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Erschienen in:
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2020 | OriginalPaper | Buchkapitel

3. Bayesian Regression and Gaussian Processes

verfasst von : Matthew F. Dixon, Igor Halperin, Paul Bilokon

Erschienen in: Machine Learning in Finance

Verlag: Springer International Publishing

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Abstract

This chapter introduces Bayesian regression and shows how it extends many of the concepts in the previous chapter. We develop kernel based machine learning methods—specifically Gaussian process regression, an important class of Bayesian machine learning methods—and demonstrate their application to “surrogate” models of derivative prices. This chapter also provides a natural starting point from which to develop intuition for the role and functional form of regularization in a frequentist setting—the subject of subsequent chapters.

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Vorheriges Kapitel Probabilistic Modeling
Nächstes Kapitel Feedforward Neural Networks
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Fußnoten
1
Surrogate models learn the output of an existing mathematical or statistical model as a function of input data.
 
2
Note that the factor of 2 in the denominator of the second term does not cancel out because the derivative is w.r.t. \(\sigma _n^2\) and not σ n.
 
3
This is in contrast to non-linear regressions commonly used in finance, which attempt to parameterize a non-linear function with a set of weights.
 
4
This choice is not a real limitation in practice (since it is for the prior) and does not prevent the mean of the predictor from being nonzero.
 
5
Gardner et al. (2018) explored 5 different approximation methods known in the numerical analysis literature.
 
6
Note that the plot uses the original coordinates and not the re-scaled coordinates.
 
7
Such maturities might correspond to exposure evaluation times in CVA simulation as in Crépey and Dixon (2020). The option model versus GP model are observed to produce very similar values.
 
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Metadaten
Titel
Bayesian Regression and Gaussian Processes
verfasst von
Matthew F. Dixon
Igor Halperin
Paul Bilokon
Copyright-Jahr
2020
Buch
Machine Learning in Finance

Print ISBN: 978-3-030-41067-4

Electronic ISBN: 978-3-030-41068-1

Copyright-Jahr: 2020

DOI
https://doi.org/10.1007/978-3-030-41068-1_3