Wedge Sampling: New Method Achieves Nearly-Linear Sample Complexity for Tensor Completion
Researchers introduced Wedge Sampling, a non-adaptive sampling scheme that enables efficient tensor completion with nearly-linear sample complexity in tensor dimension n. The method structures observations into length-two patterns in a bipartite graph, strengthening spectral signals for initialization compared to standard uniform sampling. This work suggests that the statistical-to-computational gap in tensor completion is largely due to uniform sampling limitations, not fundamental algorithmic barriers.
A new paper on arXiv presents Wedge Sampling, a structured sampling approach for recovering low-rank tensors from partial observations. Unlike conventional uniform entry sampling, which draws observations independently from all possible entries, wedge sampling allocates measurements to structured two-element patterns in a bipartite graph. This design choice enhances the spectral properties needed for efficient initialization algorithms. The authors prove that polynomial-time algorithms can achieve both weak and exact recovery using nearly linear sample complexity—a substantial improvement over the typical Õ(n^{k/2}) requirement under uniform sampling for order-k tensors. The method is modular and can be combined with existing refinement procedures (spectral or gradient-based) using only an additional Õ(n) uniformly sampled entries. The results suggest that the long-standing statistical-to-computational gap in tensor completion is primarily an artifact of the uniform sampling model rather than an inherent computational barrier.
What's missing
The paper does not discuss experimental validation on real-world datasets or synthetic benchmarks, focusing instead on theoretical guarantees. Practical runtime comparisons with existing methods and guidance on parameter selection for wedge sampling are not addressed.
What different sources said
- arXiv cs.LGCenter
Wedge Sampling: Efficient Tensor Completion with Nearly-Linear Sample Complexity
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