Generalized belief propagation for probabilistic systems
First Claim
1. A computer implemented method for determining probabilities of states of a system represented by a model including a plurality of nodes connected by links, each node representing possible states of a corresponding part of the system, and each link representing statistical dependencies between possible states of related nodes, comprising:
- grouping the plurality of nodes into arbitrary-sized clusters such that every node is included in at least one cluster and each link is completely contained in at least one cluster;
identifying nodes in intersections of clusters, and intersections of intersections of clusters as regions of nodes;
defining messages based on the regions of nodes, each message having associated sets of source nodes and destination nodes and a value and a rule depending on other messages and selected links connecting the source nodes and destination nodes;
assigning initial values to the messages;
updating the value of each message using the associated rule; and
determining approximate probabilities of the states of the system from the messages when a termination condition is reached.
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Abstract
A method determines approximate probabilities of states of a system represented by a model. The model includes nodes connected by links. Each node represents possible states of a corresponding part of the system, and each link represents statistical dependencies between possible states of related nodes. The nodes are grouped into arbitrary sized clusters such that every node is included in at least one cluster and each link is completely contained in at least one cluster. Messages, based on the arbitrary sized cluster, are defined. Each message has associated sets of source nodes and destination nodes, and a value and a rule depending on other messages and on selected links connecting the source nodes and destination nodes. The value of each message is updated until a termination condition is reached. When the termination condition is reached, approximate probabilities of the states of the system are determined from the values of the messages.
129 Citations
14 Claims
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1. A computer implemented method for determining probabilities of states of a system represented by a model including a plurality of nodes connected by links, each node representing possible states of a corresponding part of the system, and each link representing statistical dependencies between possible states of related nodes, comprising:
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grouping the plurality of nodes into arbitrary-sized clusters such that every node is included in at least one cluster and each link is completely contained in at least one cluster;
identifying nodes in intersections of clusters, and intersections of intersections of clusters as regions of nodes;
defining messages based on the regions of nodes, each message having associated sets of source nodes and destination nodes and a value and a rule depending on other messages and selected links connecting the source nodes and destination nodes;
assigning initial values to the messages;
updating the value of each message using the associated rule; and
determining approximate probabilities of the states of the system from the messages when a termination condition is reached. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13)
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14. A computer implemented method for determining probabilities of states of a system represented by a model including a plurality of nodes connected by links, each node representing possible states of a corresponding part of the system, and each link representing statistical dependencies between possible states of neighboring nodes, comprising:
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grouping the plurality of nodes into arbitrary-sized clusters such that every node is included in at least one cluster, and each link is completely contained in at least one cluster;
identifying nodes in intersecting clusters, and intersections of intersecting clusters as regions, and intersections of regions as sub-regions;
discarding duplicate regions and sub-regions;
arranging the regions and sub-regions in a top-to-bottom hierarchy of intersections;
defining messages between regions and direct sub-regions directly connected in the hierarchy, each message having associated sets of source nodes and destination nodes and a value and a rule depending on other messages and selected links connecting the source nodes and destination nodes, the destination nodes being those nodes in the sub-region, and the source nodes being those nodes in the region and outside the sub-region;
assigning initial values to the messages;
updating the value of each message using the associated rule until a termination condition is reached;
determining approximate probabilities of the states of the system from the messages when a termination condition is reached.
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Specification