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相关矩阵的平衡参数化AI 解读

We introduce the balanced correlation parametrization (BCP), which maps positive-definite correlation matrices one-to-one onto the set of symmetric hollow matrices. A key feature of the parametrization is that both the transformation and its inverse are available in closed form. It combines marginal and partial correlations, is inverse-consistent and equivariant under variable permutations and sign changes, and preserves block structure. A novel property of BCP is that it…

循环重心编码器：预测、模拟及其在时间序列分析中的应用AI 解读

This dissertation has two parts. In the first part we theoretically develop a framework that extends the optimal transport barycenter problem from independent data with observed covariates to processes whose relevant covariate is their own history. Given a stationary stochastic process, our framework shows there exists an invertible transport map that extracts from it an iid component whose distribution is the barycenter of the conditional distributions of the input process…

重尾模型中的基于比率的因果发现AI 解读

In many complex systems, such as river networks and financial markets, extreme events propagate from causes to their effects, and the largest observations carry the most information about the underlying causal structure. Existing methods for causal discovery in extremes, however, are tailored to specific mechanisms, such as linear or max-linear models. This work develops causal discovery for heavy-tailed homogeneous structural causal models, a flexible class that contains…