Sum Product Algorithm

Algorithm sum product algorithm the overall strategy

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Unformatted text preview: Sum-Product Algorithm Sum-Product Algorithm The overall strategy is simple message passing To compute gi (xi ), form a rooted tree at xi Apply the following two rules: Product Rule: At a variable node, take the product of descendants Instructor: Arindam Banerjee The Sum-Product Algorithm Sum-Product Algorithm The overall strategy is simple message passing To compute gi (xi ), form a rooted tree at xi Apply the following two rules: Product Rule: At a variable node, take the product of descendants Sum-product Rule: Instructor: Arindam Banerjee The Sum-Product Algorithm Sum-Product Algorithm The overall strategy is simple message passing To compute gi (xi ), form a rooted tree at xi Apply the following two rules: Product Rule: At a variable node, take the product of descendants Sum-product Rule: At a factor node, take the product of f with descendants; then perform not-sum over the parent of f Instructor: Arindam Banerjee The Sum-Product Algorithm Sum-Product Algorithm The overall strategy is simple message passing To compute gi (xi ), form a rooted tree at xi Apply the following two rules: Product Rule: At a variable node, take the product of descendants Sum-product Rule: At a factor node, take the product of f with descendants; then perform not-sum over the parent of f Known as the sum-product algorithm Instructor: Arindam Banerjee The Sum-Product Algorithm Computing All Marginals Interested in computing all marginal functions gi (xi ) Instructor: Arindam Banerjee The Sum-Product Algorithm Computing All Marginals Interested in computing all marginal functions gi (xi ) One option is to repeat the sum-product for every single node Instructor: Arindam Banerjee The Sum-Product Algorithm Computing All Marginals Interested in computing all marginal functions gi (xi ) One option is to repeat the sum-product for every single node Complexity of O (n2 ) Instructor: Arindam Banerjee The Sum-Product Algorithm Computing All Marginals Interested in computing all marginal functions gi (xi ) One option is to repeat the sum-product for every single node Complexity of O (n2 ) Repeat computations can be avoided Instructor: Arindam Banerjee The Sum-Product Algorithm Computing All Marginals Interested in computing all marginal functions gi (xi ) One option is to repeat the sum-product for every single node Complexity of O (n2 ) Repeat computations can be avoided Sum-product algorithm for general trees Instructor: Arindam Banerjee The Sum-Product Algorithm Sum Product Upd...
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