This content will become publicly available on November 27, 2022

Matrix Completion with Model-free Weighting
In this paper, we propose a novel method for matrix completion under general non- uniform missing structures. By controlling an upper bound of a novel balancing error, we construct weights that can actively adjust for the non-uniformity in the empirical risk without explicitly modeling the observation probabilities, and can be computed efficiently via convex optimization. The recovered matrix based on the proposed weighted empirical risk enjoys appealing theoretical guarantees. In particular, the proposed method achieves stronger guarantee than existing work in terms of the scaling with respect to the observation probabilities, under asymptotically heterogeneous missing settings (where entry-wise observation probabilities can be of different orders). These settings can be regarded as a better theoretical model of missing patterns with highly varying probabilities. We also provide a new minimax lower bound under a class of heterogeneous settings. Numerical experiments are also provided to demonstrate the effectiveness of the proposed method.
Authors:
; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10303652
Journal Name:
Proceedings of Machine Learning Research
ISSN:
2640-3498
3. Abstract Subspace clustering is the unsupervised grouping of points lying near a union of low-dimensional linear subspaces. Algorithms based directly on geometric properties of such data tend to either provide poor empirical performance, lack theoretical guarantees or depend heavily on their initialization. We present a novel geometric approach to the subspace clustering problem that leverages ensembles of the $K$-subspace (KSS) algorithm via the evidence accumulation clustering framework. Our algorithm, referred to as ensemble $K$-subspaces (EKSSs), forms a co-association matrix whose $(i,j)$th entry is the number of times points $i$ and $j$ are clustered together by several runs of KSS withmore »