Graph Machine Learning

Why `True is False is False` -> False? Stumbled upon this little question why True is False is False evaluates to False in python. The answer is as simple as the question, but not obvious and many people could not answer it. So I wrote a quick post about it.

Other telegram channels There are many other interesting channels, below are English-speaking that I follow. If I miss something valuable, feel free to send them to me and I will update the post. https://t.me/opendatascience https://t.me/ArtificialIntelligencedl https://t.me/ai_machinelearning_big_data https://t.me/j_links https://t.me/ArtificialIntelligenceArticles https://t.me/snakers4 https://t.me/loss_function_porn https://t.me/yegor256news Also quite useful aggregator https://infomate.club/ml/

On the universal equivariant functions Yesterday's post was followed by a conversation with Andreas Loukas on the power of graph neural networks. There is one detail about the current analysis of GNN, which I didn't pay much attention before, even though I encountered it (it's a recurring phenomenon for me, when some major insight is given one sentence in the paper and is not highlighted in CAPITAL letters). The insight is that there are two types of GNN, anonymous and non-anonymous. Anonymous case means you are invariant to the order of nodes, for example when you use the sum aggregation over nodes. It was shown that anonymous case is equivalent to WL algorithm and therefore has a lot limitations such as not being able to count subgraphs or distinguish graphons, etc. So the current anonymous models are not universal: they cannot compute all the functions of the inputs. It's a weaker model than non-anonymous case, when you give some orderings to the nodes and then you iterate over all orderings. Non-anonymous models have additional node features, for example one-hot encodings of their position in adjacency matrix, which is one of the sufficient conditions for GNN to be universal. There are then two scenarios. Either you consider all possible permutations, in which case it grows in factorial terms and essentially it's a cheat. Or you resort to a single permutation, but then do not enjoy the invariance property of GNN, i.e. for different orderings it can give different set of embeddings for the same nodes. So it's interesting to see if there are universal equivariant functions that do not use all node permutations, which is still an open question.

How hard is graph isomorphism for graph neural networks? This is a new work by Andreas Loukas that sheds a little bit more light into the theory behind GNN. The analysis relies on the amount of information nodes should exchange in order to detect isomorphism class of each graph. This problem of finding isomorphism class is called graph canonization problem, which is probably even harder than graph isomorphism. As such a GNN model needs to output a number for each possible graph up to isomorphism, and needless to say the number of non-isomorphic graphs grows closely to factorial terms. Hence the experiments, while support the theory, are done only on very small graphs ~10 nodes.

Fresh picks from ArXiv This week has more papers from upcoming ACL, SIGIR, and KDD; a new survey on combinatorial optimization on graphs; and Borsuk's conjecture 🐹 Conferences • Joint Item Recommendation and Attribute Inference: An Adaptive Graph Convolutional Network Approach SIGIR 20 • ATBRG: Adaptive Target-Behavior Relational Graph Network for Effective Recommendation SIGIR 20 • Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks KDD 20 • Understanding Negative Sampling in Graph Representation Learning KDD 20 • Leveraging Graph to Improve Abstractive Multi-Document Summarization ACL 20 • M2GRL: A Multi-task Multi-view Graph Representation Learning Framework for Web-scale Recommender Systems KDD 20 • Graph Structure Learning for Robust Graph Neural Networks KDD 20 Surveys • Learning Combinatorial Optimization on Graphs: A Survey with Applications to Networking • How to Build a Graph-Based Deep Learning Architecture in Traffic Domain: A Survey • Motif Discovery Algorithms in Static and Temporal Networks: A Survey Graph Theory • The Weisfeiler-Leman dimension of distance-hereditary graphs • Counterexamples to Borsuk's conjecture from a third strongly regular graph • A Group-Theoretic Framework for Knowledge Graph Embedding

Social network data set Anton @xgfsru shared a data set VK1M (password 1234), with first 1M users from social network vk.com (data is taken via public API). In addition to the friends of each user, the file contains meta-information such as education, country, birthday of each node. It can be useful for node classification or regression tasks as well as community or anomaly detection.

