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因果模型的推断等价类AI 解读

Causal models in the same Markov equivalence class are, in the absence of strong assumptions, statistically indistinguishable at any sample size. For modest sample sizes there is also the possibility that several such classes are compatible with the data, pointing to a confidence set of causal models as the appropriate presentation of evidence. Non-identifiability of Gaussian causal models from the same Markov equivalence class corresponds to a plurality of…

回归图与诱导稀疏性的重新参数化AI 解读

That parametrization and sparsity are inherently linked raises the possibility that relevant models, not obviously sparse in their natural formulation, exhibit a population-level sparsity after reparametrization. In covariance models, positive-definiteness enforces additional constraints on how sparsity can legitimately manifest. It is therefore natural to consider reparametrization maps in which sparsity respects positive definiteness. The main purpose of this paper is to…

具有统计保证的分布式估计与推断AI 解读

This paper studies hypothesis testing and parameter estimation in the context of the divide and conquer algorithm. In a unified likelihood based framework, we propose new test statistics and point estimators obtained by aggregating various statistics from $k$ subsamples of size $n/k$, where $n$ is the sample size. In both low dimensional and high dimensional settings, we address the important question of how to choose $k$ as $n$ grows large, providing a theoretical upper…