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High-Dimensional Gaussian Process Inference with Derivatives
Filip de Roos · Alexandra Gessner · Philipp Hennig

Thu Jul 22 08:45 PM -- 08:50 PM (PDT) @
Although it is widely known that Gaussian processes can be conditioned on observations of the gradient, this functionality is of limited use due to the prohibitive computational cost of $\mathcal{O}(N^3 D^3)$ in data points $N$ and dimension $D$. The dilemma of gradient observations is that a single one of them comes at the same cost as $D$ independent function evaluations, so the latter are often preferred. Careful scrutiny reveals, however, that derivative observations give rise to highly structured kernel Gram matrices for very general classes of kernels (inter alia, stationary kernels). We show that in the \emph{low-data} regime $N

Author Information

Filip de Roos (University of Tübingen)

PhD student in the International Max Planck Research School for Intelligent Systems ([IMPRS-IS](https://imprs.is.mpg.de/)). I am supervised by Prof. Philipp Hennig at the [University of Tübingen](https://uni-tuebingen.de/en/fakultaeten/mathematisch-naturwissenschaftliche-fakultaet/fachbereiche/informatik/lehrstuehle/methods-of-machine-learning/start/). Currently I am finishing up my dissertation on *Probabilistic Linear Algebra for Stochastic Optimization*. My research interest include and are not limited to: - Gaussian Processes - Optimization - Probabilistic Numerics

Alexandra Gessner (University of Tuebingen)
Philipp Hennig (University of Tübingen)

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