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The pc-algorithm of the Algebraic Bayesian Network Secondary Structure Training 1

19th Russian Conference on Artificial Intelligence (RCAI)

作者： Kharitonov, Nikita Abramov, Maxim Tulupyev, Alexander St Petersburg State Univ St Petersburg Russia Russian Acad Sci St Petersburg Fed Res Ctr St Petersburg Russia

ISBN: (数字)9783030868550

ISBN: (纸本)9783030868550;9783030868543

Algebraic Bayesian networks and Bayesian belief networks are one of the probabilistic graphical models. One of the main tasks which need to be solved during the networks' handling is the model structure training. This paper is dedicated to the automation of this process for algebraic Bayesian networks. This work relates to the pc-algorithm for algebraic Bayesian network secondary structure training. The algorithm is based on the pc-algorithm for Belief Bayesian networks training. The algorithm pseudocode and usage example are described. The provided algorithm helps investigate the full-automated machine learning of algebraic Bayesian networks. Earlier, the structure was provided by experts.

关键词： Algebraic bayesian networks Bayesian belief networks Probabilistic graphical models Structure training pc-algorithm

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Identification of Direction of Time in Vector Autoregressive Systems Using pc algorithm 6th

Identification of Direction of Time in Vector Autoregressive...

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6th International Conference on Communications, Signal Processing, and Systems (ICCSPS)

作者： Alipourfard, Borzou Gao, Jean X. Univ Texas Arlington Dept Comp Sci & Engn Arlington TX 76019 USA

ISBN: (纸本)9789811065712;9789811065705

In this paper we study whether it is possible to identify the direction of time in vector autoregressive processes. We prove a result regarding time reversibility of such systems and propose an algorithm to identify the direction of time when the system is not reversible. We first show that it is possible to utilize the pc-algorithm to identify the directed acyclic graph corresponding to a vector autoregressive process. The identified directed acyclic graph is then used to determine the direction of time. We test our proposed algorithm both on simulated data and real data consisting of EEG recordings.

关键词： Direction of time Vector autoregressive process Time reversibility Directed acyclic graphs pc-algorithm

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Default count-based network models for credit contagion

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 2022年第1期73卷 139-152页

作者： Agosto, Arianna Ahelegbey, Daniel Felix Univ Pavia Dept Econ & Management I-27100 Pavia Italy

Interconnectedness between economic institution and sectors, already recognised as a trigger of the great financial crisis in 2008-2009, is assuming growing importance in financial systems. In this article, we study contagion effects between corporate sectors using financial network models, in which the significant links are identified through conditional independence testing. While the existing financial network literature is mostly focused on Gaussian processes, our approach is based on discrete data. We indeed test dependence in the conditional mean (and volatility) of default counts in different economic sector estimated from Poisson autoregressive models, and in their shocks. Our empirical application to Italian corporate defaults in the 1996-2018 period reveals evidence of a high inter-sector vulnerability, especially at the onset of the global financial crisis in 2008 and in the following years. Many contagion effects between corporate sectors are indeed found in the shock component of the default count dynamics.

关键词： Financial networks inter-sector contagion Poisson autoregressive models vector autoregressive models conditional Granger causality pc-algorithm

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Multiple imputation and test-wise deletion for causal discovery with incomplete cohort data

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STATISTICS IN MEDICINE 2022年第23期41卷 4716-4743页

作者： Witte, Janine Foraita, Ronja Didelez, Vanessa Leibniz Inst Prevent Res & Epidemiol BIPS Bremen Germany Univ Bremen Fac Math & Comp Sci Bremen Germany

Causal discovery algorithms estimate causal graphs from observational data. This can provide a valuable complement to analyses focusing on the causal relation between individual treatment-outcome pairs. Constraint-based causal discovery algorithms rely on conditional independence testing when building the graph. Until recently, these algorithms have been unable to handle missing values. In this article, we investigate two alternative solutions: test-wise deletion and multiple imputation. We establish necessary and sufficient conditions for the recoverability of causal structures under test-wise deletion, and argue that multiple imputation is more challenging in the context of causal discovery than for estimation. We conduct an extensive comparison by simulating from benchmark causal graphs: as one might expect, we find that test-wise deletion and multiple imputation both clearly outperform list-wise deletion and single imputation. Crucially, our results further suggest that multiple imputation is especially useful in settings with a small number of either Gaussian or discrete variables, but when the dataset contains a mix of both neither method is uniformly best. The methods we compare include random forest imputation and a hybrid procedure combining test-wise deletion and multiple imputation. An application to data from the IDEFICS cohort study on diet- and lifestyle-related diseases in European children serves as an illustrating example.

