scholarly journals Cutset Bayesian Networks: A New Representation for Learning Rao-Blackwellised Graphical Models

2019 ◽  
Author(s):  
Tahrima Rahman ◽  
Shasha Jin ◽  
Vibhav Gogate
Keyword(s):  
Bayesian Networks ◽  
Graphical Models ◽  
Prediction Accuracy ◽  
Probabilistic Models ◽  
Probability Distributions ◽  
Main Idea ◽  
Exact Inference ◽  
Trade Off ◽  
Probability Estimates ◽  
Prediction Time

Recently there has been growing interest in learning probabilistic models that admit poly-time inference called tractable probabilistic models from data. Although they generalize poorly as compared to intractable models, they often yield more accurate estimates at prediction time. In this paper, we seek to further explore this trade-off between generalization performance and inference accuracy by proposing a novel, partially tractable representation called cutset Bayesian networks (CBNs). The main idea in CBNs is to partition the variables into two subsets X and Y, learn a (intractable) Bayesian network that represents P(X) and a tractable conditional model that represents P(Y|X). The hope is that the intractable model will help improve generalization while the tractable model, by leveraging Rao-Blackwellised sampling which combines exact inference and sampling, will help improve the prediction accuracy. To compactly model P(Y|X), we introduce a novel tractable representation called conditional cutset networks (CCNs) in which all conditional probability distributions are represented using calibrated classifiers—classifiers which typically yield higher quality probability estimates than conventional classifiers. We show via a rigorous experimental evaluation that CBNs and CCNs yield more accurate posterior estimates than their tractable as well as intractable counterparts.

scholarly journals Uniqueness of the Level Two Bayesian Network Representing a Probability Distribution

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Linda Smail
Keyword(s):  
Artificial Intelligence ◽  
Probability Distribution ◽  
Bayesian Networks ◽  
Bayesian Network ◽  
Probabilistic Models ◽  
Probability Distributions ◽  
Random Variables ◽  
Inference Problem ◽  
Computation Algorithm

Bayesian Networks are graphic probabilistic models through which we can acquire, capitalize on, and exploit knowledge. they are becoming an important tool for research and applications in artificial intelligence and many other fields in the last decade. This paper presents Bayesian networks and discusses the inference problem in such models. It proposes a statement of the problem and the proposed method to compute probability distributions. It also uses D-separation for simplifying the computation of probabilities in Bayesian networks. Given a Bayesian network over a family of random variables, this paper presents a result on the computation of the probability distribution of a subset of using separately a computation algorithm and D-separation properties. It also shows the uniqueness of the obtained result.

scholarly journals Structured Bayesian Networks: From Inference to Learning with Routes

2019 ◽  
Vol 33 ◽  
pp. 7957-7965
Author(s):  
Yujia Shen ◽  
Anchal Goyanka ◽  
Adnan Darwiche ◽  
Arthur Choi
Keyword(s):  
Bayesian Networks ◽  
Graphical Models ◽  
Learning Algorithm ◽  
Simple Algorithm ◽  
Gps Data ◽  
Inference Algorithm ◽  
Exact Inference ◽  
Polynomial Size ◽  
Traditional Approaches ◽  
Domain Constraints

Structured Bayesian networks (SBNs) are a recently proposed class of probabilistic graphical models which integrate background knowledge in two forms: conditional independence constraints and Boolean domain constraints. In this paper, we propose the first exact inference algorithm for SBNs, based on compiling a given SBN to a Probabilistic Sentential Decision Diagram (PSDD). We further identify a tractable subclass of SBNs, which have PSDDs of polynomial size. These SBNs yield a tractable model of route distributions, whose structure can be learned from GPS data, using a simple algorithm that we propose. Empirically, we demonstrate the utility of our inference algorithm, showing that it can be an order-ofmagnitude more efficient than more traditional approaches to exact inference. We demonstrate the utility of our learning algorithm, showing that it can learn more accurate models and classifiers from GPS data.

scholarly journals Computation of Kullback–Leibler Divergence in Bayesian Networks

Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1122
Author(s):  
Serafín Moral ◽  
Andrés Cano ◽  
Manuel Gómez-Olmedo
Keyword(s):  
Probability Distribution ◽  
Bayesian Networks ◽  
Graphical Models ◽  
Probability Distributions ◽  
Computer Code ◽  
Efficient Computation ◽  
True Probability ◽  
Direct Computation ◽  
Leibler Divergence ◽  
Deletion Algorithm

Kullback–Leibler divergence KL(p,q) is the standard measure of error when we have a true probability distribution p which is approximate with probability distribution q. Its efficient computation is essential in many tasks, as in approximate computation or as a measure of error when learning a probability. In high dimensional probabilities, as the ones associated with Bayesian networks, a direct computation can be unfeasible. This paper considers the case of efficiently computing the Kullback–Leibler divergence of two probability distributions, each one of them coming from a different Bayesian network, which might have different structures. The paper is based on an auxiliary deletion algorithm to compute the necessary marginal distributions, but using a cache of operations with potentials in order to reuse past computations whenever they are necessary. The algorithms are tested with Bayesian networks from the bnlearn repository. Computer code in Python is provided taking as basis pgmpy, a library for working with probabilistic graphical models.

scholarly journals Belief propagation for networks with loops

2021 ◽  
Vol 7 (17) ◽  
pp. eabf1211
Author(s):  
Alec Kirkley ◽  
George T. Cantwell ◽  
M. E. J. Newman
Keyword(s):  
Graphical Models ◽  
Message Passing ◽  
Probabilistic Models ◽  
Belief Propagation ◽  
Probability Distributions ◽  
Fast Calculation ◽  
Potential Applications ◽  
The Common ◽  
Bayesian Graphical Models ◽  
Standing Problem

Belief propagation is a widely used message passing method for the solution of probabilistic models on networks such as epidemic models, spin models, and Bayesian graphical models, but it suffers from the serious shortcoming that it works poorly in the common case of networks that contain short loops. Here, we provide a solution to this long-standing problem, deriving a belief propagation method that allows for fast calculation of probability distributions in systems with short loops, potentially with high density, as well as giving expressions for the entropy and partition function, which are notoriously difficult quantities to compute. Using the Ising model as an example, we show that our approach gives excellent results on both real and synthetic networks, improving substantially on standard message passing methods. We also discuss potential applications of our method to a variety of other problems.

Reconciling internal and external satisfaction through probabilistic graphical models

2017 ◽  
Vol 9 (3/4) ◽  
pp. 347-370 ◽  
Author(s):  
Flaminia Musella ◽  
Roberta Guglielmetti Mugion ◽  
Hendry Raharjo ◽  
Laura Di Pietro
Keyword(s):  
Customer Satisfaction ◽  
Bayesian Networks ◽  
Graphical Models ◽  
Object Oriented ◽  
Holistic Approach ◽  
Probabilistic Graphical Models ◽  
Model Parameters ◽  
Holistic View ◽  
Content Type ◽  
External Customer

Purpose This paper aims to holistically reconcile internal and external customer satisfaction using probabilistic graphical models. The models are useful not only in the identification of the most sensitive factors for the creation of both internal and external customer satisfaction but also in the generation of improvement scenarios in a probabilistic way. Design/methodology/approach Standard Bayesian networks and object-oriented Bayesian networks are used to build probabilistic graphical models for internal and external customers. For each ward, the model is used to evaluate satisfaction drivers by category, and scenarios for the improvement of overall satisfaction variables are developed. A global model that is based on an object-oriented network is modularly built to provide a holistic view of internal and external satisfaction. The linkage is created by building a global index of internal and external satisfaction based on a linear combination. The model parameters are derived from survey data from an Italian hospital. Findings The results that were achieved with the Bayesian networks are consistent with the results of previous research, and they were obtained by using a partial least squares path modelling tool. The variable ‘Experience’ is the most relevant internal factor for the improvement of overall patient satisfaction. To improve overall employee satisfaction, the variable ‘Product/service results’ is the most important. Finally, for a given target of overall internal and external satisfaction, external satisfaction is more sensitive to improvement than internal satisfaction. Originality/value The novelty of the paper lies in the efforts to link internal and external satisfaction based on a probabilistic expert system that can generate improvement scenarios. From an academic viewpoint, this study moves the service profit chain theory (Heskett et al., 1994) forward by delivering operational guidelines for jointly managing the factors that affect internal and external customer satisfaction in service organizations using a holistic approach.

