Laurent Carraro

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Beyond both estalished frameworks of derivative-based descent and stochastic search algorithms, the rise of expensive optimization problems creates the need for new specific approaches and procedures. The word ”expensive” —which refers to price and/or time issues— implies severely restricted budgets in terms of objective function evaluations. Such(More)
The situation of time consuming computer experiments is considered, where the output is deterministic and the data generating function is of high complexity. In such situations the underlying functions often are non additive but at the same time, not all interactions are active. Hence neither a model considering all interactions as well as an additive model(More)
We study the class of Azéma–Yor processes defined from a general semimartingale with a continuous running supremum process. We show that they arise as unique strong solutions of the Bachelier stochastic differential equation which we prove is equivalent to the Drawdown equation. Solutions of the latter have the drawdown property: they always stay above a(More)
We consider the problem of designing adapted kernels for approximating functions invariant under a known finite group action. We introduce the class of argumentwise invariant kernels, and show that they characterize centered square-integrable random fields with invariant paths, as well as Reproducing Kernel Hilbert Spaces of invariant functions. Two(More)
Given a reproducing kernel Hilbert space (H, 〈., .〉) of real-valued functions and a suitable measure μ over the source space D ⊂ R, we decompose H as the sum of a subspace of centered functions for μ and its orthogonal in H. This decomposition leads to a special case of ANOVA kernels, for which the functional ANOVA representation of the best predictor can(More)
Kriging-based exploration strategies often rely on a single Ordinary Kriging model which parametric covariance kernel is selected a priori or on the basis of an initial data set. Since choosing an unadapted kernel can radically harm the results, we wish to reduce the risk of model misspecification. Here we consider the simultaneous use of multiple kernels(More)
In the study of computer codes, filling space as uniformly as possible is important to describe the complexity of the investigated phenomenon. However, this property is not conserved by reducing the dimension. Some numeric experiment designs are conceived in this sense as Latin hypercubes or orthogonal arrays, but they consider only the projections onto the(More)
Load balancing constitutes a crucial task to realize for the performance of parallel applications. However it adds an overhead which, instead, can degrade the performance of the applications. Therefore, it is essential to decide when it is worthwhile to run the load balancing. This paper rst presents a probabilistic analysis of the time complexity of an(More)
Our goal in the present work is to give an insight on some important questions to be asked when choosing a Kriging model for the analysis of numerical experiments. We are especially concerned about the cases where the size of the design of experiments is small relatively to the algebraic dimension of the inputs. We first fix the notations and recall some(More)
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