A matrix interpolation between classical and free max operations: I. The univariate case

On generalized max-linear models and their statistical interpolation

We propose a way how to generate a max-stable process in $C[0,1]$ from a max-stable random vector in $\mathbb R^d$ by generalizing the \emph{max-linear model} established by \citet{wansto11}. It turns out that if the random vector follows some finite dimensional distribution of some initial max-stable process, the approximating processes converge uniformly to the original process and the pointwise mean squared error can be represented in a closed form. The obtained results carry over to the case of generalized Pareto processes. The introduced method enables the reconstruction of the initial pr…

Generalization of the Kimeldorf-Wahba correspondence for constrained interpolation

In this paper, we extend the correspondence between Bayes' estimation and optimal interpolation in a Reproducing Kernel Hilbert Space (RKHS) to the case of linear inequality constraints such as boundedness, monotonicity or convexity. In the unconstrained interpolation case, the mean of the posterior distribution of a Gaussian Process (GP) given data interpolation is known to be the optimal interpolation function minimizing the norm in the RKHS associated to the GP. In the constrained case, we prove that the Maximum A Posteriori (MAP) or Mode of the posterior distribution is the optimal constra…

用于全局离散优化的张量交叉插值及其在贝叶斯网络推断中的应用

Tensor cross interpolation for global discrete optimization with application to Bayesian network inference

本文提出利用张量交叉近似寻找似然函数全局最大值，以解决全局离散优化问题，并通过网络流行病观测准确推断接触网络。