Graph Machine Learning research groups: ChristosFaloutsos I do a series of posts on the groups in graph research. The sixth is Christos Faloutsos. He was an advisor for many current professors in GML such as Jure Leskovec, Leman Akoglu, Stephan Guennemman, and Bruno Ribeiro. Christos Faloutsos (~1960) - Affiliation: Carnegie Mellon University; Amazon - Education: Ph.D. at University of Toronto in 1987 (supervised by Stavros Christodoulakis); - h-index: 131; - Awards: ACM fellow, best paper awards at KDD, SIGMOD, ICDM; - Interests: data mining; database; anomaly detection in graphs.

CVPR 2020 Computer Vision and Pattern Recognition (CVPR) conference is the top conference in CV and has had increasing focus on application of graphs to images. Here are some facts about CVPR 2020. Papers link Dates: June 14-19 Where: Virtual • 6,656 total papers • 1,470 accepted papers • 22% acceptance rate • ~69 graph papers (~5% of total)

ACL 2020 stats ACL (Association for Computational Linguistics) is the top conferences in NLP. Each year there are more and more papers that use graphs with natural language. Dates: July 5-10 Where: Online • 3088 submissions (2906 submissions in 2019) • 571/208 long and short papers (25% overall acceptance rate; 447/213 in 2019) • 42/6 long/short graph papers (7%/3% of total)

Fresh picks from ArXiv This week highlights papers on scene graph generation, isomorphism testing by GNNs and WL, and weight estimation of pork cuts 🐖 GNN • How hard is graph isomorphism for graph neural networks? by Andreas Loukas • Neural Stochastic Block Model & Scalable Community-Based Graph Learning • Graph Density-Aware Losses for Novel Compositions in Scene Graph Generation • Structured Query-Based Image Retrieval Using Scene Graphs • Isometric Transformation Invariant and Equivariant Graph Convolutional Networks • SpectralWeight: a spectral graph wavelet framework for weight prediction of pork cuts Conferences • Integrating Semantic and Structural Information with Graph Convolutional Network for Controversy Detection ACL 20 • GoGNN: Graph of Graphs Neural Network for Predicting Structured Entity Interactions IJCAI 20 • Document Modeling with Graph Attention Networks for Multi-grained Machine Reading Comprehension ACL 20 Graph Theory • Acyclic edge coloring conjecture is true on planar graphs without intersecting triangles • The Weifeiler-Leman Algorithm and Recognition of Graph Properties Surveys • Visual Relationship Detection using Scene Graphs: A Survey • Foundations and modelling of dynamic networks using Dynamic Graph Neural Networks: A survey • Recent Advances in SQL Query Generation: A Survey • Explainable Reinforcement Learning: A Survey

Learning graph structure to help classification I just recently discussed an idea whether it's possible to create a graph from a non-graph classification data set and improve classification performance by doing it and I found two works on it. First approach just tries different values for knn to connect the points into a graph, obtains a graph for each parameter setting, and verifies the performance of classification of a graph model on the obtained graph. Clearly the problem with it is that you have to do classification many many times for different parameters of your knn. Second approach (ICML 2019, link to presentation) is more data-driven: instead of freezing the parameters of knn, it uses a graph generative model that would generate a graph from the points. Then a graph neural network would make a classification prediction and, together with parameters of generative model, would be updated by backpropagation. It's still quite heavy as you need to update parameters of two different models instead of one. Perhaps, there are future works that would create the graphs at little computational cost and would boost the results for classification pipelines.

AI and Theorem Proving One of the topics that caught my attention was on using AI to automate theorem proving. Apparently, there is already a conference on this. At ICLR there was a paper on using graph networks for theorem proving. I think besides this conference, which mainly explores how you can model mathematical logic using embeddings, another type of theorem proving is on smart pruning of combinatorial spaces (e.g. you have large space of graphs, from which you need to pick some particular examples).