Wedge Sampling
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Wedge Sampling: Efficient Tensor Completion with Nearly-Linear Sample Complexity
arXiv:2602.05869v2 Announce Type: replace-cross Abstract: We introduce Wedge Sampling, a new non-adaptive sampling scheme for low-rank tensor completion. We study recovery of an order-$k$ low-rank tensor of dimension $n \times \cdots \times n$ from a subset of its entries. Unlike the standard uniform entry model (i.e., i.i.d. samples from $[n]^k$), wedge sampling allocates observations to structured length-two patterns (wedges) in an associated bipartite sampling graph.
Information-Theoretic Bounds for Sparse Covariance Estimation in the Vertical-Split Distributed Model
Announce Type: new Abstract: We study the minimax estimation error for distributed covariance matrix estimation in the vertical-split (feature-split) setting, where two agents each observe different coordinates of $m$ i.i.d. and communicate a limited number of bits to a central server. [2025] established nearly tight bounds for dense (unstructured) cross-covariance matrices, we investigate whether imposing elementwise $s$-sparsity on the cross-covariance $C_{21}$ can reduce the required...
Scientists may have debunked one of humanity's oldest habits
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