@article{BussasSawadeKuhnetal.2017,
  author    = {Bussas, Matthias and Sawade, Christoph and Kuhn, Nicolas and Scheffer, Tobias and Landwehr, Niels},
  title     = {Varying-coefficient models for geospatial transfer learning},
  series = {Machine learning},
  volume    = {106},
  journal   = {Machine learning},
  publisher = {Springer},
  address   = {Dordrecht},
  issn      = {0885-6125},
  doi       = {10.1007/s10994-017-5639-3},
  pages     = {1419 -- 1440},
  year      = {2017},
  abstract  = {We study prediction problems in which the conditional distribution of the output given the input varies as a function of task variables which, in our applications, represent space and time. In varying-coefficient models, the coefficients of this conditional are allowed to change smoothly in space and time; the strength of the correlations between neighboring points is determined by the data. This is achieved by placing a Gaussian process (GP) prior on the coefficients. Bayesian inference in varying-coefficient models is generally intractable. We show that with an isotropic GP prior, inference in varying-coefficient models resolves to standard inference for a GP that can be solved efficiently. MAP inference in this model resolves to multitask learning using task and instance kernels. We clarify the relationship between varying-coefficient models and the hierarchical Bayesian multitask model and show that inference for hierarchical Bayesian multitask models can be carried out efficiently using graph-Laplacian kernels. We explore the model empirically for the problems of predicting rent and real-estate prices, and predicting the ground motion during seismic events. We find that varying-coefficient models with GP priors excel at predicting rents and real-estate prices. The ground-motion model predicts seismic hazards in the State of California more accurately than the previous state of the art.},
  language  = {en}
}