Markov Blanket Research Articles

Multiscale integration: beyond internalism and externalism

We present a multiscale integrationist interpretation of the boundaries of cognitive systems, using the Markov blanket formalism of the variational free energy principle. This interpretation is intended as a corrective for the philosophical debate over internalist and externalist interpretations of cognitive boundaries; we stake out a compromise position. We first survey key principles of new radical (extended, enactive, embodied) views of cognition. We then describe an internalist interpretation premised on the Markov blanket formalism. Having reviewed these accounts, we develop our positive multiscale account. We argue that the statistical seclusion of internal from external states of the system—entailed by the existence of a Markov boundary—can coexist happily with the multiscale integration of the system through its dynamics. Our approach does not privilege any given boundary (whether it be that of the brain, body, or world), nor does it argue that all boundaries are equally prescient. We argue that the relevant boundaries of cognition depend on the level being characterised and the explanatory interests that guide investigation. We approach the issue of how and where to draw the boundaries of cognitive systems through a multiscale ontology of cognitive systems, which offers a multidisciplinary research heuristic for cognitive science.

Improving Bayesian network local structure learning via data-driven symmetry correction methods

Learning the structure of a Bayesian network (BN) from data is NP-hard. To efficiently handle high-dimensional datasets, many BN local structure learning algorithms are proposed. These learning algorithms can be categorized into two types: constraint-based and score-based. These learning algorithms learn the local structures separately for each node. As a result, asymmetric pairs of neighbors and Markov blankets create conflicts between the local structures. To resolve the conflicts, symmetry correction is required. The commonly used AND-rule symmetry correction method, which simply drops nodes in asymmetric pairs from the neighbor sets and Markov blankets of both nodes, may result in loss of information in learning the BN. In this paper, we propose a hybrid framework that combines a local structure learning algorithm of a particular type (either constraint-based or score-based) with a data-driven symmetry correction method of the other type. The score-based symG method and the constraint-based symC method are proposed to be used in the hybrid framework. Empirical results show that performances of constraint-based learning algorithms are improved by using the proposed score-based symG method. Similarly, the performance of score-based local learning algorithm is better when symC is used, compared to using symG.

Three-Fast-Inter Incremental Association Markov Blanket learning algorithm

The Markov blanket is a crucial concept in Bayesian network, and a useful tool for Bayesian network structure learning and causal feature selection. Finding an efficient Markov blanket discovery method is one of the core issues in machining learning, and has been widely studied. The Markov blanket discovery methods are mainly divided into two categories: Non-topology based and topology based. Topology based method is data-efficient, but not time-efficient, while non-topology based method is time-efficient, but not data-efficient. Due to the wide existence of the high-dimensional data with limited samples in practical applications, especially in the medical and biological study with expensive sample collection, we combine the advantages of Inter Incremental Association Markov blanket (Inter-IAMB) and Fast Incremental Association Markov blanket (Fast-IAMB), and propose the Three-Fast-Inter Incremental Association Markov blanket learning (Fit-IAMB) algorithm. Experiments showed that Fit-IAMB had comparable accuracy and much better efficiency than state-of-the-art algorithms, especially for the high-dimensional data with limited samples.

Somatic multicellularity as a satisficing solution to the prediction-error minimization problem

