Tag: sufficient
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On Conditional Stochastic Interpolation for Generative Nonlinear Sufficient Dimension Reduction
On Conditional Stochastic Interpolation for Generative Nonlinear Sufficient Dimension Reduction arXiv:2512.18971v1 Announce Type: new Abstract: Identifying low-dimensional sufficient structures in nonlinear sufficient dimension reduction (SDR) has long been a fundamental yet challenging problem. Most existing methods lack theoretical guarantees of exhaustiveness in identifying lower dimensional structures, either at the population level or at the sample…
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A Statistical Theory of Contrastive Learning via Approximate Sufficient Statistics
A Statistical Theory of Contrastive Learning via Approximate Sufficient Statistics arXiv:2503.17538v1 Announce Type: new Abstract: Contrastive learning — a modern approach to extract useful representations from unlabeled data by training models to distinguish similar samples from dissimilar ones — has driven significant progress in foundation models. In this work, we develop a new theoretical framework…
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Fr’echet Cumulative Covariance Net for Deep Nonlinear Sufficient Dimension Reduction with Random Objects
Fr’echet Cumulative Covariance Net for Deep Nonlinear Sufficient Dimension Reduction with Random Objects arXiv:2502.15374v1 Announce Type: new Abstract: Nonlinear sufficient dimension reductioncitep{libing_generalSDR}, which constructs nonlinear low-dimensional representations to summarize essential features of high-dimensional data, is an important branch of representation learning. However, most existing methods are not applicable when the response variables are complex non-Euclidean…