A Unified Approach to Coreset Learning
This work addresses the limitation of coreset construction being problem-dependent and time-consuming, offering a generic approach that could enhance practical applications in machine learning, though it is incremental in its relaxation of coreset definitions.
The paper tackles the problem of constructing coresets, which are small weighted subsets approximating loss functions, by proposing a learning-based algorithm that relaxes the definition to approximate average loss, enabling efficient coreset computation for deep networks and classic ML problems with comparable or better results than existing methods.
Coreset of a given dataset and loss function is usually a small weighed set that approximates this loss for every query from a given set of queries. Coresets have shown to be very useful in many applications. However, coresets construction is done in a problem dependent manner and it could take years to design and prove the correctness of a coreset for a specific family of queries. This could limit coresets use in practical applications. Moreover, small coresets provably do not exist for many problems. To address these limitations, we propose a generic, learning-based algorithm for construction of coresets. Our approach offers a new definition of coreset, which is a natural relaxation of the standard definition and aims at approximating the \emph{average} loss of the original data over the queries. This allows us to use a learning paradigm to compute a small coreset of a given set of inputs with respect to a given loss function using a training set of queries. We derive formal guarantees for the proposed approach. Experimental evaluation on deep networks and classic machine learning problems show that our learned coresets yield comparable or even better results than the existing algorithms with worst-case theoretical guarantees (that may be too pessimistic in practice). Furthermore, our approach applied to deep network pruning provides the first coreset for a full deep network, i.e., compresses all the network at once, and not layer by layer or similar divide-and-conquer methods.