ABSTRACTAdaptive success in the biosphere requires the dynamic ability to adjust physiological, transcriptional, and behavioral responses to environmental conditions. From chemical networks to organisms to whole communities, biological entities at all levels of organization seek to optimize their predictive power. Here, we argue that this fundamental drive provides a novel perspective on the origin of multicellularity. One way for unicellular organisms to minimize surprise with respect to external inputs is to be surrounded by reproductively-disabled, i.e. somatic copies of themselves – highly predictable agents which in effect reduce uncertainty in their microenvironments. We show that the transition to multicellularity can be modeled as a phase transition driven by environmental threats. We present modeling results showing how multicellular bodies can arise if non-reproductive somatic cells protect their reproductive parents from environmental lethality. We discuss how a somatic body can be interpreted as a Markov blanket around one or more reproductive cells, and how the transition to somatic multicellularity can be represented as a transition from exposure of reproductive cells to a high-uncertainty environment to their protection from environmental uncertainty by this Markov blanket. This is, effectively, a transition by the Markov blanket from transparency to opacity for the variational free energy of the environment. We suggest that the ability to arrest the cell cycle of daughter cells and redirect their resource utilization from division to environmental threat amelioration is the key innovation of obligate multicellular eukaryotes, that the nervous system evolved to exercise this control over long distances, and that cancer is an escape by somatic cells from the control of reproductive cells. Our quantitative model illustrates the evolutionary dynamics of this system, provides a novel hypothesis for the origin of multicellular animal bodies, and suggests a fundamental link between the architectures of complex organisms and information processing in proto-cognitive cellular agents.

A Structure Data-Driven Framework for Virtual Metrology Modeling

Virtual metrology (VM) has been widely studied in the semiconductor industry with the purpose of decreasing the cycle time and reducing the expensive metrology measurements. Ideally, a VM model should not only be able to provide accurate predictions but also present an interpretable and rational structure to accommodate fundamental restrictions and relationships that are known to be present in the process. The last aspects have been missing in the VM models proposed hitherto. Therefore, in this article, we propose a novel framework by combining in a single VM model the capability to learn from data with the ability to incorporate the domain knowledge on the process. Thus, the new methodology can use the best of both information sources: data and the subject-matter expert (SME) knowledge. The framework consists of two phases. In the first phase, a Gaussian Bayesian network (GBN) is used to extract the implicit relationships between the metrology and production/process variables. In the second phase, the target response variable is defined, the predictors are selected through the associated Markov blanket, and finally, an empirical model is estimated to accurately predict the response. The proposed framework was tested and its effectiveness was confirmed through a real industrial data from a chemical–mechanical polishing (CMP) process in semiconductor fabrication. The physical meaning of the model obtained was also scrutinized by an SME. Note to Practitioners— Unlike the conventional virtual metrology (VM) techniques that model the x–y relationship based only on process data, the proposed method aims at consolidating the process knowledge from experts into an extensive relational structure. Not only the x–y model is inferred but also the relationships among the predictors are revealed. The structure is illustrated in a form of a connected graph so that the correlation between parameters can be expressed explicitly, which is also compatible with the physical laws. With the clear visualization of the correlation structure of variables, the practitioners are able to utilize the result in different applications. The learned structure can be further integrated into the plant advanced process control system, including VM, process monitoring and diagnosis, and run-to-run (R2R) control.

Feature Selection With Ensemble Learning Based on Improved Dempster-Shafer Evidence Fusion

Feature selection or attribute reduction is an important data preprocessing technique for dimensionality reduction in machine learning and data mining. In this paper, a novel feature selection ensemble learning algorithm is proposed based on Tsallis entropy and Dempster–Shafer evidence theory (TSDS). First, an improved correlation criterion is used to obtain the relevant feature based on Tsallis entropy. A forward sequential approximate Markov blanket is then defined to eliminate the redundant feature. An ensemble learning is employed to achieve approximately optimal global feature selection, which can acquire the feature subsets from different perspectives. Finally, by fusing all the feature subsets, the improved evidence theory approach is utilized to gain the final feature subset. To verify the effectiveness of TSDS, nine datasets from two different domains are used in the experimental analysis. The experimental results demonstrate that the proposed algorithm can select feature subset more effectively and enhance the classification performance significantly.