关键词： causal inference causal search MICE missing values pc-algorithm structure learning

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A longitudinal causal graph analysis investigating modifiable risk factors and obesity in a European cohort of children and adolescents

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SCIENTIFIC REPORTS 2024年第1期14卷 1-14页

作者： Foraita, Ronja Witte, Janine Boernhorst, Claudia Gwozdz, Wencke Pala, Valeria Lissner, Lauren Lauria, Fabio Reisch, Lucia A. Molnar, Denes De Henauw, Stefaan Moreno, Luis Veidebaum, Toomas Tornaritis, Michael Pigeot, Iris Didelez, Vanessa Leibniz Inst Prevent Res & Epidemiol BIPS Achterstr 30 D-28359 Bremen Germany Univ Bremen Fac Math & Comp Sci Bremen Germany Justus Liebig Univ Dept Consumer Res Commun & Food Sociol Giessen Germany Copenhagen Business Sch Dept Management Soc & Commun Frederiksberg Denmark Fdn IRCCS Ist Nazl Tumori Milano Epidemiol & Prevent Unit Milan Italy Univ Gothenburg Sahlgrenska Acad Inst Med Sch Publ Hlth & Community Med Gothenburg Sweden CNR Inst Food Sci Avellino Italy Univ Cambridge El Erian Inst Behav Econ & Policy Cambridge England Univ Pecs Sch Med Dept Paediat Pecs Hungary Univ Ghent Fac Med & Hlth Sci Dept Publ Hlth & Primary Care Ghent Belgium Univ Zaragoza Inst Invest Sanitaria Aragon IIS Aragon IA2 GENUD Growth Exercise Nutr & Dev Res Grp Zaragoza Spain Natl Inst Hlth Dev Dept Chron Dis Tallinn Estonia Res & Educ Inst Child Hlth Strovolos Cyprus

Childhood obesity is a complex disorder that appears to be influenced by an interacting system of many factors. Taking this complexity into account, we aim to investigate the causal structure underlying childhood obesity. Our focus is on identifying potential early, direct or indirect, causes of obesity which may be promising targets for prevention strategies. Using a causal discovery algorithm, we estimate a cohort causal graph (CCG) over the life course from childhood to adolescence. We adapt a popular method, the so-called pc-algorithm, to deal with missing values by multiple imputation, with mixed discrete and continuous variables, and that takes background knowledge such as the time-structure of cohort data into account. The algorithm is then applied to learn the causal structure among 51 variables including obesity, early life factors, diet, lifestyle, insulin resistance, puberty stage and cultural background of 5112 children from the European IDEFICS/*** cohort across three waves (2007-2014). The robustness of the learned causal structure is addressed in a series of alternative and sensitivity analyses;in particular, we use bootstrap resamples to assess the stability of aspects of the learned CCG. Our results suggest some but only indirect possible causal paths from early modifiable risk factors, such as audio-visual media consumption and physical activity, to obesity (measured by age- and sex-adjusted BMI z-scores) 6 years later.

