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Measuring the sensitivity of Gaussian processes to kernel choice
Will Stephenson · Soumya Ghosh · Tin Nguyen · Mikhail Yurochkin · Sameer Deshpande · Tamara Broderick

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in Your Model is Wrong: Robustness and misspecification in probabilistic modeling »

Gaussian processes (GPs) are used to make medical and scientific decisions, including in cardiac care and monitoring of carbon dioxide emissions. But the choice of GP kernel is often somewhat arbitrary. In particular, uncountably many kernels typically align with qualitative prior knowledge (e.g. function smoothness or stationarity). But in practice, data analysts choose among a handful of convenient standard kernels (e.g. squared exponential). In the present work, we ask: Would decisions made with a GP differ under other, qualitatively interchangeable kernels? We show how to formulate this sensitivity analysis as a constrained optimization problem over a finite-dimensional space. We can then use standard optimizers to identify substantive changes in relevant decisions made with a GP. We demonstrate in both synthetic and real-world examples that decisions made with a GP can exhibit substantial sensitivity to kernel choice, even when prior draws are qualitatively interchangeable to a user.

Author Information

Will Stephenson (MIT)
Soumya Ghosh (MIT-IBM Watson AI Lab, IBM Research)
Tin Nguyen (MIT)
Mikhail Yurochkin (IBM Research, MIT-IBM Watson AI Lab)
Sameer Deshpande (University of Wisconsin--Madison)
Tamara Broderick (MIT)

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