Online Feature Selection for Streaming Features Using Self-Adaption Sliding-Window Sampling

In recent years, online feature selection has been a research topic on streaming feature mining, as it can reduce the dimensionality of the streaming features by removing the irrelevant and redundant features in real time. There are many representative research efforts on the online feature selection with streaming features, i.e., alpha − investing , online streaming feature selection ( OSFS ), and scalable and accurate online approach ( SAOLA ) for feature selection. In these studies, alpha-investing has limited prediction accuracy and a large number of selected features. SAOLA sometimes offers outstanding efficiency in running time and prediction accuracy but possesses a large number of selected features. OSFS offers high prediction accuracy in many datasets, but its running time increases exponentially with an increasing number of features with low redundancy and high relevance. To address the limitations of the above-mentioned works, we propose an online learning algorithm named OSFAS , which samples streaming features in real-time by a self-adaption sliding-window and discards the irrelevant and redundant features by conditional independence. The OSFAS obtains an approximate Markov blanket with high prediction accuracy, meanwhile reducing the number of selected features. The efficiency of the proposed OSFASW algorithm was validated in a performance test on widely used datasets, e.g., NIPS 2003 and causality workbench . Through the extensive experimental results, we demonstrate that OSFAS significantly improves the prediction accuracy and requires a smaller number of selected features than alpha − investing , OSFS , and SAOLA .

Online Streaming Feature Selection via Conditional Independence

Online feature selection is a challenging topic in data mining. It aims to reduce the dimensionality of streaming features by removing irrelevant and redundant features in real time. Existing works, such as Alpha-investing and Online Streaming Feature Selection (OSFS), have been proposed to serve this purpose, but they have drawbacks, including low prediction accuracy and high running time if the streaming features exhibit characteristics such as low redundancy and high relevance. In this paper, we propose a novel algorithm about online streaming feature selection, named ConInd that uses a three-layer filtering strategy to process streaming features with the aim of overcoming such drawbacks. Through three-layer filtering, i.e., null-conditional independence, single-conditional independence, and multi-conditional independence, we can obtain an approximate Markov blanket with high accuracy and low running time. To validate the efficiency, we implemented the proposed algorithm and tested its performance on a prevalent dataset, i.e., NIPS 2003 and Causality Workbench. Through extensive experimental results, we demonstrated that ConInd offers significant performance improvements in prediction accuracy and running time compared to Alpha-investing and OSFS. ConInd offers 5.62% higher average prediction accuracy than Alpha-investing, with a 53.56% lower average running time compared to that for OSFS when the dataset is lowly redundant and highly relevant. In addition, the ratio of the average number of features for ConInd is 242% less than that for Alpha-investing.

The Anatomy of Inference: Generative Models and Brain Structure.

To infer the causes of its sensations, the brain must call on a generative (predictive) model. This necessitates passing local messages between populations of neurons to update beliefs about hidden variables in the world beyond its sensory samples. It also entails inferences about how we will act. Active inference is a principled framework that frames perception and action as approximate Bayesian inference. This has been successful in accounting for a wide range of physiological and behavioral phenomena. Recently, a process theory has emerged that attempts to relate inferences to their neurobiological substrates. In this paper, we review and develop the anatomical aspects of this process theory. We argue that the form of the generative models required for inference constrains the way in which brain regions connect to one another. Specifically, neuronal populations representing beliefs about a variable must receive input from populations representing the Markov blanket of that variable. We illustrate this idea in four different domains: perception, planning, attention, and movement. In doing so, we attempt to show how appealing to generative models enables us to account for anatomical brain architectures. Ultimately, committing to an anatomical theory of inference ensures we can form empirical hypotheses that can be tested using neuroimaging, neuropsychological, and electrophysiological experiments.

Making Worlds in a Waking Dream: Where Bion Intersects Friston on the Shaping and Breaking of Psychic Reality.

