By Panos Pardalos, Mario Pavone, Giovanni Maria Farinella, Vincenzo Cutello
This e-book constitutes revised chosen papers from the 1st overseas Workshop on computing device studying, Optimization, and large info, MOD 2015, held in Taormina, Sicily, Italy, in July 2015.
The 32 papers offered during this quantity have been conscientiously reviewed and chosen from seventy three submissions. They take care of the algorithms, tools and theories correct in info technology, optimization and computer studying.
Read or Download Machine Learning, Optimization, and Big Data: First International Workshop, MOD 2015, Taormina, Sicily, Italy, July 21-23, 2015, Revised Selected Papers PDF
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Additional info for Machine Learning, Optimization, and Big Data: First International Workshop, MOD 2015, Taormina, Sicily, Italy, July 21-23, 2015, Revised Selected Papers
G5 ◦ G . dg6 (G(X)) [g8 ] ◦ dG(X) [g6 ] ◦ dX [G] , where the gj ’s are the functions introduced in Fig. 1. The gj ’s and their respective diﬀerentials are as follow: – g1 : X ∈ Dq → g1 (X) = (μn (xj ))1≤j≤q ∈ IRq , dX [g1 ] (H) = ( ∇μn (xj ), Hj,1:d )1≤j≤q , with ∇μn (xj ) = ∇μ(xj ) + ∂cn (xj ) ∂x 1≤ ≤d C −1 n (y 1:n − μ(x1:n )). q q – g2 : X ∈ Dq → g2 (X) = (Cn (xj , x ))1≤j, ≤q ∈ S++ . S++ is the set of q × q positive deﬁnite matrices. , dX [g2 ] (H) = ∇x Cn (xj , x ), Hj,1:d + ∇x Cn (x , xj ), H ,1:d 1≤j, ≤q with ∇x Cn (x, x ) = ∇x C(x, x ) − ∂cn (x) ∂xp 1≤p≤d C −1 n cn (x ).
The diﬀerence between conditional risks is α/2. For the W2 loss function one has Risk(W2 ; H1,1 , δ H ) = Risk(W2 ; H1,1 , δ Hg ) = 0 (Sh0 = Sh0 ) but the comparison can be obtained from the following relations: lim 0 Sh0 →Sh α Risk(W2 ; H1,1 , δ H ) = 1− , 2 −0 lim Sh0 →Sh0 −0 Risk(W2 ; H1,1 , δ Hg ) = 1−α, It means that in a neighborhood of concentration point Sh0 , Hg-procedures is more accurate than H-procedure for W2 loss function. The diﬀerence between conditional risks is α/2. Behavior of Risk(W2 ) for N = 2 as a function of threshold Sh0 is illustrated on the Fig.
Yn+q = f (xn+q ). ,i (f (xj )). In this section, we ﬁrst deﬁne the Gaussian process (GP) surrogate model used to make the decisions. , [3,12,14] for a deﬁnition and [7,14] for a proof). 1 Gaussian Process Modeling The objective function f is a priori assumed to be a sample from a Gaussian process Y ∼ GP(μ, C), where μ(·) and C(·, ·) are respectively the mean and covariance function of Y . At ﬁxed μ(·) and C(·, ·), conditioning Y on the set of observations An yields a GP posterior Y (x)|An ∼ GP(μn , Cn ) with: μn (x) = μ(x) + cn (x) C −1 n (y 1:n − μ(x1:n )), and Cn (x, x ) = C(x, x ) − cn (x) C −1 n cn (x ), (1) (2) where cn (x) = (C(x, xi ))1≤i≤n , and C n = (C(xi , xj ))1≤i,j≤n .
Machine Learning, Optimization, and Big Data: First International Workshop, MOD 2015, Taormina, Sicily, Italy, July 21-23, 2015, Revised Selected Papers by Panos Pardalos, Mario Pavone, Giovanni Maria Farinella, Vincenzo Cutello