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Surrogate kernel-based methods offer a flexible solution to structured outputprediction by leveraging the kernel trick in both input and output spaces. Incontrast to energy-based models, they avoid to pay the cost of inference duringtraining, while enjoying statistical guarantees. However, withoutapproximation, these approaches are condemned to be used only on a limitedamount of training data. In this paper, we propose to equip surrogate kernelmethods with approximations based on sketching, seen as low rank projections offeature maps both on input and output feature maps. We showcase the approach onInput Output Kernel ridge Regression (or Kernel Dependency Estimation) andprovide excess risk bounds that can be in turn directly plugged on the finalpredictive model. An analysis of the complexity in time and memory show thatsketching the input kernel mostly reduces training time while sketching theoutput kernel allows to reduce the inference time. Furthermore, we show thatGaussian and sub-Gaussian sketches are admissible sketches in the sense thatthey induce projection operators ensuring a small excess risk. Experiments ondifferent tasks consolidate our findings.

Sketch In, Sketch Out: Accelerating both Learning and Inference for Structured Prediction with Kernels