With the publication of Wilfred Bion’s text ‘Learning from Experience,’ psychoanalysis was afforded a new schema for understanding the processes and implications involved in an infant’s contact with their caregivers. As a result, our conception of some of the most fundamental phenomena of psychic life was significantly enriched. By proposing his theory of alpha-functioning, Bion mapped out how meaningful connexions to the internal and external worlds become established in the mind. In contrast, and through working clinically with psychotic patients, Bion revealed how these ties can catastrophically come undone. It is with these ideas, as well as their links to a corresponding set of neuroscientific constructs relating to the Markov blanket and principally developed by Karl Friston, that this paper is concerned. Through an investigation of the psychic functioning originally dubbed ‘dream-work-alpha,’ the paper’s first section focuses on how Bion conceived of the creation of a ‘contact-barrier’ that allows for the differentiation of consciousness from an unconscious mind. Casting the ramifications of this organisation in sharp relief, the psychotic disorganisation of the contact-barrier is then explored. The discussion subsequently broadens to incorporate contemporary theories from free energy neuroscience that bear significant and illuminating relations to the psychoanalytic ideas espoused by Bion over half a century ago. Finally, through posing a series of three questions with accompanying discussions, a superimposition of these theoretical schemas is attempted. These suggestions directly address, (1) whether there is an intimate connexion between the interoceptive contact-barrier and the exteroceptive Markov blanket, (2) whether a disobjectalising of the contact-barrier may be reflected as a tear in the functional fabric of the Markov blanket, and (3) what the clinical implications are of working at the level of the projected surface. Ultimately, the aim of the paper is to expose relevant points of contact within and between the varying conceptual frameworks; frameworks that ultimately derive from disciplines that are both concerned with examining the underlying mechanisms of the mind-brain.

Abstract 1127: Role of NRF1 regulatory gene-networks in glioblastoma

Abstract Nuclear Respiratory Factor 1 (NRF1), a transcription factor historically known to regulate several mitochondrial genes, has been recently implicated in human cancers. We have previously demonstrated the importance of NRF1 in estrogen driven breast cancer. The NRF1 motif exhibits some of the strongest pioneer activity (pioneer index indicates an increase in chromatin opening activity during developmental process) in mouse embryonic stem cells. Both neurogenesis and synaptogenesis are controlled by NRF1 regulated genes. There is a strong association of NRF1 with human fetal brain and neural development. To begin our study of the effect of NRF1 on glioblastoma pathogenesis, we examined whether NRF1 contributes to the acquisition of multipotent neural stem/progenitor cell (NSPC) properties in adult human brain cells. We generated NRF1 overexpressing stable human brain cerebral cortex astrocytes. Both 17β-estradiol (E2, 100 pg/ml) and NRF1 overexpression increased the percentage of cells co-expressing SOX2 and Nestin by 8 and 20%, respectively as shown by flow cytometry. Nestin is an intermediate filament protein important for guaranteeing neural stem pluripotent stem cell (NSPC) self-renewal while SOX2 is expressed at the earliest development stage of the brain and functions as a marker of neural development. SOX2 also plays a key role in the maintenance of neural stem cell (NSC) properties, including proliferation/survival, self-renewal, and neurogenesis. Multipotency allows NSPCs to differentiate into the neurons, astrocytes or oligodendrocytes. NRF1-induced SOX2+Nestin+ NSPCs expressed the neuronal marker β-III-tubulin, the neural phenotype, and neurosphere formation. NRF1 induced NSPCs were subjected to FACS analysis after FITC Annexin V and Propidium Iodide staining. Dead cells stained positive for both FITC Annexin V and PI and these cells are lowest in NRF1+ (0.42%) compared to vector control (4%). In summary, overexpression of NRF1 suppresses cellular senescence and increases resistance to apoptosis. Both are major barriers to cell reprogramming that may contribute in the generation of glioblastoma stem cells. To investigate the role of NRF1 gene network in glioblastoma, we used Bayesian network (BN) analysis on TCGA based RNA-seq data of 154 glioblastoma patients samples. NRF1 based gene association networks were significantly different in low overall survival (OS) patients compared with high OS patients. Specifically, TNFRSF10B, HGF, EBF4, and PAX5 showed up consistently as first degree Markov Blanket genes of NRF1 in low OS (<6mo) glioblastoma patients but not in the high OS patients. In conclusion, these data provide evidence in support of the role for NRF1 in glioblastoma. Clarifying these NRF1 driven complex mechanisms can be a guiding force in the development of new treatments to slow or prevent the development of glioblastoma. Citation Format: Kaumudi Bhawe, Jayanta Das, Changwon Yoo, Deodutta Roy. Role of NRF1 regulatory gene-networks in glioblastoma [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2018; 2018 Apr 14-18; Chicago, IL. Philadelphia (PA): AACR; Cancer Res 2018;78(13 Suppl):Abstract nr 1127.

