A Survey on Graph Kernels

Graph kernels have become an established and widely-used technique for solving classification tasks on graphs. This survey gives a comprehensive overview of techniques for kernel-based graph classification developed in the past 15 years. We describe and categorize graph kernels based on properties inherent to their design, such as the nature of their extracted graph features, their method of computation and their applicability to problems in practice. In an extensive experimental evaluation, we study the classification accuracy of a large suite of graph kernels on established benchmarks as well as new datasets. We compare the performance of popular kernels with several baseline methods and study the effect of applying a Gaussian RBF kernel to the metric induced by a graph kernel. In doing so, we find that simple baselines become competitive after this transformation on some datasets. Moreover, we study the extent to which existing graph kernels agree in their predictions (and prediction errors) and obtain a data-driven categorization of kernels as result. Finally, based on our experimental results, we derive a practitioner's guide to kernel-based graph classification

Kernel methods in genomics and computational biology

Support vector machines and kernel methods are increasingly popular in genomics and computational biology, due to their good performance in real-world applications and strong modularity that makes them suitable to a wide range of problems, from the classification of tumors to the automatic annotation of proteins. Their ability to work in high dimension, to process non-vectorial data, and the natural framework they provide to integrate heterogeneous data are particularly relevant to various problems arising in computational biology. In this chapter we survey some of the most prominent applications published so far, highlighting the particular developments in kernel methods triggered by problems in biology, and mention a few promising research directions likely to expand in the future

Applying Deep Learning to Fast Radio Burst Classification

Upcoming Fast Radio Burst (FRB) surveys will search $\sim$10\,$^3$ beams on sky with very high duty cycle, generating large numbers of single-pulse candidates. The abundance of false positives presents an intractable problem if candidates are to be inspected by eye, making it a good application for artificial intelligence (AI). We apply deep learning to single pulse classification and develop a hierarchical framework for ranking events by their probability of being true astrophysical transients. We construct a tree-like deep neural network (DNN) that takes multiple or individual data products as input (e.g. dynamic spectra and multi-beam detection information) and trains on them simultaneously. We have built training and test sets using false-positive triggers from real telescopes, along with simulated FRBs, and single pulses from pulsars. Training of the DNN was independently done for two radio telescopes: the CHIME Pathfinder, and Apertif on Westerbork. High accuracy and recall can be achieved with a labelled training set of a few thousand events. Even with high triggering rates, classification can be done very quickly on Graphical Processing Units (GPUs). That speed is essential for selective voltage dumps or issuing real-time VOEvents. Next, we investigate whether dedispersion back-ends could be completely replaced by a real-time DNN classifier. It is shown that a single forward propagation through a moderate convolutional network could be faster than brute-force dedispersion; but the low signal-to-noise per pixel makes such a classifier sub-optimal for this problem. Real-time automated classification may prove useful for bright, unexpected signals, both now and in the era of radio astronomy when data volumes and the searchable parameter spaces further outgrow our ability to manually inspect the data, such as for SKA and ngVLA

Kernel methods in machine learning

We review machine learning methods employing positive definite kernels. These methods formulate learning and estimation problems in a reproducing kernel Hilbert space (RKHS) of functions defined on the data domain, expanded in terms of a kernel. Working in linear spaces of function has the benefit of facilitating the construction and analysis of learning algorithms while at the same time allowing large classes of functions. The latter include nonlinear functions as well as functions defined on nonvectorial data. We cover a wide range of methods, ranging from binary classifiers to sophisticated methods for estimation with structured data.Comment: Published in at http://dx.doi.org/10.1214/009053607000000677 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org