This document corresponds to a 2h class on kriging, also known as conditional Gaussian Processes (GP) or Gaussian Process Regression (GPR). The class was part of the MNMUQ2019 summer school on uncertainty quantification. In the first part of the class, we introduce basics of GPR up to a point where it could be coded by a motivated student. The seco...
Published in G3 (Bethesda, Md.)
The genetic merit of individuals can be estimated using models with dense markers and pedigree information. Early genomic models accounted only for additive effects. However, the prediction of non-additive effects is important for different forest breeding systems where the whole genotypic value can be captured through clonal propagation. In this s...
Published in Plant Methods
BackgroundThe selection of hybrids is an essential step in maize breeding. However, evaluating a large number of hybrids in field trials can be extremely costly. However, genomic models can be used to predict the expected performance of un-tested genotypes. Bayesian models offer a very flexible framework for hybrid prediction. The Bayesian methodol...
Published in BMC Genomics
BackgroundGenomic selection (GS) can increase genetic gain by reducing the length of breeding cycle in forest trees. Here we genotyped 1370 control-pollinated progeny trees from 128 full-sib families in Norway spruce (Picea abies (L.) Karst.), using exome capture as genotyping platform. We used 116,765 high-quality SNPs to develop genomic predictio...
The design of sparse quadratures for the approximation of integral operators related to symmetric positive-semidefinite kernels is addressed. Particular emphasis is placed on the approximation of the main eigenpairs of the initial operator. A special attention is drawn to the design of sparse quadratures with support included in fixed finite sets o...
Published in Computational Optimization and Applications
In this paper, interpolating curve or surface with linear inequality constraints is considered as a general convex optimization problem in a Reproducing Kernel Hilbert Space. The aim of the present paper is to propose an approximation method in a very general framework based on a discretized optimization problem in a finite-dimensional Hilbert spac...
Regularization is used to find a solution that both fits the data and is sufficiently smooth, and thereby is very effective for designing and refining learning algorithms. But the influence of its exponent remains poorly understood. In particular, it is unclear how the exponent of the reproducing kernel Hilbert space~(RKHS) regularization term affe...
Optimal transport (OT) defines a powerful framework to compare probability distributions in a geometrically faithful way. However, the practical impact of OT is still limited because of its computational burden. We propose a new class of stochastic optimization algorithms to cope with large-scale problems routinely encountered in machine learning a...
Published in Signal, Image and Video Processing
Adaptive channel equalization is a signal processing technique to mitigate inter-symbol interference in a time dispersive channel. For adaptive equalization, minimum mean square error (MMSE) criterion-based reproducing kernel Hilbert spaces (RKHS) approaches such as the kernel least mean squares (KLMS) algorithm and its variants have been suggested...
In this paper, we discuss the dependency between the kernel choice and the model class it represents. This is typically an undesired relationship, forcing the user to accept a trade-off between an acceptable variance characteristic and flexibility in the underlying function. Hence, a method is proposed in this paper that explicitly constrains the s...
