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Fidelity correlation

As explained in Bayesian Optimization in Action

A fidelity correlation is a parameter describing how informative observations at one fidelity are about function values at another fidelity.

Fidelity correlation measures how informative an observation at one fidelity is about function values at another. Higher correlation lets a multifidelity Gaussian process transfer more information and reduce posterior uncertainty. section 9.2.2

Its effect on the covariance model is direct:

  • High correlation produces high covariance with nearby points, making low-fidelity observations informative. section 9.2.2
  • Low correlation produces low covariance, so posterior uncertainty remains higher. section 9.2.2

Toy comparison

A multifidelity GP trained only on low-fidelity observations shows less uncertainty when the correlation value is 0.9 than when it is 0.5. section 9.2.2

from botorch.models.gp_regression_fidelity
import SingleTaskMultiFidelityGP         #1
 
model = SingleTaskMultiFidelityGP(
train_x_full, train_y, data_fidelity=1)  #2

BoTorch records the fidelity-correlation column through data_fidelity when constructing SingleTaskMultiFidelityGP. section 9.2.2

How Bayesian Optimization in Action covers it

How deep it goes
Explains covariance and uncertainty effects with correlation values 0.5 and 0.9, but defers multifidelity Matérn-kernel details.
Examples
Compares low-fidelity-only predictions at correlation values 0.5 and 0.9.
What you can do after
Apply it via BoTorch by specifying the fidelity column in SingleTaskMultiFidelityGP.
How it connects
Connects fidelity correlation to Gaussian processes, covariance functions, Matérn kernels, and posterior uncertainty.
Cover of Bayesian Optimization in Action
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Related concepts

This explainer was generated by Manning's knowledge graph from the text of Bayesian Optimization in Action. The section links point to the parts of the book it draws on.