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Adaptive random fou...
Adaptive random fourier features with metropolis sampling
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- Kammonen, Aku, 1984- (författare)
- KTH,Numerisk analys, NA
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- Kiessling, Jonas (författare)
- H-Ai AB, Grevgatan 23,114 53, Stockholm, Sweden
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- Plecháč, Petr (författare)
- Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA
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- Sandberg, Mattias (författare)
- KTH,Numerisk analys, NA
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- Szepessy, Anders, 1960- (författare)
- KTH,Numerisk analys, NA
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(creator_code:org_t)
- American Institute of Mathematical Sciences, 2019
- 2019
- Engelska.
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Ingår i: Foundations of Data Science. - : American Institute of Mathematical Sciences. - 2639-8001. ; 0:0, s. 0-0
- Relaterad länk:
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http://dx.doi.org/10...
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https://www.aimscien...
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https://urn.kb.se/re...
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https://doi.org/10.3...
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Abstract
Ämnesord
Stäng
- The supervised learning problem todetermine a neural network approximation $\mathbb{R}^d\ni x\mapsto\sum_{k=1}^K\hat\beta_k e^{{\mathrm{i}}\omega_k\cdot x}$with one hidden layer is studied asa random Fourier features algorithm. The Fourier features, i.e., the frequencies $\omega_k\in\mathbb{R}^d$,are sampled using an adaptive Metropolis sampler.The Metropolis test accepts proposal frequencies $\omega_k'$, having corresponding amplitudes $\hat\beta_k'$, with the probability$\min\big\{1, (|\hat\beta_k'|/|\hat\beta_k|)^\gamma\big\}$,for a certain positive parameter $\gamma$, determined by minimizing the approximation error for given computational work.This adaptive, non-parametric stochastic method leads asymptotically, as $K\to\infty$, to equidistributed amplitudes $|\hat\beta_k|$, analogous to deterministic adaptive algorithms for differential equations. The equidistributed amplitudes are shown to asymptotically correspond to the optimal density for independent samples in random Fourier features methods.Numerical evidence is provided in order to demonstrate the approximation properties and efficiency of the proposed algorithm. The algorithm is testedboth on synthetic data and a real-world high-dimensional benchmark.
Ämnesord
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Probability Theory and Statistics (hsv//eng)
Nyckelord
- Random Fourier features
- neural networks
- Metropolis algorithm
- stochastich gradient descent
- Numerical Analysis
- Numerisk analys
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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