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PUlasso：仅有正例与未标记数据的高维变量选择AI 解读

In various real-world problems, we are presented with classification problems with positive and unlabeled data, referred to as presence-only responses. In this article we study variable selection in the context of presence only responses where the number of features or covariates p is large. The combination of presence-only responses and high dimensionality presents both statistical and computational challenges. In this article, we develop the PUlasso algorithm for variable…

高维多响应张量回归的凸正则化AI 解读

In this paper, we present a general convex optimization approach for solving high-dimensional multiple response tensor regression problems under low-dimensional structural assumptions. We consider using convex and weakly decomposable regularizers assuming that the underlying tensor lies in an unknown low-dimensional subspace. Within our framework, we derive general risk bounds of the resulting estimate under fairly general dependence structure among covariates. Our framework…

因果推断中忠实性假设的几何结构AI 解读

Many algorithms for inferring causality rely heavily on the faithfulness assumption. The main justification for imposing this assumption is that the set of unfaithful distributions has Lebesgue measure zero, since it can be seen as a collection of hypersurfaces in a hypercube. However, due to sampling error the faithfulness condition alone is not sufficient for statistical estimation, and strong-faithfulness has been proposed and assumed to achieve uniform or…