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Global Identifiability of Overcomplete Dictionary Learning via L1 and Volume Minimization

ICLR 2025 · Learning theory and algorithms › Matrix and tensor methods · approach: Sparse regression with guarantees · 0 citations (OpenAlex)

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Proposes a dictionary learning formulation combining weighted L1 norms of coefficient-matrix rows with the log-volume of the dictionary, and shows it guarantees global identifiability in the overcomplete setting.

Problem

Identifying the true overcomplete dictionary (more atoms than signal dimension) and sparse coefficients from data in dictionary learning, where existing identifiability guarantees are limited.

Approach

Replaces the usual sparsity penalty with a weighted sum of l1 norms of the rows of the coefficient matrix plus the log of the dictionary matrix volume, and proves this objective guarantees global identifiability of the overcomplete dictionary.

Key results

• The proposed formulation (weighted l1 row norms of the coefficient matrix plus log-volume of the dictionary) is shown to guarantee global identifiability of overcomplete dictionaries.

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