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Rank of tensors of -out-of- k functions: An application in probabilistic inference

Jiří Vomlel (2011)

Kybernetika

Bayesian networks are a popular model for reasoning under uncertainty. We study the problem of efficient probabilistic inference with these models when some of the conditional probability tables represent deterministic or noisy -out-of- k functions. These tables appear naturally in real-world applications when we observe a state of a variable that depends on its parents via an addition or noisy addition relation. We provide a lower bound of the rank and an upper bound for the symmetric border rank...

Representations of the general linear group over symmetry classes of polynomials

Yousef Zamani, Mahin Ranjbari (2018)

Czechoslovak Mathematical Journal

Let V be the complex vector space of homogeneous linear polynomials in the variables x 1 , ... , x m . Suppose G is a subgroup of S m , and χ is an irreducible character of G . Let H d ( G , χ ) be the symmetry class of polynomials of degree d with respect to G and χ . For any linear operator T acting on V , there is a (unique) induced operator K χ ( T ) End ( H d ( G , χ ) ) acting on symmetrized decomposable polynomials by K χ ( T ) ( f 1 * f 2 * ... * f d ) = T f 1 * T f 2 * ... * T f d . In this paper, we show that the representation T K χ ( T ) of the general linear group G L ( V ) is equivalent to the direct sum of χ ( 1 ) copies of a representation...

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