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| URI | http://purl.tuc.gr/dl/dias/15DF46BD-9435-46FE-8EAC-A8B6557F4385 | - |
| Γλώσσα | en | - |
| Μέγεθος | 24 pages | en |
| Τίτλος | The generalization error of dictionary learning with moreau envelopes | en |
| Δημιουργός | Georgogiannis Alexandros | en |
| Δημιουργός | Γεωργογιαννης Αλεξανδρος | el |
| Εκδότης | International Machine Learning Society | en |
| Περίληψη | This 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). | en |
| Τύπος | Πλήρης Δημοσίευση σε Συνέδριο | el |
| Τύπος | Conference Full Paper | en |
| Άδεια Χρήσης | http://creativecommons.org/licenses/by/4.0/ | en |
| Ημερομηνία | 2019-10-18 | - |
| Ημερομηνία Δημοσίευσης | 2018 | - |
| Θεματική Κατηγορία | Artificial intelligence | en |
| Θεματική Κατηγορία | Dictionary learning | en |
| Θεματική Κατηγορία | Approximation errors | en |
| Βιβλιογραφική Αναφορά | A. Georgogiannis, "The generalization error of dictionary learning with moreau envelopes," in 35th International Conference on Machine Learning, 2018, pp. 2764-2787. | en |
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