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This letter addresses the problem of estimating block sparse signal with unknown group partitions in a multiple measurement vector (MMV) setup. We propose a Bayesian framework by applying an adaptive total variation (TV) penalty on the hyper-parameter space of the sparse signal. The main contributions are two-fold. 1) We extend the TV penalty beyond the immediate neighbor, thus enabling better capture of the signal structure. 2) A dynamic framework is provided to learn the regularization weights for the TV penalty based on the statistical dependencies between the entries of tentative blocks, thus eliminating the need for fine-tuning. The superior performance of the proposed method is empirically demonstrated by extensive computer simulations with the state-of-art benchmarks. The proposed solution exhibits both excellent performance and robustness against sparsity model mismatch.
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A Topological Regularizer for Classifiers via Persistent Homology
Regularization plays a crucial role in supervised learning. Most existing methods enforce a global regularization in a structure agnostic manner. In this paper, we initiate a new direction and propose to enforce the structural simplicity of the classification boundary by regularizing over its topological complexity. In particular, our measurement of topological complexity incorporates the importance of topological features (e.g., connected components, handles, and so on) in a meaningful manner, and provides a direct control over spurious topological structures. We incorporate the new measurement as a topological penalty in training classifiers. We also propose an efficient algorithm to compute the gradient of such penalty. Our method provides a novel way to topologically simplify the global structure of the model, without having to sacrifice too much of the flexibility of the model. We demonstrate the effectiveness of our new topological regularizer on a range of synthetic and real-world datasets.
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- PAR ID:
- 10106119
- Date Published:
- Journal Name:
- Proceedings of Machine Learning Research
- Volume:
- 89
- ISSN:
- 2640-3498
- Page Range / eLocation ID:
- 2573-2582
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Conference Paper:
- The DOI is not currently available.
