Covariance functions

Variograms, Mercer kernels, positive definite operators, spare reproducing kernels for that Hilbert space I bought on eBay real cheap


This is usually in the context of Gaussian processes where everything can work out nicely if you are lucky, but other kernel machines are OK too. The goal for most of these is to maximise the marginal posterior likelihood, a.k.a. model evidence, as is conventional in Bayesian ML.

Learning kernel hyperparameters

🏗

Learning kernel composition

Automating kernel design by some composition of simpler atomic kernels. AFAICT this started from summaries like (Genton 2001) and went via Duvenaud’s aforementioned notes to became a small industry (Lloyd et al. 2014; D. K. Duvenaud, Nickisch, and Rasmussen 2011; D. Duvenaud et al. 2013; Grosse et al. 2012). A prominent example was the Automated statistician project by David Duvenaud, James Robert Lloyd, Roger Grosse and colleagues, which works by greedy combinatorial search over possible compositions.

More fashionable, presumably, are the differentiable search methods. For example, the AutoGP system (Krauth et al. 2016; Bonilla, Krauth, and Dezfouli 2019) incorporates tricks like these to use gradient descent to design kernels for Gaussian processes. (Sun et al. 2018) construct deep networks of composed kernels. I imagine the Deep Gaussian Process literature is also of this kind, but have not read it.

Hyperkernels

Kernels on kernels, for kernel learning kernels. 🏗 (Ong, Smola, and Williamson 2005, 2002; Ong and Smola 2003; Kondor and Jebara 2006)

References

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