Gaussian Processes Over Graphs

Venkitaraman, Arun; Chatterjee, Saikat; Händel, Peter

doi:10.1109/icassp40776.2020.9053859

Cited by 17 publications

(11 citation statements)

References 46 publications

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“…Using discrete kernels in GPs is a relatively unexplored area, possibly due to the difficulties in hyper-parameter optimization and inducing point selection. Discrete kernels have been used on graphs [42] and strings [43] (also for biological problems [23]), but so far only on relatively small datasets with full GPs. In parallel work, [33] study GPs on strings for Bayesian optimization, but their problems are small they do not use inducing points or any other scalability approach.…”

Section: Related Work A: Sparse Gaussian Processesmentioning

confidence: 99%

Sparse Gaussian Processes on Discrete Domains

et al. 2021

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Kernel methods on discrete domains have shown great promise for many challenging data types, for instance, biological sequence data and molecular structure data. Scalable kernel methods like Support Vector Machines may offer good predictive performances but do not intrinsically provide uncertainty estimates. In contrast, probabilistic kernel methods like Gaussian Processes offer uncertainty estimates in addition to good predictive performance but fall short in terms of scalability. While the scalability of Gaussian processes can be improved using sparse inducing point approximations, the selection of these inducing points remains challenging. We explore different techniques for selecting inducing points on discrete domains, including greedy selection, determinantal point processes, and simulated annealing. We find that simulated annealing, which can select inducing points that are not in the training set, can perform competitively with support vector machines and full Gaussian processes on synthetic data, as well as on challenging real-world DNA sequence data.

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Section: Related Work A: Sparse Gaussian Processesmentioning

confidence: 99%

Sparse Gaussian Processes on Discrete Domains

et al. 2021

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“…A second option is to leverage notions of graph convolutions for the same purpose (Opolka and Liò, 2020;Walker and Glocker, 2019). From a slightly different perspective, the studies by Venkitaraman et al (2020); Zhi et al (2020) follow the literature of multi-output GPs with a separable kernel design. Finally, a Matérn GP on graphs has been proposed by Borovitskiy et al (2021), although their model resembles kernels on graphs (Smola and Kondor, 2003).…”

Section: Related Workmentioning

confidence: 99%

“…A GP model on graphs would allow for modelling uncertainty associated with the nodes in the graph and making predictions on unlabelled nodes. A key requirement in building GPs on graphs is incorporating the graph information into the design of the GP kernel, for example using convolution-like operations (Ng et al, 2018;Walker and Glocker, 2019;Opolka and Liò, 2020; or following the separable kernel design of multi-output GPs (Venkitaraman et al, 2020;Zhi et al, 2020).…”

Section: Introductionmentioning

confidence: 99%

Adaptive Gaussian Processes on Graphs via Spectral Graph Wavelets

Opolka¹,

Zhi²,

Lió³

et al. 2021

Preprint

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Graph-based models require aggregating information in the graph from neighbourhoods of different sizes. In particular, when the data exhibit varying levels of smoothness on the graph, a multi-scale approach is required to capture the relevant information. In this work, we propose a Gaussian process model using spectral graph wavelets, which can naturally aggregate neighbourhood information at different scales. Through maximum likelihood optimisation of the model hyperparameters, the wavelets automatically adapt to the different frequencies in the data, and as a result our model goes beyond capturing low frequency information. We achieve scalability to larger graphs by using a spectrum-adaptive polynomial approximation of the filter function, which is designed to yield a low approximation error in dense areas of the graph spectrum. Synthetic and real-world experiments demonstrate the ability of our model to infer scales accurately and produce competitive performances against state-of-the-art models in graph-based learning tasks.

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“…Using discrete kernels in GPs is a relatively unexplored area, possibly due to the difficulties in hyper-parameter optimization and inducing point selection. Discrete kernels have been used on graphs [35] and strings [2] (also for biological problems [31]), but so far only on relatively small data sets with full GPs. To the best of our knowledge, we are the first to address the scalability problem with discrete GPs using inducing points and discrete optimization.…”

Section: Related Workmentioning

confidence: 99%

Scalable Gaussian Processes on Discrete Domains

Fortuin,

Dresdner,

Strathmann

et al. 2018

Preprint

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Kernel methods on discrete domains have shown great promise for many challenging data types, for instance, biological sequence data and molecular structure data. Scalable kernel methods like Support Vector Machines may offer good predictive performances but do not intrinsically provide uncertainty estimates. In contrast, probabilistic kernel methods like Gaussian Processes offer uncertainty estimates in addition to good predictive performance but fall short in terms of scalability. We present the first sparse Gaussian Process approximation framework on discrete input domains. Our framework achieves good predictive performance as well as uncertainty estimates using discrete optimization techniques. We present competitive results comparing our framework to baseline methods such as Support Vector Machines and full Gaussian Processes on synthetic data as well as on challenging real-world DNA sequence data.

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Gaussian Processes Over Graphs

Cited by 17 publications

References 46 publications

Sparse Gaussian Processes on Discrete Domains

Sparse Gaussian Processes on Discrete Domains

Adaptive Gaussian Processes on Graphs via Spectral Graph Wavelets

Scalable Gaussian Processes on Discrete Domains

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