The generalization error of dictionary learning with moreau envelopesThe generalization error of dictionary learning with moreau envelopes
Πλήρης Δημοσίευση σε Συνέδριο
Conference Full Paper
2019-10-182018enThis is a theoretical study on the sample complexity of dictionary learning with general type of reconstruction losses. The goal is to estimate a m × d matrix D of unit-norm columns when the only available information is a set of training samples. Points x in R m are subsequently approximated by the linear combination Da after solving the problem mina∈Rd Φ(x - Da) + g(a) with function g being either an indicator function or a sparsity promoting regularizer. Here is considered the case where Φ(x) = inf z∈Rm ||x - z||2 2 + h(||z||2) and h is an even and univariate function on the real line. Connections are drawn between Φ and the Moreau envelope of h. A new sample complexity result concerning the k-sparse dictionary problem removes the spurious condition regarding the coherence of D appearing in previous works. Finally comments are made on the approximation error of certain families of losses. The derived generalization bounds are of order O( p log n/n).http://creativecommons.org/licenses/by/4.0/2764-278735th International Conference on Machine Learning
Georgogiannis Alexandros
Γεωργογιαννης Αλεξανδρος
International Machine Learning Society
Artificial intelligence
Dictionary learning
Approximation errors