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极值图模型中的参数与非参数对称性AI 解读

Abstract Coloured graphical models provide a parsimonious approach to modeling high-dimensional data by exploiting symmetries in the model parameters. In this work, we introduce the notion of colouring for extremal graphical models on generalized multivariate Pareto distributions, a natural class of limiting distributions for threshold exceedances. Thanks to a stability property of the generalized multivariate Pareto distributions, coloured extremal tree models can be…

多元极值中的全正性AI 解读

Positive dependence is present in many real world data sets and has appealing stochastic properties that can be exploited in statistical modeling and in estimation. In particular, the notion of multivariate total positivity of order 2 (MTP2) is a convex constraint and acts as an implicit regularizer in the Gaussian case. We study positive dependence in multivariate extremes and introduce EMTP2, an extremal version of MTP2. This notion turns out to appear prominently in…