. These deficiencies can represent large errors in absolute estimates of probabilities, and while relative and renormalized probabilities ameliorate that, they can often make much of a net superfluous through cancelations by division. The Hyperbolic Dirac Net (HDN) based on Dirac's quantum mechanics is a solution that led naturally to avoiding these deficiencies. It encodes bidirectional probabilities in an h-complex value rediscovered by Dirac, i.e. with the imaginary number h such that hh = +1. Properties of the HDN described previously are reviewed (though emphasis is on descriptions in familiar probability terms), the issue of recurrence is introduced, methods of construction are simplified, and the severity of the quantitative differences between BNs and analogous HDNs are exemplified. There is also discussion of how results compare with other approaches in practice.