Business Process Event Log Transformation into Bayesian Belief Network

Business process (BP) mining has been recognized in business intelligence and reverse engineering fields because of the capabilities it has to discover knowledge about the implementation and execution of BP for analysis and improvement. Existing business knowledge extraction solutions in process mining context requires repeating analysis of event logs for each business knowledge extraction task. The probabilistic modelling could allow improved performance of BP analysis. Bayesian belief networks are a probabilistic modelling tool and the paper presents their application in BP mining. The paper shows that existing process mining algorithms are not suited for this, since they allow for loops in the extracted BP model that do not really exist in the event log,and presents a custom solution for directed acyclic graph extraction. The paper presents results of a synthetic log transformation into Bayesian belief network showing possible application in business intelligence extraction and improved decision support capabilities

Efficient inference in Bayes networks as a combinatorial optimization problem

AbstractA number of exact algorithms have been developed in recent years to perform probabilistic inference in Bayesian belief networks. The techniques used in these algorithms are closely related to network structures, and some of them are not easy to understand and implement. We consider the problem from the combinatorial optimization point of view and state that efficient probabilistic inference in a belief network is a problem of finding an optimal factoring given a set of probability distributions. From this viewpoint, previously developed algorithms can be seen as alternative factoring strategies. In this paper, we define a combinatorial optimization problem, the optimal factoring problem, and discuss application of this problem in belief networks. We show that optimal factoring provides insight into the key elements of efficient probabilistic inference, and demonstrate simple, easily implemented algorithms with excellent performance

Deep Gaussian Processes

In this paper we introduce deep Gaussian process (GP) models. Deep GPs are a deep belief network based on Gaussian process mappings. The data is modeled as the output of a multivariate GP. The inputs to that Gaussian process are then governed by another GP. A single layer model is equivalent to a standard GP or the GP latent variable model (GP-LVM). We perform inference in the model by approximate variational marginalization. This results in a strict lower bound on the marginal likelihood of the model which we use for model selection (number of layers and nodes per layer). Deep belief networks are typically applied to relatively large data sets using stochastic gradient descent for optimization. Our fully Bayesian treatment allows for the application of deep models even when data is scarce. Model selection by our variational bound shows that a five layer hierarchy is justified even when modelling a digit data set containing only 150 examples.Comment: 9 pages, 8 figures. Appearing in Proceedings of the 16th International Conference on Artificial Intelligence and Statistics (AISTATS) 201

A bayesian belief networks approach to risk control in construction projects

Although risk control is a key step in risk management of construction projects, very often risk measures used are based merely on personal experience and engineering judgement rather than analysis of comprehensive information relating to a specific risk. This paper deals with an approach to provide better information to derive relevant and effective risk measures for specific risks. The approach relies on developing risk models to represent interactions between risk factors and carrying out analysis to identify critical factors on which risk measures must focus. To ameliorate the problem related to the scarcity of risks information often encountered in construction projects, Bayesian Belief Networks are used and expert knowledge is elicited to augment available information. The paper describes proposed modifications to the standard methods used to develop Bayesian Belief Networks in order to deal with divergent information originated from epistemic uncertainty of risks. The\ud capacity of the proposed approach to provide better information to support risk related decision making is verified by means of an illustrative application to risk factors involved in the construction of cross passages between tunnels tubes in soft soils

Towards a Mathematical Theory of Cortical Micro-circuits

The theoretical setting of hierarchical Bayesian inference is gaining acceptance as a framework for understanding cortical computation. In this paper, we describe how Bayesian belief propagation in a spatio-temporal hierarchical model, called Hierarchical Temporal Memory (HTM), can lead to a mathematical model for cortical circuits. An HTM node is abstracted using a coincidence detector and a mixture of Markov chains. Bayesian belief propagation equations for such an HTM node define a set of functional constraints for a neuronal implementation. Anatomical data provide a contrasting set of organizational constraints. The combination of these two constraints suggests a theoretically derived interpretation for many anatomical and physiological features and predicts several others. We describe the pattern recognition capabilities of HTM networks and demonstrate the application of the derived circuits for modeling the subjective contour effect. We also discuss how the theory and the circuit can be extended to explain cortical features that are not explained by the current model and describe testable predictions that can be derived from the model