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In over two decades of research, the field of dictionary learning hasgathered a large collection of successful applications, and theoreticalguarantees for model recovery are known only whenever optimization is carriedout in the same model class as that of the underlying dictionary. This workcharacterizes the surprising phenomenon that dictionary recovery can befacilitated by searching over the space of larger over-realized models. Thisobservation is general and independent of the specific dictionary learningalgorithm used. We thoroughly demonstrate this observation in practice andprovide an analysis of this phenomenon by tying recovery measures togeneralization bounds. In particular, we show that model recovery can beupper-bounded by the empirical risk, a model-dependent quantity and thegeneralization gap, reflecting our empirical findings. We further show that anefficient and provably correct distillation approach can be employed to recoverthe correct atoms from the over-realized model. As a result, our meta-algorithmprovides dictionary estimates with consistently better recovery of theground-truth model.

Recovery and Generalization in Over-Realized Dictionary Learning