Hiding Data Helps: On the Benefits of Masking for Sparse Coding

Muthu Chidambaram, Chenwei Wu, Yu Cheng, Rong Ge
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:5600-5615, 2023.

Abstract

Sparse coding, which refers to modeling a signal as sparse linear combinations of the elements of a learned dictionary, has proven to be a successful (and interpretable) approach in applications such as signal processing, computer vision, and medical imaging. While this success has spurred much work on provable guarantees for dictionary recovery when the learned dictionary is the same size as the ground-truth dictionary, work on the setting where the learned dictionary is larger (or $\textit{over-realized}$) with respect to the ground truth is comparatively nascent. Existing theoretical results in this setting have been constrained to the case of noise-less data. We show in this work that, in the presence of noise, minimizing the standard dictionary learning objective can fail to recover the elements of the ground-truth dictionary in the over-realized regime, regardless of the magnitude of the signal in the data-generating process. Furthermore, drawing from the growing body of work on self-supervised learning, we propose a novel masking objective for which recovering the ground-truth dictionary is in fact optimal as the signal increases for a large class of data-generating processes. We corroborate our theoretical results with experiments across several parameter regimes showing that our proposed objective also enjoys better empirical performance than the standard reconstruction objective.

Cite this Paper


BibTeX
@InProceedings{pmlr-v202-chidambaram23b, title = {Hiding Data Helps: On the Benefits of Masking for Sparse Coding}, author = {Chidambaram, Muthu and Wu, Chenwei and Cheng, Yu and Ge, Rong}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {5600--5615}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/chidambaram23b/chidambaram23b.pdf}, url = {https://proceedings.mlr.press/v202/chidambaram23b.html}, abstract = {Sparse coding, which refers to modeling a signal as sparse linear combinations of the elements of a learned dictionary, has proven to be a successful (and interpretable) approach in applications such as signal processing, computer vision, and medical imaging. While this success has spurred much work on provable guarantees for dictionary recovery when the learned dictionary is the same size as the ground-truth dictionary, work on the setting where the learned dictionary is larger (or $\textit{over-realized}$) with respect to the ground truth is comparatively nascent. Existing theoretical results in this setting have been constrained to the case of noise-less data. We show in this work that, in the presence of noise, minimizing the standard dictionary learning objective can fail to recover the elements of the ground-truth dictionary in the over-realized regime, regardless of the magnitude of the signal in the data-generating process. Furthermore, drawing from the growing body of work on self-supervised learning, we propose a novel masking objective for which recovering the ground-truth dictionary is in fact optimal as the signal increases for a large class of data-generating processes. We corroborate our theoretical results with experiments across several parameter regimes showing that our proposed objective also enjoys better empirical performance than the standard reconstruction objective.} }
Endnote
%0 Conference Paper %T Hiding Data Helps: On the Benefits of Masking for Sparse Coding %A Muthu Chidambaram %A Chenwei Wu %A Yu Cheng %A Rong Ge %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-chidambaram23b %I PMLR %P 5600--5615 %U https://proceedings.mlr.press/v202/chidambaram23b.html %V 202 %X Sparse coding, which refers to modeling a signal as sparse linear combinations of the elements of a learned dictionary, has proven to be a successful (and interpretable) approach in applications such as signal processing, computer vision, and medical imaging. While this success has spurred much work on provable guarantees for dictionary recovery when the learned dictionary is the same size as the ground-truth dictionary, work on the setting where the learned dictionary is larger (or $\textit{over-realized}$) with respect to the ground truth is comparatively nascent. Existing theoretical results in this setting have been constrained to the case of noise-less data. We show in this work that, in the presence of noise, minimizing the standard dictionary learning objective can fail to recover the elements of the ground-truth dictionary in the over-realized regime, regardless of the magnitude of the signal in the data-generating process. Furthermore, drawing from the growing body of work on self-supervised learning, we propose a novel masking objective for which recovering the ground-truth dictionary is in fact optimal as the signal increases for a large class of data-generating processes. We corroborate our theoretical results with experiments across several parameter regimes showing that our proposed objective also enjoys better empirical performance than the standard reconstruction objective.
APA
Chidambaram, M., Wu, C., Cheng, Y. & Ge, R.. (2023). Hiding Data Helps: On the Benefits of Masking for Sparse Coding. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:5600-5615 Available from https://proceedings.mlr.press/v202/chidambaram23b.html.

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