scholarly journals INCREMENTAL COMPILATION OF BAYESIAN NETWORKS BASED ON MAXIMAL PRIME SUBGRAPHS

2011 ◽  
Vol 19 (02) ◽  
pp. 155-191 ◽  
Author(s):  
M. JULIA FLORES ◽  
JOSE A. GÁMEZ ◽  
KRISTIAN G. OLESEN
Keyword(s):  
Bayesian Networks ◽  
Bayesian Network ◽  
Great Improvement ◽  
Experimental Evaluation ◽  
Iterative Process ◽  
Dynamic Models ◽  
Probability Distributions ◽  
Probability Propagation ◽  
Incremental Compilation

When a Bayesian network (BN) is modified, for example adding or deleting a node, or changing the probability distributions, we usually will need a total recompilation of the model, despite feeling that a partial (re)compilation could have been enough. Especially when considering dynamic models, in which variables are added and removed very frequently, these recompilations are quite resource consuming. But even further, for the task of building a model, which is in many occasions an iterative process, there is a clear lack of flexibility. When we use the term Incremental Compilation or IC we refer to the possibility of modifying a network and avoiding a complete recompilation to obtain the new (and different) join tree (JT). The main point we intend to study in this work is JT-based inference in Bayesian networks. Apart from undertaking the triangulation problem itself, we have achieved a great improvement for the compilation in BNs. We do not develop a new architecture for BNs inference, but taking some already existing framework JT-based for probability propagation such as Hugin or Shenoy and Shafer, we have designed a method that can be successfully applied to get better performance, as the experimental evaluation will show.

scholarly journals Evaluating probabilistic programming and fast variational Bayesian inference in phylogenetics

2019 ◽  
Author(s):  
Mathieu Fourment ◽  
Aaron E. Darling
Keyword(s):  
Probabilistic Models ◽  
Probability Distributions ◽  
Mean Field ◽  
Black Box ◽  
Variational Inference ◽  
Machine Learning Techniques ◽  
Mcmc Methods ◽  
Substitution Model ◽  
Probabilistic Programming ◽  
Phylogenetic Models

AbstractRecent advances in statistical machine learning techniques have led to the creation of probabilistic programming frameworks. These frameworks enable probabilistic models to be rapidly prototyped and fit to data using scalable approximation methods such as variational inference. In this work, we explore the use of the Stan language for probabilistic programming in application to phylogenetic models. We show that many commonly used phylogenetic models including the general time reversible (GTR) substitution model, rate heterogeneity among sites, and a range of coalescent models can be implemented using a probabilistic programming language. The posterior probability distributions obtained via the black box variational inference engine in Stan were compared to those obtained with reference implementations of Markov chain Monte Carlo (MCMC) for phylogenetic inference. We find that black box variational inference in Stan is less accurate than MCMC methods for phylogenetic models, but requires far less compute time. Finally, we evaluate a custom implementation of mean-field variational inference on the Jukes-Cantor substitution model and show that a specialized implementation of variational inference can be two orders of magnitude faster and more accurate than a general purpose probabilistic implementation.