关键词： Audio-visual media consumption Causal structure learning DAG Healthy diet IDEFICS/I.Family cohort Multiple imputation pc-algorithm Physical activity Sleep Well-being

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Learning Causal Networks via Additive Faithfulness

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JOURNAL OF MACHINE LEARNING RESEARCH 2020年第1期21卷 1-38页

作者： Lee, Kuang-Yao Liu, Tianqi Li, Bing Zhao, Hongyu Temple Univ Dept Stat Sci 1810 Liacouras Walk Philadelphia PA 19122 USA Google LLC 111 8th Ave New York NY 10011 USA Penn State Univ Dept Stat 326 Thomas Bldg University Pk PA 16802 USA Yale Sch Publ Hlth Dept Biostat 60 Coll St New Haven CT 06520 USA

In this paper we introduce a statistical model, called additively faithful directed acyclic graph (AFDAG), for causal learning from observational data. Our approach is based on additive conditional independence (ACI), a recently proposed three-way statistical relation that shares many similarities with conditional independence but without resorting to multi-dimensional kernels. This distinct feature strikes a balance between a parametric model and a fully nonparametric model, which makes the proposed model attractive for handling large networks. We develop an estimator for AFDAG based on a linear operator that characterizes ACI, and establish the consistency and convergence rates of this estimator, as well as the uniform consistency of the estimated DAG. Moreover, we introduce a modified pc-algorithm to implement the estimating procedure efficiently, so that its complexity is determined by the level of sparseness rather than the dimension of the network. Through simulation studies we show that our method outperforms existing methods when commonly assumed conditions such as Gaussian or Gaussian copula distributions do not hold. Finally, the usefulness of AFDAG formulation is demonstrated through an application to a proteomics data set.

关键词： additive conditional independence additive reproducing kernel Hilbert space directed acyclic graph global Markov property normalized additive conditional covariance operator pc-algorithm

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Learning Bayesian network structures using weakest mutual-information-first strategy

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INTERNATIONAL JOURNAL OF APPROXIMATE REASONING 2019年 114卷 84-98页

作者： Qi, Xiaolong Fan, Xiaocong Gao, Yang Liu, Yanfang Nanjing Univ State Key Lab Novel Software Technol Nanjing Jiangsu Peoples R China Yili Normal Univ Dept Elect & Informat Engn Yining Peoples R China Calif State Univ Coll Sci & Math San Marcos CA USA Longyan Univ Coll Math & Informat Engn Longyan Peoples R China

In Bayesian network structure learning, the quality of the directed graph learned by the constraint-based approaches can be greatly affected by the order of choosing variable pairs and the order of selecting condition sets for testing conditional independence. Inspired by the strong connection between the degree of mutual information shared by two variables and their conditional independence, we introduce the M-ordering concept, where a matrix is precomputed from the observational data with variables ordered increasingly by their respective degree of mutual information with the target variable under concern. Given the M-ordering matrix, we propose a strategy called Weakest Mutual-Information-First Strategy (WMIF), which is integrated into the pc-algorithm in two aspects: an MI-based edge removal strategy, and an MI-based condition set generation strategy. The MI-based edge removal strategy is to always select the variable pair with the weakest mutual information to test their conditional independence;the condition set generation strategy is to construct a conditioning set where variables bearing a weaker degree of mutual information with the target variable are always considered first. We prove that the weakest MI-based edge removal strategy is sound, and our pc-MI algorithm, a pc variant empowered by the WMIF strategy, is order-independent. Moreover, in pc algorithms, the number of conditional independence tests increases exponentially with the number of random variables;we. show that the WMIF strategy can effectively reduce the complexity (bounded by o(vertical bar V vertical bar(2(vertical bar adj(X)vertical bar) - vertical bar v vertical bar(2)/2))). We have conducted experiments with both low-dimensional and high-dimensional data sets, and the results indicate that pc-MI outperforms the state-of-the-art approaches. More importantly, the order-agnostic property of pc-MI can be extremely useful when it is hard to prescribe a meaningful variable ordering as needed

关键词： Bayesian network pc-algorithm Mutual information Variable ordering Conditional independence Markov chain

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Learning causal networks via additive faithfulness

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2020年第1期21卷 1849-1886页

作者： Kuang-Yao Lee Tianqi Liu Bing Li Hongyu Zhao Department of Statistical Science Temple University Philadelphia PA Google LLC New York NY Department of Statistics Pennsylvania State University University Park PA Department of Biostatistics Yale School of Public Health New Haven CT

