Bayesian learning of structures of ordered block graphical models with an application on multistage manufacturing processes

The Ordered Block Model (OBM) is a special form of directed graphical models and is widely used in various fields. In this article, we focus on learning of structures of OBM based on prior knowledg...

[1]  Daphne Koller,et al.  Ordering-Based Search: A Simple and Effective Algorithm for Learning Bayesian Networks , 2005, UAI.

[2]  Li Zeng,et al.  Inferring the Interactions in Complex Manufacturing Processes Using Graphical Models , 2007, Technometrics.

[3]  Jing Li,et al.  A Sparse Structure Learning Algorithm for Gaussian Bayesian Network Identification from High-Dimensional Data , 2013, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[4]  Alexander J. Hartemink,et al.  Informative Structure Priors: Joint Learning of Dynamic Regulatory Networks from Multiple Types of Data , 2004, Pacific Symposium on Biocomputing.

[5]  Constantin F. Aliferis,et al.  Algorithms for Large Scale Markov Blanket Discovery , 2003, FLAIRS.

[6]  Patrik Holmström.  Modelling manufacturing systems capability , 2006 .

[7]  Kevin B. Korb,et al.  Incorporating expert knowledge when learning Bayesian network structure: A medical case study , 2011, Artif. Intell. Medicine.

[8]  Maria De Iorio,et al.  Bayesian inference for multiple Gaussian graphical models with application to metabolic association networks , 2016, 1603.06358.

[9]  Gregory F. Cooper,et al.  A Bayesian method for the induction of probabilistic networks from data , 1992, Machine Learning.

[10]  Luis M. de Campos,et al.  Independency relationships and learning algorithms for singly connected networks , 1998, J. Exp. Theor. Artif. Intell..

[11]  Xiangyu Luo,et al.  Nonparametric Bayesian learning of heterogeneous dynamic transcription factor networks , 2018, The Annals of Applied Statistics.

[12]  Jianhua Z. Huang,et al.  Covariance matrix selection and estimation via penalised normal likelihood , 2006 .

[13]  Nan Chen,et al.  Surrogate modeling of dimensional variation propagation in multistage assembly processes , 2009 .

[14]  M. Pourahmadi,et al.  Nonparametric estimation of large covariance matrices of longitudinal data , 2003 .

[15]  H. Jeffreys.  Some Tests of Significance, Treated by the Theory of Probability , 1935, Mathematical Proceedings of the Cambridge Philosophical Society.

[16]  Nir Friedman,et al.  Learning Bayesian Network Structure from Massive Datasets: The "Sparse Candidate" Algorithm , 1999, UAI.

[17]  Nir Friedman,et al.  Probabilistic Graphical Models - Principles and Techniques , 2009 .

[18]  David Heckerman,et al.  Learning Gaussian Networks , 1994, UAI.

[19]  J. Peters,et al.  Identifiability of Gaussian structural equation models with equal error variances , 2012, 1205.2536.

[20]  Tom Burr,et al.  Causation, Prediction, and Search , 2003, Technometrics.

[21]  Nir Friedman,et al.  Being Bayesian about Network Structure , 2000, UAI.

[22]  Bernhard Schölkopf,et al.  Kernel-based Conditional Independence Test and Application in Causal Discovery , 2011, UAI.

[23]  Jean Honorio,et al.  Learning Identifiable Gaussian Bayesian Networks in Polynomial Time and Sample Complexity , 2017, NIPS.

[24]  Jean-Michel Marin,et al.  Bayesian Modelling and Inference on Mixtures of Distributions , 2005 .

[25]  David Maxwell Chickering,et al.  Learning Bayesian Networks: The Combination of Knowledge and Statistical Data , 1994, Machine Learning.

[26]  Qiang Ji,et al.  Efficient Structure Learning of Bayesian Networks using Constraints , 2011, J. Mach. Learn. Res..

[27]  Jin Tian,et al.  A Branch-and-Bound Algorithm for MDL Learning Bayesian Networks , 2000, UAI.

[28]  T. Cai,et al.  A Constrained ℓ1 Minimization Approach to Sparse Precision Matrix Estimation , 2011, 1102.2233.

[29]  A. F. Smith.  A General Bayesian Linear Model , 1973 .

[30]  Qiang Zhou,et al.  Integrating GD&T into dimensional variation models for multistage machining processes , 2010 .

[31]  Jean Honorio,et al.  Information-theoretic limits of Bayesian network structure learning , 2016, AISTATS.

[32]  Nir Friedman,et al.  Data Analysis with Bayesian Networks: A Bootstrap Approach , 1999, UAI.

[33]  J. Berger,et al.  The Intrinsic Bayes Factor for Model Selection and Prediction , 1996 .

[34]  John M. Noble,et al.  The Minimal Hoppe-Beta Prior Distribution for Directed Acyclic Graphs and Structure Learning , 2016 .

[35]  Luis M. de Campos,et al.  A new approach for learning belief networks using independence criteria , 2000, Int. J. Approx. Reason..

[36]  Baba C. Vemuri,et al.  Robust Point Set Registration Using Gaussian Mixture Models , 2011, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[37]  Jianjun Shi,et al.  Quality control and improvement for multistage systems: A survey , 2009 .

[38]  Changhe Yuan,et al.  Improving the Scalability of Optimal Bayesian Network Learning with External-Memory Frontier Breadth-First Branch and Bound Search , 2011, UAI.