By Elisa Fromont, Tijl De Bie, Matthijs van Leeuwen

ISBN-10: 3319244647

ISBN-13: 9783319244648

ISBN-10: 3319244655

ISBN-13: 9783319244655

This ebook constitutes the refereed convention court cases of the 14th foreign convention on clever facts research, which used to be held in October 2015 in Saint Étienne. France. The 29 revised complete papers have been rigorously reviewed and chosen from sixty five submissions. the normal concentration of the IDA symposium sequence is on end-to-end clever help for info research. The symposium goals to supply a discussion board for uplifting learn contributions that may be thought of initial in different major meetings and journals, yet that experience a in all likelihood dramatic effect. To facilitate this, IDA 2015 will function tracks: a typical "Proceedings" music, in addition to a "Horizon" song for early-stage examine of probably ground-breaking nature.

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Extra info for Advances in Intelligent Data Analysis XIV: 14th International Symposium, IDA 2015, Saint Etienne, France, October 22–24, 2015, Proceedings

Example text

It was also shown that this can be PG (A\{(Xi = k)}) ∪ {(Xi = j)} = ∂λ i,j computed for all nodes (and hence variables X) simultaneously using the derivatives of its parents in the AC, together with the values that we store in Fv variables. To compute these derivatives, we introduce a real-valued CP variable Dv for every node v in the circuit. t ∂f λi,j : ∀i, j Di,j = ∂λ (A). Hence Di,j = PG ((A\{(Xi = k)}) ∪ {(Xi = j)}). i,j Following the formulation in [5], the constraints below encode the computation of the D variables, where we denote by Pa+ (v) the identifiers of summation parents and by Pa∗ (v) those of multiplication parents; Dv = Dw + Fv ) (Dw ∗ w∈Pa+ (v) w∈Pa (v) ∀v v ∈Ch(w) v =v D1 = 1 To formulate the free constraint from Table 2 over the CP variables, we use the fact that given (Xi = k) ∈ A: PG A\(Xi = k)) = j Di,j and that PG A = F1 .

2 are given in Table 1. Most constraints have close counterparts in the constraint-based pattern mining literature. The main difference is that the notion of (relative) frequency of a pattern in a database is replaced by the probability of the pattern in the BN. The constraints and their definitions are listed in Table 2 and explained below. Probability constraint. Query Q1 requires that the probability of a pattern A according to PG should be larger than a threshold θ. We call this constraint probability(A, G, θ) and a pattern that respects it θ-probable.

We denote such a distribution by PG . We denote by D(Xi ) the domain of variable Xi , that is, the possible values the variable can take. An assignment of value xi to variable Xi is denoted by (Xi = xi ). Definition 1 (BN pattern). A pattern A over PG is a partial assignment, that is, an assignment to a subset of the variables X in G: A = {(X1 = x1 ), . . , (Xm = xm )}, where the Xi are different variables and xi is a possible value in D(Xi ). The probability of a pattern A, denoted by PG (A), is P ((X1 = x1 ), .

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Advances in Intelligent Data Analysis XIV: 14th International Symposium, IDA 2015, Saint Etienne, France, October 22–24, 2015, Proceedings by Elisa Fromont, Tijl De Bie, Matthijs van Leeuwen

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