Multifidelity dataset

As explained in Bayesian Optimization in Action

A multifidelity training dataset is a collection of objective observations accompanied by metadata identifying the fidelity at which each observation was obtained.

A multifidelity dataset combines objective observations gathered from functions with different costs and accuracies. Each observation includes metadata describing its fidelity, allowing a Gaussian process to use inexpensive, imperfect data alongside costly, accurate evaluations. section 9.2 section 9.7

A practical multifidelity dataset typically records:

• Input features and objective values for observations from high- and low-fidelity functions. section 9.2
• A correlation value identifying how closely each fidelity matches the ground truth; higher values indicate more accurate information. section 9.7
• The fidelity metadata as an additional feature column that a multifidelity Matérn kernel can process. section 9.7

Training a multifidelity GP

Construct train_x_full by appending a fidelity column to the input features, then pass it with train_y to BoTorch’s SingleTaskMultiFidelityGP and specify the fidelity-column index. The trained model can reduce uncertainty around low-fidelity observations while fitting high-fidelity observations appropriately. section 9.2.2 section 9.2.2

Figure 9.3 The multifidelity BayesOpt loop. The GP trains on data from both the high- and low-fidelity functions, and the BayesOpt policy decides where and which function to query at each iteration of the loop.

The multifidelity BayesOpt loop shows how a GP trains on observations from both fidelity levels before a policy selects which function and location to query next. section 9.2

How Bayesian Optimization in Action covers it

How deep it goes

Defines fidelity metadata and connects it to GP kernels, posterior uncertainty, and BoTorch training without detailing kernel internals.

Examples

Uses combined high- and low-fidelity observations, correlation-valued feature columns, and BoTorch training inputs.

What you can do after

Apply it via BoTorch by appending fidelity metadata and training a SingleTaskMultiFidelityGP.

How it connects

Connects Gaussian processes, Bayesian optimization, correlation, Matérn kernels, posterior uncertainty, and querying cost.

liveBookmanning.com

Read Bayesian Optimization in Action on liveBook Get the book at manning.com

Related concepts

• Gaussian processused by · A Gaussian process is a probability distribution over functions in which every finite collection of function values has a joint Gaussian distribution.
• datasetkind of · A dataset is an organized collection of related data items, records, or observations treated as a unit for storage, processing, analysis, or computation.

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.