Gnecco, Giorgio and Kůrková, Věra and Sanguineti, Marcello Can Dictionary-Based Computational Models Outperform the Best Linear Ones? Neural Networks , 24 (8). 881 - 887. ISSN 0893-6080 (2011)
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Abstract
Approximation capabilities of two types of computational models are explored: dictionary-based models (i.e., linear combinations of n -tuples of basis functions computable by units belonging to a set called “dictionary”) and linear ones (i.e., linear combinations of n fixed basis functions). The two models are compared in terms of approximation rates, i.e., speeds of decrease of approximation errors for a growing number n of basis functions. Proofs of upper bounds on approximation rates by dictionary-based models are inspected, to show that for individual functions they do not imply estimates for dictionary-based models that do not hold also for some linear models. Instead, the possibility of getting faster approximation rates by dictionary-based models is demonstrated for worst-case errors in approximation of suitable sets of functions. For such sets, even geometric upper bounds hold.
| Item Type: | Article |
|---|---|
| Identification Number: | 10.1016/j.neunet.2011.05.014 |
| Additional Information: | Special Issue "Artificial Neural Networks: Selected Papers from ICANN 2010" |
| Uncontrolled Keywords: | Dictionary-based approximation; Linear approximation; Rates of approximation; Worst-case error; Kolmogorov width; Perceptron networks |
| Subjects: | Q Science > QA Mathematics > QA75 Electronic computers. Computer science |
| Research Area: | Computer Science and Applications |
| Depositing User: | Giorgio Gnecco |
| Date Deposited: | 17 Sep 2013 07:44 |
| Last Modified: | 17 Sep 2013 07:44 |
| URI: | http://eprints.imtlucca.it/id/eprint/1751 |
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Can dictionary-based computational models outperform the best linear ones? (deposited 13 Sep 2013 11:43)
- Can Dictionary-Based Computational Models Outperform the Best Linear Ones? (deposited 17 Sep 2013 07:44) [Currently Displayed]
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