Learning Probabilistic Graphical Models

2012 ◽  
pp. 223-236
Author(s):  
Juan I. Alonso-Barba ◽  
Jens D. Nielsen ◽  
Luis de la Ossa ◽  
Jose M. Puerta
Keyword(s):  
Graphical Models ◽  
Statistical Models ◽  
Relevant Literature ◽  
Joint Probability ◽  
Probabilistic Graphical Models ◽  
Compact Representation ◽  
Joint Probability Distribution ◽  
Inference Algorithms ◽  
Probabilistic Queries ◽  
Local Parameters

Probabilistic Graphical Models (PGM) are a class of statistical models that use a graph structure over a set of variables to encode independence relations between those variables. By augmenting the graph by local parameters, a PGM allows for a compact representation of a joint probability distribution over the variables of the graph, which allows for efficient inference algorithms. PGMs are often used for modeling physical and biological systems, and such models are then in turn used to both answer probabilistic queries concerning the variables and to represent certain causal and/or statistical relations in the domain. In this chapter, the authors give an overview of common techniques used for automatic construction of such models from a dataset of observations (usually referred to as learning), and they also review some important applications. The chapter guides the reader to the relevant literature for further study.

NetCube

2011 ◽  
pp. 471-489
Author(s):  
Dimitris Margaritis ◽  
Christos Faloutsos ◽  
Sebastian Thrun
Keyword(s):  
Bayesian Networks ◽  
Graphical Models ◽  
Parallel Implementation ◽  
Joint Probability ◽  
Reconstruction Error ◽  
Joint Probability Distribution ◽  
Conjunctive Query ◽  
Database Size ◽  
Novel Method ◽  
Don't Cares

We present a novel method for answering count queries from a large database approximately and quickly. Our method implements an approximate DataCube of the application domain, which can be used to answer any conjunctive count query that can be formed by the user. The DataCube is a conceptual device that in principle stores the number of matching records for all possible such queries. However, because its size and generation time are inherently exponential, our approach uses one or more Bayesian networks to implement it approximately. Bayesian networks are statistical graphical models that can succinctly represent the underlying joint probability distribution of the domain, and can therefore be used to calculate approximate counts for any conjunctive query combination of attribute values and “don’t cares.” The structure and parameters of these networks are learned from the database in a preprocessing stage. By means of such a network, the proposed method, called NetCube, exploits correlations and independencies among attributes to answer a count query quickly without accessing the database. Our preprocessing algorithm scales linearly on the size of the database, and is thus scalable; it is also parallelizable with a straightforward parallel implementation. We give an algorithm for estimating the count result of arbitrary que ries that is fast (constant) on the database size. Our experimental results show that NetCubes have fast generation and use, achieve excellent compression and have low reconstruction error. Moreover, they naturally allow for visualization and data mining, at no extra cost.

NetCube

2009 ◽  
pp. 2011-2036
Author(s):  
Dimitris Margaritis ◽  
Christos Faloutsos ◽  
Sebastian Thrun
Keyword(s):  
Bayesian Networks ◽  
Graphical Models ◽  
Parallel Implementation ◽  
Joint Probability ◽  
Reconstruction Error ◽  
Joint Probability Distribution ◽  
Conjunctive Query ◽  
Database Size ◽  
Novel Method ◽  
Don't Cares

We present a novel method for answering count queries from a large database approximately and quickly. Our method implements an approximate DataCube of the application domain, which can be used to answer any conjunctive count query that can be formed by the user. The DataCube is a conceptual device that in principle stores the number of matching records for all possible such queries. However, because its size and generation time are inherently exponential, our approach uses one or more Bayesian networks to implement it approximately. Bayesian networks are statistical graphical models that can succinctly represent the underlying joint probability distribution of the domain, and can therefore be used to calculate approximate counts for any conjunctive query combination of attribute values and “don’t cares.” The structure and parameters of these networks are learned from the database in a preprocessing stage. By means of such a network, the proposed method, called NetCube, exploits correlations and independencies among attributes to answer a count query quickly without accessing the database. Our preprocessing algorithm scales linearly on the size of the database, and is thus scalable; it is also parallelizable with a straightforward parallel implementation. We give an algorithm for estimating the count result of arbitrary queries that is fast (constant) on the database size. Our experimental results show that NetCubes have fast generation and use, achieve excellent compression and have low reconstruction error. Moreover, they naturally allow for visualization and data mining, at no extra cost.