Availability Estimation of Demand Buses as Human Transportation System, Using Self-Organizing Map

2011 ◽  
Vol 2 (3) ◽  
pp. 49-60
Author(s):  
Toyohide Watanabe ◽  
Kentaro Uesugi
Keyword(s):  
Cost Management ◽  
Main Idea ◽  
Transportation System ◽  
Self Organizing Map ◽  
Trade Off ◽  
Alternative Transportation ◽  
Visualization Techniques ◽  
Self Organizing

The demand bus is a new transportation means, which is timely planned and runs order by order in accordance with independent requests of individual customers. Demand buses are alternative transportation vehicles, replacing traditional routing-oriented buses. In this paper, the authors address the characteristic issues, attend to the practical operations, and estimate and evaluate the trade-off strategies between usage convenience and cost management. The main idea, which is established from the features among parameters interpretatively, is to make use of visualization techniques and apply a self-organizing map (SOM) to this visualization. The authors display the co-related classification results computed individually from several selected parameters to keep their meaningful correspondence.

scholarly journals Quantum Probabilistic Models Using Feynman Diagram Rules for Better Understanding the Information Diffusion Dynamics in Online Social Networks

2020 ◽  
Vol 34 (10) ◽  
pp. 13730-13731
Author(s):  
Ece C. Mutlu
Keyword(s):  
Social Networks ◽  
Social Learning ◽  
Complex Systems ◽  
Bayesian Networks ◽  
Online Social Networks ◽  
Information Diffusion ◽  
Probabilistic Models ◽  
Human Interaction ◽  
Multi Agent Systems ◽  
Diffusion Dynamics

This doctoral consortium presents an overview of my anticipated PhD dissertation which focuses on employing quantum Bayesian networks for social learning. The project, mainly, aims to expand the use of current quantum probabilistic models in human decision-making from two agents to multi-agent systems. First, I cultivate the classical Bayesian networks which are used to understand information diffusion through human interaction on online social networks (OSNs) by taking into account the relevance of multitude of social, psychological, behavioral and cognitive factors influencing the process of information transmission. Since quantum like models require quantum probability amplitudes, the complexity will be exponentially increased with increasing uncertainty in the complex system. Therefore, the research will be followed by a study on optimization of heuristics. Here, I suggest to use an belief entropy based heuristic approach. This research is an interdisciplinary research which is related with the branches of complex systems, quantum physics, network science, information theory, cognitive science and mathematics. Therefore, findings can contribute significantly to the areas related mainly with social learning behavior of people, and also to the aforementioned branches of complex systems. In addition, understanding the interactions in complex systems might be more viable via the findings of this research since probabilistic approaches are not only used for predictive purposes but also for explanatory aims.

Retrieving Medical Records Using Bayesian Networks

2011 ◽  
pp. 2274-2280
Author(s):  
Luis M. De Campos
Keyword(s):  
Information Retrieval ◽  
Bayesian Networks ◽  
Graphical Models ◽  
Medical Records ◽  
Network Models ◽  
Boolean Expression ◽  
Wide Range ◽  
Structured Information Retrieval ◽  
Structured Information ◽  
Bayesian Network Models

Bayesian networks (Jensen, 2001) are powerful tools for dealing with uncertainty. They have been successfully applied in a wide range of domains where this property is an important feature, as in the case of information retrieval (IR) (Turtle & Croft, 1991). This field (Baeza-Yates & Ribeiro- Neto, 1999) is concerned with the representation, storage, organization, and accessing of information items (the textual representation of any kind of object). Uncertainty is also present in this field, and, consequently, several approaches based on these probabilistic graphical models have been designed in an attempt to represent documents and their contents (expressed by means of indexed terms), and the relationships between them, so as to retrieve as many relevant documents as possible, given a query submitted by a user. Classic IR has evolved from flat documents (i.e., texts that do not have any kind of structure relating their contents) with all the indexing terms directly assigned to the document itself toward structured information retrieval (SIR) (Chiaramella, 2001), where the structure or the hierarchy of contents of a document is taken into account. For instance, a book can be divided into chapters, each chapter into sections, each section into paragraphs, and so on. Terms could be assigned to any of the parts where they occur. New standards, such as SGML or XML, have been developed to represent this type of document. Bayesian network models also have been extended to deal with this new kind of document. In this article, a structured information retrieval application in the domain of a pathological anatomy service is presented. All the medical records that this service stores are represented in XML, and our contribution involves retrieving records that are relevant for a given query that could be formulated by a Boolean expression on some fields, as well as using a text-free query on other different fields. The search engine that answers this second type of query is based on Bayesian networks.

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