Improving structure MCMC for Bayesian networks through Markov blanket resampling

Algorithms for inferring the structure of Bayesian networks from data have become an increasingly popular method for uncovering the direct and indirect influences among variables in complex systems. A Bayesian approach to structure learning uses posterior probabilities to quantify the strength with which the data and prior knowledge jointly support each possible graph feature. Existing Markov Chain Monte Carlo (MCMC) algorithms for estimating these posterior probabilities are slow in mixing and convergence, especially for large networks. We present a novel Markov blanket resampling (MBR) scheme that intermittently reconstructs the Markov blanket of nodes, thus allowing the sampler to more effectively traverse low-probability regions between local maxima. As we can derive the complementary forward and backward directions of the MBR proposal distribution, the Metropolis-Hastings algorithm can be used to account for any asymmetries in these proposals. Experiments across a range of network sizes show that the MBR scheme outperforms other state-of-the-art algorithms, both in terms of learning performance and convergence rate. In particular, MBR achieves better learning performance than the other algorithms when the number of observations is relatively small and faster convergence when the number of variables in the network is large.

A multiobjective Bayesian networks approach for joint prediction of tumor local control and radiation pneumonitis in nonsmall-cell lung cancer (NSCLC) for response-adapted radiotherapy.

Individualization of therapeutic outcomes in NSCLC radiotherapy is likely to be compromised by the lack of proper balance of biophysical factors affecting both tumor local control (LC) and side effects such as radiation pneumonitis (RP), which are likely to be intertwined. Here, we compare the performance of separate and joint outcomes predictions for response-adapted personalized treatment planning. A total of 118 NSCLC patients treated on prospective protocols with 32 cases of local progression and 20 cases of RP grade 2 or higher (RP2) were studied. Sixty-eight patients with 297 features before and during radiotherapy were used for discovery and 50 patients were reserved for independent testing. A multiobjective Bayesian network (MO-BN) approach was developed to identify important features for joint LC/RP2 prediction using extended Markov blankets as inputs to develop a BN predictive structure. Cross-validation (CV) was used to guide the MO-BN structure learning. Area under the free-response receiver operating characteristic (AU-FROC) curve was used to evaluate joint prediction performance. Important features including single nucleotide polymorphisms (SNPs), micro RNAs, pretreatment cytokines, pretreatment PET radiomics together with lung and tumor gEUDs were selected and their biophysical inter-relationships with radiation outcomes (LC and RP2) were identified in a pretreatment MO-BN. The joint LC/RP2 prediction yielded an AU-FROC of 0.80 (95% CI: 0.70-0.86) upon internal CV. This improved to 0.85 (0.75-0.91) with additional two SNPs, changes in one cytokine and two radiomics PET image features through the course of radiotherapy in a during-treatment MO-BN. This MO-BN model outperformed combined single-objective Bayesian networks (SO-BNs) during-treatment [0.78 (0.67-0.84)]. AU-FROC values in the evaluation of the MO-BN and individual SO-BNs on the testing dataset were 0.77 and 0.68 for pretreatment, and 0.79 and 0.71 for during-treatment, respectively. MO-BNs can reveal possible biophysical cross-talks between competing radiotherapy clinical endpoints. The prediction is improved by providing additional during-treatment information. The developed MO-BNs can be an important component of decision support systems for personalized response-adapted radiotherapy.