NetCube

2007 ◽  
pp. 54-83
Author(s):  
Dimitris Margaritis ◽  
Christos Faloutsos ◽  
Sebastian Thrun
Keyword(s):  
Bayesian Networks ◽  
Graphical Models ◽  
Parallel Implementation ◽  
Joint Probability ◽  
Reconstruction Error ◽  
Joint Probability Distribution ◽  
Conjunctive Query ◽  
Database Size ◽  
Novel Method ◽  
Don't Cares

We present a novel method for answering count queries from a large database approximately and quickly. Our method implements an approximate DataCube of the application domain, which can be used to answer any conjunctive count query that can be formed by the user. The DataCube is a conceptual device that in principle stores the number of matching records for all possible such queries. However, because its size and generation time are inherently exponential, our approach uses one or more Bayesian networks to implement it approximately. Bayesian networks are statistical graphical models that can succinctly represent the underlying joint probability distribution of the domain, and can therefore be used to calculate approximate counts for any conjunctive query combination of attribute values and “don’t cares.” The structure and parameters of these networks are learned from the database in a preprocessing stage. By means of such a network, the proposed method, called NetCube, exploits correlations and independencies among attributes to answer a count query quickly without accessing the database. Our preprocessing algorithm scales linearly on the size of the database, and is thus scalable; it is also parallelizable with a straightforward parallel implementation. We give an algorithm for estimating the count result of arbitrary queries that is fast (constant) on the database size. Our experimental results show that NetCubes have fast generation and use, achieve excellent compression and have low reconstruction error. Moreover, they naturally allow for visualization and data mining, at no extra cost.

Pseudo Independent Models

2011 ◽  
pp. 935-940
Author(s):  
Yang Xiang
Keyword(s):  
Probability Distribution ◽  
Computer System ◽  
Conditional Probability ◽  
Graphical Models ◽  
Intelligent Systems ◽  
Probabilistic Reasoning ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Conditional Probability Distribution ◽  
Binary Variables

Graphical models such as Bayesian networks (BNs) (Pearl, 1988) and decomposable Markov networks (DMNs) (Xiang, Wong & Cercone, 1997) have been applied widely to probabilistic reasoning in intelligent systems. Figure1 illustrates a BN and a DMN on a trivial uncertain domain: A virus can damage computer files, and so can a power glitch. A power glitch also causes a VCR to reset. The BN in (a) has four nodes, corresponding to four binary variables taking values from {true, false}. The graph structure encodes a set of dependence and independence assumptions (e.g., that f is directly dependent on v, and p but is independent of r, once the value of p is known). Each node is associated with a conditional probability distribution conditioned on its parent nodes (e.g., P(f | v, p)). The joint probability distribution is the product P(v, p, f, r) = P(f | v, p) P(r | p) P(v) P(p). The DMN in (b) has two groups of nodes that are maximally pair-wise connected, called cliques. Each clique is associated with a probability distribution (e.g., clique {v, p, f} is assigned P(v, p, f)). The joint probability distribution is P(v, p, f, r) = P(v, p, f) P(r, p) / P(p), where P(p) can be derived from one of the clique distributions. The networks, for instance, can be used to reason about whether there are viruses in the computer system, after observations on f and r are made.

Learning Bayesian Networks

2011 ◽  
pp. 315-321
Author(s):  
Marco F. Ramoni ◽  
Paola Sebastiani
Keyword(s):  
Probability Distribution ◽  
Bayesian Networks ◽  
Bayesian Network ◽  
Graphical Models ◽  
Graphical Model ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Probabilistic Graphical Model ◽  
Conditional Probability Distribution ◽  
Statistics And Probability

Born at the intersection of artificial intelligence, statistics, and probability, Bayesian networks (Pearl, 1988) are a representation formalism at the cutting edge of knowledge discovery and data mining (Heckerman, 1997). Bayesian networks belong to a more general class of models called probabilistic graphical models (Whittaker, 1990; Lauritzen, 1996) that arise from the combination of graph theory and probability theory, and their success rests on their ability to handle complex probabilistic models by decomposing them into smaller, amenable components. A probabilistic graphical model is defined by a graph, where nodes represent stochastic variables and arcs represent dependencies among such variables. These arcs are annotated by probability distribution shaping the interaction between the linked variables. A probabilistic graphical model is called a Bayesian network, when the graph connecting its variables is a directed acyclic graph (DAG). This graph represents conditional independence assumptions that are used to factorize the joint probability distribution of the network variables, thus making the process of learning from a large database amenable to computations. A Bayesian network induced from data can be used to investigate distant relationships between variables, as well as making prediction and explanation, by computing the conditional probability distribution of one variable, given the values of some others.

