Machine Learning (stat.ML)

Abstract: Low-rank tensor analysis has received widespread attention with many practical applications. However, the tensor data are often contaminated by outliers or sample-specific corruptions. How to recover the tensor data that are corrupted by outliers and perform data clustering remains a challenging problem. This paper develops an outlier-robust tensor low-rank representation (OR-TLRR) method for simultaneous outlier detection and tensor data clustering based on the tensor singular value decomposition (t-SVD) algebraic framework. It is motivated by the recently proposed tensor-tensor product induced by invertible linear transforms that satisfy certain conditions. For tensor observations with arbitrary outlier corruptions, OR-TLRR has provable performance guarantee for exactly recovering the row space of clean data and detecting outliers under mild conditions. Moreover, an extension of OR-TLRR is also proposed to handle the case when parts of the data are missing. Finally, extensive experimental results on both synthetic and real data demonstrate the effectiveness of the proposed algorithms.

Abstract: We study the generalization properties of batched predictors, i.e., models tasked with predicting the mean label of a small set (or batch) of examples. The batched prediction paradigm is particularly relevant for models deployed to determine the quality of a group of compounds in preparation for offline testing. By utilizing a suitable generalization of the Rademacher complexity, we prove that batched predictors come with exponentially stronger generalization guarantees as compared to the standard per-sample approach. Surprisingly, the proposed bound holds independently of overparametrization. Our theoretical insights are validated experimentally for various tasks, architectures, and applications.