Prediction of post-operative residual disease in advanced-stage ovarian cancer (AOC) using whole transcriptome expression: An exploratory analysis of the AGO-OVAR 11 (ICON7) trial.

5550 Background: Complete resection (CR) at primary debulking surgery is the single most important prognostic factor in AOC. It has been demonstrated, that suboptimal debulking (residual disease > 1cm) might be associated with TCGA molecular subtypes and de novo generated gene expression (GE) signatures. The aim of this study was to validate previous findings and to investigate the impact whole transcriptome GE analyses might have on postoperative residual tumor prediction in a phase III ovarian cancer frontline trial. Methods: Core biopsies from formalin fixed paraffin embedded tumor tissue of FIGO stage IIIC/IV AGO-OVAR 11/ICON7 pts were used to generate whole-genome DASL GE data. TCGA molecular subtype and two previously published GE debulking signatures (7 genes and 11 genes) were correlated with size of residual disease (CR vs. any residual disease). Logistic Regression (LR), support vector machine with polynomial kernel, and random forest were used as classifiers. We built models with all GE features as well as gene selected with HITON-PC, a method that select the markov blanket of the outcome. Results: 283 pts met inclusion criteria, of those 114 (40.3%) had complete resection. Previous reported debulking signatures using 7 and 11 genes respectively did not predict residual disease in this cohort. Best Area under the Curve (AUC) for 7 gene signature was generated using LR 0.50 ± 0.05, while 11 gene signature had an AUC of 0.53 ± 0.04. Similarly, TCGA molecular subtypes (AUC = 0.56 ± 0.04), an independent de novo developed signature (AUC = 0.51 ± 0.04) and the total gene expression data set using all 21,000 genes (AUC = 0.55 ± 0.03) were not able to predict residual disease status. Conclusions: In contrast to previous findings, we were not able to predict residual disease using GE in tumor samples from the AGO-OVAR11/ICON7 phase III trial. A standardized radical surgical approach resulting in a higher frequency of complete resection might allow detection of biologic factors responsible for sub-optimal debulking. The ongoing AGO-OVAR TRUST trial might be able to address this important clinical question.

Mining Markov Blankets Without Causal Sufficiency

Markov blankets (MBs) in Bayesian networks (BNs) play an important role in both local causal discovery and large-scale BN structure learning. Almost all existing MB discovery algorithms are designed under the assumption of causal sufficiency, which states that there are no latent common causes for two or more of the observed variables in data. However, latent common causes are ubiquitous in many applications, and hence, this assumption is often violated in practice. Thus, developing algorithms for discovering MBs without assuming causal sufficiency is of practical significance, and it is crucial for causal structure learning in real-world data. In this paper, we focus on addressing this problem. Specifically, we adopt a maximal ancestral graph (MAG) model to represent latent common causes and the concept of MBs without assuming causal sufficiency. Then, we propose an effective and efficient algorithm to discover the MB of a target variable in an MAG. Using benchmark and real-world data sets, the experiments validate the algorithm proposed in this paper.

Development of a Fully Cross-Validated Bayesian Network Approach for Local Control Prediction in Lung Cancer.