Learning Bayesian Networks

2011 ◽  
pp. 674-677
Author(s):  
Marco F. Ramoni ◽  
Paola Sebastiani
Keyword(s):  
Probability Distribution ◽  
Bayesian Networks ◽  
Bayesian Network ◽  
Graphical Models ◽  
Graphical Model ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Probabilistic Graphical Model ◽  
Conditional Probability Distribution ◽  
Statistics And Probability

Born at the intersection of artificial intelligence, statistics, and probability, Bayesian networks (Pearl, 1988) are a representation formalism at the cutting edge of knowledge discovery and data mining (Heckerman, 1997). Bayesian networks belong to a more general class of models called probabilistic graphical models (Whittaker, 1990; Lauritzen, 1996) that arise from the combination of graph theory and probability theory, and their success rests on their ability to handle complex probabilistic models by decomposing them into smaller, amenable components. A probabilistic graphical model is defined by a graph, where nodes represent stochastic variables and arcs represent dependencies among such variables. These arcs are annotated by probability distribution shaping the interaction between the linked variables. A probabilistic graphical model is called a Bayesian network, when the graph connecting its variables is a directed acyclic graph (DAG). This graph represents conditional independence assumptions that are used to factorize the joint probability distribution of the network variables, thus making the process of learning from a large database amenable to computations. A Bayesian network induced from data can be used to investigate distant relationships between variables, as well as making prediction and explanation, by computing the conditional probability distribution of one variable, given the values of some others.

scholarly journals Graphical Model Market Maker for Combinatorial Prediction Markets

2018 ◽  
Vol 63 ◽  
pp. 421-460
Author(s):  
Kathryn Blackmond Laskey ◽  
Wei Sun ◽  
Robin Hanson ◽  
Charles Twardy ◽  
Shou Matsumoto ◽  
...  
Keyword(s):  
Probability Distribution ◽  
Joint Distribution ◽  
Graphical Model ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Prediction Markets ◽  
Probability Models ◽  
Prediction Market ◽  
Market Mechanisms ◽  
Inference Algorithms

We describe algorithms for use by prediction markets in forming a crowd consensus joint probability distribution over thousands of related events. Equivalently, we describe market mechanisms to efficiently crowdsource both structure and parameters of a Bayesian network. Prediction markets are among the most accurate methods to combine forecasts; forecasters form a consensus probability distribution by trading contingent securities. A combinatorial prediction market forms a consensus joint distribution over many related events by allowing conditional trades or trades on Boolean combinations of events. Explicitly representing the joint distribution is infeasible, but standard inference algorithms for graphical probability models render it tractable for large numbers of base events. We show how to adapt these algorithms to compute expected assets conditional on a prospective trade, and to find the conditional state where a trader has minimum assets, allowing full asset reuse. We compare the performance of three algorithms: the straightforward algorithm from the DAGGRE (Decomposition-Based Aggregation) prediction market for geopolitical events, the simple block-merge model from the SciCast market for science and technology forecasting, and a more sophisticated algorithm we developed for future markets.

Learning Bayesian Networks

2011 ◽  
pp. 1124-1128
Author(s):  
Marco F. Ramoni ◽  
Paola Sebastiani
Keyword(s):  
Probability Distribution ◽  
Bayesian Networks ◽  
Bayesian Network ◽  
Graphical Models ◽  
Graphical Model ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Probabilistic Graphical Model ◽  
Conditional Probability Distribution ◽  
Statistics And Probability

Born at the intersection of artificial intelligence, statistics, and probability, Bayesian networks (Pearl, 1988) are a representation formalism at the cutting edge of knowledge discovery and data mining (Heckerman, 1997). Bayesian networks belong to a more general class of models called probabilistic graphical models (Whittaker, 1990; Lauritzen, 1996) that arise from the combination of graph theory and probability theory, and their success rests on their ability to handle complex probabilistic models by decomposing them into smaller, amenable components. A probabilistic graphical model is defined by a graph, where nodes represent stochastic variables and arcs represent dependencies among such variables. These arcs are annotated by probability distribution shaping the interaction between the linked variables. A probabilistic graphical model is called a Bayesian network, when the graph connecting its variables is a directed acyclic graph (DAG). This graph represents conditional independence assumptions that are used to factorize the joint probability distribution of the network variables, thus making the process of learning from a large database amenable to computations. A Bayesian network induced from data can be used to investigate distant relationships between variables, as well as making prediction and explanation, by computing the conditional probability distribution of one variable, given the values of some others.

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