Learning Bayesian Networks using the Constrained Maximum a Posteriori Probability Method

Purely data-driven methods often fail to learn accurate conditional probability table (CPT) parameters of discrete Bayesian networks (BNs) when training data are scarce or incomplete. A practical and efficient means of overcoming this problem is to introduce qualitative parameter constraints derived from expert judgments. To exploit such knowledge, in this paper, we provide a constrained maximum a posteriori (CMAP) method to learn CPT parameters by incorporating convex constraints. To further improve the CMAP method, we present a type of constrained Bayesian Dirichlet priors that is compatible with the given constraints. Combined with the CMAP method, we propose an improved expectation maximum algorithm to process incomplete data. Experiments are conducted on learning standard BNs from complete and incomplete data. The results show that the proposed method outperforms existing methods, especially when data are extremely limited or incomplete. This finding suggests the potential effective application of CMAP to real-world problems. Moreover, a real facial action unit (AU) recognition case with incomplete data is conducted by applying different parameter learning methods. The results show that the recognition accuracy of respective recognition methods can be improved by the AU BN, which is trained by the proposed method

Causal Modelling Based on Bayesian Networks for Preliminary Design of Buildings

Bayesian networks are a very general and powerful tool that can be used for a large number of problems involving uncertainty: reasoning, learning, planning and perception. They provide a language that supports efficient algorithms for the automatic construction of expert systems in several different contexts. The range of applications of Bayesian networks currently extends over almost all fields including engineering, biology and medicine, information and communication technologies and finance. This book is a collection of original contributions to the methodology and applications of Bayesian networks. It contains recent developments in the field and illustrates, on a sample of applications, the power of Bayesian networks in dealing the modeling of complex systems. Readers that are not familiar with this tool, but have some technical background, will find in this book all necessary theoretical and practical information on how to use and implement Bayesian networks in their own work. There is no doubt that this book constitutes a valuable resource for engineers, researchers, students and all those who are interested in discovering and experiencing the potential of this major tool of the century

Neuro-fuzzy knowledge processing in intelligent learning environments for improved student diagnosis

In this paper, a neural network implementation for a fuzzy logic-based model of the diagnostic process is proposed as a means to achieve accurate student diagnosis and updates of the student model in Intelligent Learning Environments. The neuro-fuzzy synergy allows the diagnostic model to some extent "imitate" teachers in diagnosing students' characteristics, and equips the intelligent learning environment with reasoning capabilities that can be further used to drive pedagogical decisions depending on the student learning style. The neuro-fuzzy implementation helps to encode both structured and non-structured teachers' knowledge: when teachers' reasoning is available and well defined, it can be encoded in the form of fuzzy rules; when teachers' reasoning is not well defined but is available through practical examples illustrating their experience, then the networks can be trained to represent this experience. The proposed approach has been tested in diagnosing aspects of student's learning style in a discovery-learning environment that aims to help students to construct the concepts of vectors in physics and mathematics. The diagnosis outcomes of the model have been compared against the recommendations of a group of five experienced teachers, and the results produced by two alternative soft computing methods. The results of our pilot study show that the neuro-fuzzy model successfully manages the inherent uncertainty of the diagnostic process; especially for marginal cases, i.e. where it is very difficult, even for human tutors, to diagnose and accurately evaluate students by directly synthesizing subjective and, some times, conflicting judgments

Possibilistic networks parameter learning: Preliminary empirical comparison

International audienceLike Bayesian networks, possibilistic ones compactly encode joint uncertainty representations over a set of variables. Learning possibilistic networks from data in general and from imperfect or scarce data in particular, has not received enough attention. Indeed, only few works deal with learning the structure and the parameters of a possibilistic network from a dataset. This paper provides a preliminary comparative empirical evaluation of two approaches for learning the parameters of a possibilistic network from empirical data. The first method is a possibilistic approach while the second one first learns imprecise probability measures then transforms them into possibility distributions by means of probability-possibility transformations. The comparative evaluation focuses on learning belief networks on datasets with missing data and scarce datasets

Probabilistic graphical models parameter learning with transferred prior and constraints

Learning accurate Bayesian networks (BNs) is a key challenge in real-world applications, especially when training data are hard to acquire. Two approaches have been used to address this challenge: 1) introducing expert judgements and 2) transferring knowledge from related domains. This is the first paper to present a generic framework that combines both approaches to improve BN parameter learning. This framework is built upon an extended multinomial parameter learning model, that itself is an auxiliary BN. It serves to integrate both knowledge transfer and expert constraints. Experimental results demonstrate improved accuracy of the new method on a variety of benchmark BNs, showing its potential to benefit many real-world problems