On improving generalization in a class of learning problems with the method of small parameters for weakly-controlled optimal gradient systems
Shranjeno v:
| izdano v: | arXiv.org (Dec 11, 2024), p. n/a |
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| Glavni avtor: | |
| Izdano: |
Cornell University Library, arXiv.org
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| Teme: | |
| Online dostop: | Citation/Abstract Full text outside of ProQuest |
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| LEADER | 00000nab a2200000uu 4500 | ||
|---|---|---|---|
| 001 | 3144199832 | ||
| 003 | UK-CbPIL | ||
| 022 | |a 2331-8422 | ||
| 035 | |a 3144199832 | ||
| 045 | 0 | |b d20241211 | |
| 100 | 1 | |a Befekadu, Getachew K | |
| 245 | 1 | |a On improving generalization in a class of learning problems with the method of small parameters for weakly-controlled optimal gradient systems | |
| 260 | |b Cornell University Library, arXiv.org |c Dec 11, 2024 | ||
| 513 | |a Working Paper | ||
| 520 | 3 | |a In this paper, we provide a mathematical framework for improving generalization in a class of learning problems which is related to point estimations for modeling of high-dimensional nonlinear functions. In particular, we consider a variational problem for a weakly-controlled gradient system, whose control input enters into the system dynamics as a coefficient to a nonlinear term which is scaled by a small parameter. Here, the optimization problem consists of a cost functional, which is associated with how to gauge the quality of the estimated model parameters at a certain fixed final time w.r.t. the model validating dataset, while the weakly-controlled gradient system, whose the time-evolution is guided by the model training dataset and its perturbed version with small random noise. Using the perturbation theory, we provide results that will allow us to solve a sequence of optimization problems, i.e., a set of decomposed optimization problems, so as to aggregate the corresponding approximate optimal solutions that are reasonably sufficient for improving generalization in such a class of learning problems. Moreover, we also provide an estimate for the rate of convergence for such approximate optimal solutions. Finally, we present some numerical results for a typical case of nonlinear regression problem. | |
| 653 | |a System dynamics | ||
| 653 | |a Datasets | ||
| 653 | |a Random noise | ||
| 653 | |a Parameter estimation | ||
| 653 | |a Learning | ||
| 653 | |a Nonlinear control | ||
| 653 | |a Functions (mathematics) | ||
| 653 | |a Perturbation theory | ||
| 653 | |a Nonlinear dynamics | ||
| 653 | |a Optimization | ||
| 653 | |a Functionals | ||
| 773 | 0 | |t arXiv.org |g (Dec 11, 2024), p. n/a | |
| 786 | 0 | |d ProQuest |t Engineering Database | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/3144199832/abstract/embedded/ZKJTFFSVAI7CB62C?source=fedsrch |
| 856 | 4 | 0 | |3 Full text outside of ProQuest |u http://arxiv.org/abs/2412.08772 |