Graph Machine Learning

Graph Machine Learning research groups: Karsten Borgwardt I do a series of posts on the groups in graph research. The third is Karsten Borgwardt. His group at ETH Zurich is working on computational biology and his lab is well known for development of some of commonly used graph kernels (e.g. Weisfeiler-Leman, graphlet, shortest path). Karsten Borgwardt (1980) - Affiliation: ETH Zurich; - Education: Ph.D. at Ludwig-​Maximilians-University in Munich in 2007 (supervised by Hans-​Peter Kriegel); - h-index: 47; - Awards: Krupp Award, best papers at NeurIPS; - Interests: graph kernels; molecular graph representation; computational biology

Some notes on reconstruction conjecture Studying reconstruction conjecture is going down the rabbit hole 🐇 It seems so simple, but after a few steps its complexity unfolds and you find yourself reading another paper that provides some extra insights which only steer you away from the target. Formulation. You have a graph. You delete one vertex from it, and put obtained subgraph to a list, called deck. Then you return to the original graph, delete another vertex and again add obtained subgraph to the deck. And so on, for all n different vertices. The main question is whether there are two non-isomorphic graphs that have the same deck. Difficulty. I already wrote about this conjecture, showing that if you delete more than 1 vertex then there are indeed two different graphs with the same decks. That's the fact that you delete only one vertex makes it more difficult. Now think, you have n subgraphs, each has (n-1) original vertices, it seems you just have so much information as an input, O(n^3), to say everything about the original graph, which has only O(n^2). But no, it's still very hard to solve it. So what if we have a deck instead and try to recover original graph. Can we do it fast? I'm maybe wrong, but it seems there is no known polynomial-time algorithms and even the complexity of this problem is not clear. This paper, for specific type of graphs, shows an algorithm O(n^8), which is the biggest factor I've seen for poly-time algorithms. This paper studies some similar problems related to reconstruction conjecture, showing that just checking that a graph has specific deck is already equivalent to graph isomorphism. Finally, there is a manual 1991 on all major achievements to date showing that reconstruction conjecture is solved for some families of graphs such as regular graphs. Insights. After reading all this, I have the following thoughts. * It would be cool to write a paper on the algorithm for reconstruction of the graph from its deck. I have some trivial idea how to do it via graph isomorphism solver and some heuristics. Actually the problem is not purely abstract and has a lot of important applications to chemoinformatics for example, so it's interesting. * It would be cool to write a follow-up paper which uses RL to improve heuristics. Graph reconstruction is under radar compared to TSP, so it would be first-of-its-kind RL algorithm for such problem. * Initially I had the idea that if I take hard instances for graph isomorphism and compute decks for such graphs then I would get the same decks for non-isomorphic graphs, solving reconstruction conjecture. The reason why I thought this was that hard non-isomorphic graphs are very similar to each other, so their subgraphs would be identical. But, regular graphs are already proved to be reconstructible, so many hard instances won't work (such as SRG or Miyazaki graphs). Then, there are "very hard" graphs, which are half-regular (there are only two values for degrees across all nodes). I tried those, but found that decks are completely different for non-isomorphic graphs. So my idea failed and I spent two days reading, thinking, and implementing it 😀

Graph Representation Learning Workshop ICML 20 One of the places that gather a lot of researchers in GML is the workshop on Graph Representation Learning. This year it will appear at ICML 20. You can submit short papers (4 pages), including the works that you can resubmit later to a full conference elsewhere. This year there will be a separate track on using graphs for COVID-19 resolution. Deadline: 29th May.

RL for TSP There is already a rich literature on applying RL methods for Traveling Salesman Problem (TSP). In one line of research the solution is built incrementally, one node at a time. This is for example in a popular paper, Attention, Learn to Solve Routing Problems!. Recently another approach appeared: start with some solution to TSP and update this solution by swapping nodes. For example, Learning 2-opt Heuristics for the Traveling Salesman Problem via Deep Reinforcement Learning uses policy gradient method and shows that it significantly outperforms incremental approaches.

Fresh picks from ArXiv This week is full of CVPR papers with graphs, surveys on recommendation, and a historical note of the discovery of TSP algorithm is USSR 👨‍🚀 CVPR • HOPE-Net: A Graph-based Model for Hand-Object Pose Estimation • Graph Structured Network for Image-Text Matching • Spatio-Temporal Graph for Video Captioning with Knowledge Distillation • Multi-Modal Graph Neural Network for Joint Reasoning on Vision and Scene Text • Disentangling and Unifying Graph Convolutions for Skeleton-Based Action Recognition • Deep Homography Estimation for Dynamic Scenes • Iterative Context-Aware Graph Inference for Visual Dialog • Geometrically Principled Connections in Graph Neural Networks with Michael Bronstein • LiDAR-based Online 3D Video Object Detection with Graph-based Message Passing and Spatiotemporal Transformer Attention WebConf • Graph Enhanced Representation Learning for News Recommendation Survey • Deep Learning on Knowledge Graph for Recommender System: A Survey • Heterogeneous Network Representation Learning: Survey, Benchmark, Evaluation, and Beyond — essentially a survey on KG • A historical note on the 3/2-approximation algorithm for the metric traveling salesman problem — show that Christofides algorithm used for TSP was discovered in USSR around the same time • A Survey on Conversational Recommender Systems Graph Theory • Longest paths in random hypergraphs • A Fast Algorithm for the Product Structure of Planar Graphs • Counterexamples to "A Conjecture on Induced Subgraphs of Cayley Graphs"

CS 520 Knowledge Graphs Video Materials It seems that they will make the lectures available on YouTube👍

Network Epidemiology Online Workshop Series In April, there are seminars, tutorials, and discussion groups organized by University of Maryland to study how network science can help fighting virus contamination. It's for free, although there is a limitation on the number of participants (~150). There are two tracks: just listen to the tutorials or additionally participate in the groups. Lectures through Zoom. Deadline for application: tomorrow, 7th April.

Knowledge Graph course 2019 Michael Galkin had a course on knowledge graphs in 2019 and there are presentations of the course (though most in Russian) if you are interested.

​Deep Graph Library v0.4.3 In version 0.4.3, a popular GNN library DGL has now support for TensorFlow (originally supported PyTorch only), spin-off packages for Knowledge Graphs and Life Sciences (DGL-KE and DGL-LifeSci) and more flexible distributed training. For me it's really interesting to see a big uplift in training time against PyTorch-BigGraph library, this looks great.

CS 520: Knowledge Graphs There is no promise for the materials afterwards, but here is a page where presentations can be stored (so far there is a single presentation from Michael Galkin).

Graph Isomorphism Software Open-source software for finding isomorphism or canonical forms of graphs. * Nauty/Traces * Bliss * saucy * conauto * Gi-ext

CS 520: Knowledge Graphs Today starts a Stanford course on knowledge graphs. It's available for everyone for free via Zoom (although there is no guarantee to have the videos afterwards).