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Read Online or Download Advances in Intelligent Data Analysis XIII: 13th International Symposium, IDA 2014, Leuven, Belgium, October 30 – November 1, 2014. Proceedings PDF
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Additional info for Advances in Intelligent Data Analysis XIII: 13th International Symposium, IDA 2014, Leuven, Belgium, October 30 – November 1, 2014. Proceedings
P ) of the polynomial g(z) = j=1 (1 + κj z) = 1 − j=1 φj z j p satisfy i=1 φi xi (t) = x(t). Therefore, the new parameter φ = (φ1 , . . , φp ) ∈ p R shall be adopted. 1 19 Matching Correlations From the closed formula for the covariance γ and the relationship between κ and φ, we have a mapping (φ, σ 2 ) → γ(t), for each t. Since ρ(T ) := (ρ(1), . . , ρ(T ))tr = (γ(1), . . , γ(T ))tr /γ(0) does not depend on σ 2 , these equations determine a map C : (φ, T ) → ρ(T ) = C(φ, T ), for each T .
There is a 1 in n chance of selecting the right variable, and to move it to the correct cluster there are √n clusters. There are n variables to choose from and they can be moved to √n-1 clusters, as one cluster can be ruled out and that is the cluster it originated from. Assume that Pr(correct move) = P = 1/(n√n), Let Q = 1-P The chance a single move occurs after T iterations is as follows: i −1 Pr(T = 1) = P, Pr(T = 2) = PQ, Pr(T = 3) = PQ2 ... Pr(T = i) = PQ If we have d moves to make, then the probability that all of the d moves are made after T iterations of the Hill Climbing algorithms is: Pr(All d moves after T iterations) = (1-QT)d Let us assume that there is some acceptable level of confidence α that all the moves have been made, then we wish to compute a T for which this might happen: α = (1 − QT )d α 1 / d = 1 − QT Q = 1−α T 5 1/ d T ln(Q) = ln(1 − α 1 / d ) T= ln(1 − α 1 / d ) ln(Q ) (5) Experimental Procedure Two experiments that modularise the dataset were designed for this paper.
6 A State Space Representation of the OU(p) Process The decomposition of the OU(p) process xκ,σ (t) as a linear combination of simpler processes of order 1 (Thm. 1), leads to an expression of the process by means of a state space model. This provides a uniﬁed approach for computing the likelihood of xκ,σ (t) through a Kalman ﬁlter. Moreover, it can be used to show that xκ,σ (t) is an ARMA(p, p − 1) whose coeﬃcients can be computed from κ. In order to ease notation, we consider that the components of κ are all diﬀerent.