The purpose of this study is to demonstrate that a Bayesian network (BN) approach can explore hierarchical biophysical relationships that influence tumor response and predict tumor local control (LC) in non-small-cell lung cancer (NSCLC) patients before and during radiotherapy from a large-scale dataset. Our BN building approach has two steps. First, relevant biophysical predictors influencing LC before and during the treatment are selected through an extended Markov blanket (eMB) method. From this eMB process, the most robust BN structure for LC prediction was found via a wrapper-based approach. Sixty-eight patients with complete feature information were used to identify a full BN model for LC prediction before and during the treatment. Fifty more recent patients with some missing information were reserved for independent testing of the developed pre- and during-therapy BNs. A nested cross-validation (N-CV) was developed to evaluate the performance of the two-step BN approach. An ensemble BN model is generated from the N-CV sampling process to assess its similarity with the corresponding full BN model, and thus evaluate the sensitivity of our BN approach. Our results show that the proposed BN development approach is a stable and robust approach to identify hierarchical relationships among biophysical features for LC prediction. Furthermore, BN predictions can be improved by incorporating during treatment information.

Core Dependency Networks

Many applications infer the structure of a probabilistic graphical model from data to elucidate the relationships between variables. But how can we train graphical models on a massive data set? In this paper, we show how to construct coresets---compressed data sets which can be used as proxy for the original data and have provably bounded worst case error---for Gaussian dependency networks (DNs), i.e., cyclic directed graphical models over Gaussians, where the parents of each variable are its Markov blanket. Specifically, we prove that Gaussian DNs admit coresets of size independent of the size of the data set. Unfortunately, this does not extend to DNs over members of the exponential family in general. As we will prove, Poisson DNs do not admit small coresets. Despite this worst-case result, we will provide an argument why our coreset construction for DNs can still work well in practice on count data.To corroborate our theoretical results, we empirically evaluated the resulting Core DNs on real data sets. The results demonstrate significant gains over no or naive sub-sampling, even in the case of count data.

Finding a set of candidate parents using dependency criterion for the K2 algorithm

One of the most effective structure-learning methods in a Bayesian network is the K2 algorithm. Because the performance of the K2 algorithm depends on the node ordering, more effective node ordering inference methods are needed. In this paper, we introduce a novel method for finding a set of candidate parents for each node as input for the K2 algorithm. Based on the fact that the candidate parents are identified by estimated Markov Blanket, we first estimate the Markov Blanket of a variable by using the L1-regularized Markov Blanket. We then determine the candidate parents of a variable through its Markov blanket by introducing a new scoring function based on the dependency criterion. Then the candidate parents are used as input for the K2 algorithm for learning Bayesian network structure. Experimental results over most of the datasets indicate that the proposed method avoids creating extra edges and significantly outperforms the previous methods.

SMMB: a stochastic Markov blanket framework strategy for epistasis detection in GWAS

Large scale genome-wide association studies (GWAS) are tools of choice for discovering associations between genotypes and phenotypes. To date, many studies rely on univariate statistical tests for association between the phenotype and each assayed single nucleotide polymorphism (SNP). However, interaction between SNPs, namely epistasis, must be considered when tackling the complexity of underlying biological mechanisms. Epistasis analysis at large scale entails a prohibitive computational burden when addressing the detection of more than two interacting SNPs. In this paper, we introduce a stochastic causal graph-based method, SMMB, to analyze epistatic patterns in GWAS data. We present Stochastic Multiple Markov Blanket algorithm (SMMB), which combines both ensemble stochastic strategy inspired from random forests and Bayesian Markov blanket-based methods. We compared SMMB with three other recent algorithms using both simulated and real datasets. Our method outperforms the other compared methods for a majority of simulated cases of 2-way and 3-way epistasis patterns (especially in scenarii where minor allele frequencies of causal SNPs are low). Our approach performs similarly as two other compared methods for large real datasets, in terms of power, and runs faster. Parallel version available on https://ls2n.fr/listelogicielsequipe/DUKe/128/. Supplementary data are available at Bioinformatics online.

Hierarchical Markov blankets and adaptive active inference: Comment on “Answering Schrödinger's question: A free-energy formulation” by Maxwell James Désormeau Ramstead et al.

Hierarchical Markov blankets and adaptive active inference: Comment on “Answering Schrödinger's question: A free-energy formulation” by Maxwell James Désormeau Ramstead et al.