Displaying similar documents to “Rank of tensors of ℓ -out-of- k functions: An application in probabilistic inference”

Cycle-free cuts of mutual rank probability relations

Karel De Loof, Bernard De Baets, Hans De Meyer (2014)

Kybernetika

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It is well known that the linear extension majority (LEM) relation of a poset of size n ≥ 9 can contain cycles. In this paper we are interested in obtaining minimum cutting levels α m such that the crisp relation obtained from the mutual rank probability relation by setting to 0 its elements smaller than or equal to α m , and to 1 its other elements, is free from cycles of length m . In a first part, theoretical upper bounds for α m are derived using known transitivity properties of the mutual rank...

Discriminating between causal structures in Bayesian Networks given partial observations

Philipp Moritz, Jörg Reichardt, Nihat Ay (2014)

Kybernetika

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Given a fixed dependency graph G that describes a Bayesian network of binary variables X 1 , ⋯ , X n , our main result is a tight bound on the mutual information I c ( Y 1 , ⋯ , Y k ) = ∑ j = 1 k H ( Y j ) / c - H ( Y 1 , ⋯ , Y k ) of an observed subset Y 1 , ⋯ , Y k of the variables X 1 , ⋯ , X n . Our bound depends on certain quantities that can be computed from the connective structure of the nodes in G . Thus it allows to discriminate between different dependency graphs for a probability distribution, as we show from numerical experiments.

Estimation and prediction in regression models with random explanatory variables

Nguyen Bac-Van

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The regression model X(t),Y(t);t=1,...,n with random explanatory variable X is transformed by prescribing a partition S 1 , . . . , S k of the given domain S of X-values and specifying X ( 1 ) , . . . , X ( n ) ∩ S i = X i 1 , . . . , X i α ( i ) , i = 1 , . . . , k . Through the conditioning α ( i ) = a ( i ) , i = 1 , . . . , k , X i 1 , . . . , X i α ( i ) ; i = 1 , . . . , k = x 11 , . . . , x k a ( k ) the initial model with i.i.d. pairs (X(t),Y(t)),t=1,...,n, becomes a conditional fixed-design ( x 11 , . . . , x k a ( k ) ) model Y i j , i = 1 , . . . , k ; j = 1 , . . . , a ( i ) where the response variables Y i j are independent and distributed according to the mixed conditional distribution Q ( · , x i j ) of Y given X at the observed value x i j .Afterwards, we investigate the case ( Q ) E ( Y ' | x ) = ∑ i = 1 k b i ( x ) θ i I S i ( x ) , ( Q ) D ( Y | x ) = ∑ i = 1 k d i ( x ) Σ i I S i ( x ) which...