Graphical Models: Core Ideas and Notions Decomposition: Under certain conditions a distribution (... more Graphical Models: Core Ideas and Notions Decomposition: Under certain conditions a distribution (e.g. a probability distribution) on a multi-dimensional domain, which encodes prior or generic knowledge about this domain, can be decomposed into a set 1 of (overlapping) distributions on lower-dimensional subspaces. Simplified Reasoning: If such a decomposition is possible, it is sufficient to know the distributions on the subspaces to draw all inferences in the domain under consideration that can be drawn using the original distribution . Such a decomposition can nicely be represented as a graph (in the sense of graph theory), and therefore it is called a Graphical Model. The graphical representation encodes conditional independences that hold in the distribution, describes a factorization of the probability distribution, indicates how evidence propagation has to be carried out.
Starting from a general characterization of logical inferences, I consider abductive reasoning, w... more Starting from a general characterization of logical inferences, I consider abductive reasoning, which aims at finding likely causes for observed symptoms. Such inferences are not truth preserving and thus it is necessary to assess their conclusions, to compare different explanations of the same findings, and finally to select the “best” hypothesis. Since in a large number of applications probabilistic graphical models are a mathematically sound and also very convenient tool for these operations, I discuss how they can be used to make abductive inference feasible.
Graphical Models: Core Ideas and Notions Decomposition: Under certain conditions a distribution (... more Graphical Models: Core Ideas and Notions Decomposition: Under certain conditions a distribution (e.g. a probability distribution) on a multi-dimensional domain, which encodes prior or generic knowledge about this domain, can be decomposed into a set 1 of (overlapping) distributions on lower-dimensional subspaces. Simplified Reasoning: If such a decomposition is possible, it is sufficient to know the distributions on the subspaces to draw all inferences in the domain under consideration that can be drawn using the original distribution . Such a decomposition can nicely be represented as a graph (in the sense of graph theory), and therefore it is called a Graphical Model. The graphical representation encodes conditional independences that hold in the distribution, describes a factorization of the probability distribution, indicates how evidence propagation has to be carried out.
Starting from a general characterization of logical inferences, I consider abductive reasoning, w... more Starting from a general characterization of logical inferences, I consider abductive reasoning, which aims at finding likely causes for observed symptoms. Such inferences are not truth preserving and thus it is necessary to assess their conclusions, to compare different explanations of the same findings, and finally to select the “best” hypothesis. Since in a large number of applications probabilistic graphical models are a mathematically sound and also very convenient tool for these operations, I discuss how they can be used to make abductive inference feasible.
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