In this paper we introduce a statistical model, called additively faithful directed acyclic graph (AFDAG), for causal learning from observational data. Our approach is based on additive conditional independence (ACI), a recently proposed three-way statistical relation that shares many similarities with conditional independence but without resorting to multi-dimensional kernels. This distinct feature strikes a balance between a parametric model and a fully nonparametric model, which makes the proposed model attractive for handling large networks. We develop an estimator for AFDAG based on a linear operator that characterizes ACI, and establish the consistency and convergence rates of this estimator, as well as the uniform consistency of the estimated DAG. Moreover, we introduce a modi_ed pc-algorithm to implement the estimating procedure efficiently, so that its complexity is determined by the level of sparseness rather than the dimension of the network. Through simulation studies we show that our method outperforms existing methods when commonly assumed conditions such as Gaussian or Gaussian copula distributions do not hold. Finally, the usefulness of AFDAG formulation is demonstrated through an application to a proteomics data set.

关键词： additive conditional independence additive reproducing kernel Hilbert space directed acyclic graph global Markov property normalized additive conditional covariance operator pc-algorithm

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Analyzing customer satisfaction in self-service technology adopted in airports

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JOURNAL OF MARKETING ANALYTICS 2018年第1期6卷 6-18页

作者： Yau, Hon Keung Tang, Ho Yi Horace City Univ Hong Kong Dept Syst Engn & Engn Management Kowloon Tong Kowloon Hong Kong Peoples R China

Customer satisfaction level is one of key performance indicators in the service industry. The various factors affecting this are studied to maintain an excellent relationship with customers. Self-service technology (SST) is widely implemented by companies in service sector. This paper proposes to apply the customer satisfaction survey to investigate factors influencing the customer satisfaction. The relationships among the factors are discovered using pc-algorithm. The critical factors are identified to be inputs in regression tree and ANN to estimate the customer satisfaction level. By means of comparison of models, importance of selected inputs is quantified and discussed. The results show that customer satisfaction has strong connectivity relationship with personal service attributes as well as affective and temporal commitment by running pc-algorithm. ANN validated by 10-fold cross validation is the best among the models. The most important factor influencing the satisfaction level to the companies is the customer's desire of continuing a relationship. The key benefit of the proposed approach is to avoid making subjective decisions, for instance, building a plausible initial path models in the analysis. The analytical results facilitate the decision-making process and better resource allocation in the airline and state its future development of self-service technology.

关键词： Self-service technology Predictive Modelling Customer Satisfaction pc-algorithm

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Inferring Functional Connectivity in fMRI Using Minimum Partial Correlation

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International Journal of Automation and computing 2017年第4期14卷 371-385页

作者： Lei Nie Xian Yang Paul M. Matthews Zhi-Wei Xu Yi-Ke Guo Department of Computing Imperial College London London SW7 2AZ UK Department of Medicine Imperial College London London SW7 2AZ UK Institute of Computing Technology Chinese Academy of Sciences Beijing 100190 China School of Computer Engineering and Science Shanghai University Shanghai 200444 China

Functional connectivity has emerged as a promising approach to study the functional organisation of the brain and to define features for prediction of brain state. The most widely used method for inferring functional connectivity is Pearson＇s correlation, but it cannot differentiate direct and indirect effects. This disadvantage is often avoided by computing the partial correlation between two regions controlling all other regions, but this method suffers from Berkson＇s paradox. Some advanced methods, such as regularised inverse covariance, have been applied. However, these methods usually depend on some parameters. Here we propose use of minimum partial correlation as a parameter-free measure for the skeleton of functional connectivity in functional magnetic resonance imaging （flVIRI）. The minimum partial correlation between two regions is the minimum of absolute values of partial correlations by controlling all possible subsets of other regions. Theoretically, there is a direct effect between two regions if and only if their minimum partial correlation is non-zero under faithfulness and Gaussian assumptions. The elastic pc-algorithm is designed to efficiently approximate minimum partial correlation within a computational time budget. The simulation study shows that the proposed method outperforms others in most cases and its application is illustrated using a resting-state fMRI dataset from the human connectome project.

关键词： Functional connectivity functional magnetic resonance imaging （fMRI） network modelling partial correlation pc-algorithm resting-state networks.

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