Learning Bayesian Networks Structure with Continuous Variables

2006 ◽  
pp. 448-456 ◽  
Author(s):  
Shuang-Cheng Wang ◽  
Xiao-Lin Li ◽  
Hai-Yan Tang
Keyword(s):  
Bayesian Networks ◽  
Continuous Variables ◽  
Networks Structure

scholarly journals Gaussian Mixture Reduction for Time-Constrained Approximate Inference in Hybrid Bayesian Networks

2019 ◽  
Vol 9 (10) ◽  
pp. 2055 ◽  
Author(s):  
Cheol Young Park ◽  
Kathryn Blackmond Laskey ◽  
Paulo C. G. Costa ◽  
Shou Matsumoto
Keyword(s):  
Bayesian Networks ◽  
Message Passing ◽  
Random Variables ◽  
Computation Time ◽  
Gaussian Mixture ◽  
Image Understanding ◽  
Approximate Inference ◽  
Continuous Variables ◽  
Hybrid Bayesian Networks ◽  
Trade Off

Hybrid Bayesian Networks (HBNs), which contain both discrete and continuous variables, arise naturally in many application areas (e.g., image understanding, data fusion, medical diagnosis, fraud detection). This paper concerns inference in an important subclass of HBNs, the conditional Gaussian (CG) networks, in which all continuous random variables have Gaussian distributions and all children of continuous random variables must be continuous. Inference in CG networks can be NP-hard even for special-case structures, such as poly-trees, where inference in discrete Bayesian networks can be performed in polynomial time. Therefore, approximate inference is required. In approximate inference, it is often necessary to trade off accuracy against solution time. This paper presents an extension to the Hybrid Message Passing inference algorithm for general CG networks and an algorithm for optimizing its accuracy given a bound on computation time. The extended algorithm uses Gaussian mixture reduction to prevent an exponential increase in the number of Gaussian mixture components. The trade-off algorithm performs pre-processing to find optimal run-time settings for the extended algorithm. Experimental results for four CG networks compare performance of the extended algorithm with existing algorithms and show the optimal settings for these CG networks.

scholarly journals The application of Bayesian networks in natural hazard analyses

2013 ◽  
Vol 1 (5) ◽  
pp. 5805-5854
Author(s):  
K. Vogel ◽  
C. Riggelsen ◽  
O. Korup ◽  
F. Scherbaum
Keyword(s):  
Bayesian Networks ◽  
Bayesian Network ◽  
Domain Knowledge ◽  
Natural Hazard ◽  
Hazard Analysis ◽  
Flood Damage ◽  
Continuous Variables ◽  
Real World Data ◽  
Ground Motion Model ◽  
Hazard Assessments

Abstract. In natural hazards we face several uncertainties due to our lack of knowledge and/or the intrinsic randomness of the underlying natural processes. Nevertheless, deterministic analysis approaches are still widely used in natural hazard assessments, with the pitfall of underestimating the hazard with potentially disastrous consequences. In this paper we show that the Bayesian network approach offers a flexible framework for capturing and expressing a broad range of different uncertainties as those encountered in natural hazard assessments. Although well studied in theory, the application of Bayesian networks on real-world data is often not straightforward and requires specific tailoring and adaption of existing algorithms. We demonstrate by way of three case studies (a ground motion model for a seismic hazard analysis, a flood damage assessment, and a landslide susceptibility study) the applicability of Bayesian networks across different domains showcasing various properties and benefits of the Bayesian network framework. We offer suggestions as how to tackle practical problems arising along the way, mainly concentrating on the handling of continuous variables, missing observations, and the interaction of both. We stress that our networks are completely data-driven, although prior domain knowledge can be included if desired.

AN INTRODUCTION TO HIDDEN MARKOV MODELS AND BAYESIAN NETWORKS

2001 ◽  
Vol 15 (01) ◽  
pp. 9-42 ◽  
Author(s):  
ZOUBIN GHAHRAMANI
Keyword(s):  
Bayesian Networks ◽  
Hidden Markov Models ◽  
Markov Models ◽  
Recent Literature ◽  
Hidden Markov ◽  
Continuous Variables ◽  
State Variables ◽  
Exact Inference ◽  
Markov Chain Sampling ◽  
Inference Algorithms

We provide a tutorial on learning and inference in hidden Markov models in the context of the recent literature on Bayesian networks. This perspective makes it possible to consider novel generalizations of hidden Markov models with multiple hidden state variables, multiscale representations, and mixed discrete and continuous variables. Although exact inference in these generalizations is usually intractable, one can use approximate inference algorithms such as Markov chain sampling and variational methods. We describe how such methods are applied to these generalized hidden Markov models. We conclude this review with a discussion of Bayesian methods for model selection in generalized HMMs.

Sign in / Sign up

Export Citation Format

Share Document