Graph Machine Learning
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Everything about graph theory, computer science, machine learning, etc.


If you have something worth sharing with the community, reach out @gimmeblues, @chaitjo.

Admins: Sergey Ivanov; Michael Galkin; Chaitanya K. Joshi
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Combinatorial Optimization + ML

How can you solve traveling salesman problem (TSP) with ML? One way is to train the agent to make decisions about the next step. This requires that you either imitate already existing solutions or obtain the reward and then update the policy. This works if you have a solver to the problem which can generate solutions or if the problem is easy enough to converge to optimal value fast (e.g. Euclidean TSP).

For harder problems, you can integrate ML inside the solver (which has exponential runtime in the worst-case). So your solver still guarantees the optimality of the solutions but heuristic choices, which exist in most solvers, are done by ML. This is what Exact Combinatorial Optimization with Graph Convolutional Neural Networks (https://arxiv.org/abs/1906.01629) proposes for Branch & Bound procedure, which heuristically chooses the next node for branching. Results are quite impressive, showing that you can decrease the running time of SOTA solvers while preserving optimality, even if the branching choice of ML model does not have guarantees.
Graphs in Industry
What should be the order of authors in your ML paper?

The more you write papers, the more you ask questions like this.

On some occasions, it's a bit more subtle than you expect. For example, one guy did experiments and another made all the theory. Who should go first? It's not clear.

So I asked a few experienced professors and here are the insights:

* The first author is the one who did the most for the paper. If there is more than one, put a corresponding sign.
* The last places are reserved for supervisors.
* The middle are sorted by contribution.

But no one has any precise formula for computing contribution. So I proposed one.

Check it out in my latest blog post and clap if you like it 👏
WebConf 2020 stats (April 20-24, Taipei)

1129 number of submissions
217 accepted
19% acceptance rate
~30% graph papers
Network Science Institute at Northeastern University
networkscienceinstitute.org

With the director Albert-László Barabási, the focus is on biological networks, epidemiology, and formation.
They also have a YouTube channel with guest presentations on graph theory.
Fresh picks from ArXiv
ICML and KDD 20 submissions, AISTATS 20, Graph Isomorphism, and Review


ICML 20 submissions
Graph Convolutional Gaussian Processes For Link Prediction
When Labelled Data Hurts: Deep Semi-Supervised Classification with the Graph 1-Laplacian
Improving Graph Neural Network Representations of Logical Formulae with Subgraph Pooling
Differentiable Graph Module (DGM) for Graph Convolutional Network by group of Michael Bronstein
Deep Multi-Task Augmented Feature Learning via Hierarchical Graph Neural Network
Graph Universal Adversarial Attacks: A Few Bad Actors Ruin Graph Learning Models
Towards Similarity Graphs Constructed by Deep Reinforcement Learning by Yandex team
Connectivity-driven Communication in Multi-agent Reinforcement Learning through Diffusion Processes on Graphs
Explainable Deep Modeling of Tabular Data using TableGraphNet
Graph Filtration Learning
Graph Prolongation Convolutional Networks
Deep Coordination Graphs
Unifying Graph Convolutional Neural Networks and Label Propagation by group of Jure Leskovec

KDD 20 submissions
Disease State Prediction From Single-Cell Data Using Graph Attention Networks
Entity Context and Relational Paths for Knowledge Graph Completion by group of Jure Leskovec

Theory
Generalization and Representational Limits of Graph Neural Networks by group of Tommi Jaakkola

Graph Isomorphism
A polynomial time parallel algorithm for graph isomorphism using a quasipolynomial number of processors
Isomorphism for Random k-Uniform Hypergraphs

Review
Hypergraphs: an introduction and review
Do Deep Graph Neural Networks exist?

One of the open questions in GNN literature is whether deep GNN, i.e. GNN with many layers (e.g. more than 10), is useful.

There is a theoretical paper, What graph neural networks cannot learn: depth vs width, that proves that at least the number of layers * the embedding size of each layer should be proportional to the number of the nodes in the graph if GNN can compute many Turing computable functions. So if a graph has 10K nodes, then d*w = O(10K). For example, common embedding size, w, is 128 or 256, which means that a number of layers should be 40.

There is a cost associated with each layer: each node has to look at every neighbor and aggregate its information. So most of the implementations have up to 5 layers for obvious reasons, it's very time-consuming to compute.

Somewhat contrary, another theoretical paper, Graph Neural Networks Exponentially Lose Expressive Power for Node Classification, shows that under the certain conditions on the graph, GNN will essentially carry only degree information for each node, which is the most local property you can have for a node. This does not contradict the previous paper as (1) this paper works in a limit, (2) previous paper says that if d*w < O(n) then there is an instance of a graph for which GNN fails, which does not mean the result is universal for all graphs, and (3) this paper has certain conditions to hold which are only applicable to a narrow family of graphs.

Beyond this, there is a question of double descent, whether it occurs in GNN setting, which is yet the next question to solve.

So, my response is that for now we still have little understanding if deep GNN is useful and if so, how we can make them efficient in practice.
NeurIPS 2019 stats

6743 number of submissions
1428 accepted
21% acceptance rate
75 graph papers (5% of accepted)
Ringel’s conjecture is proved.

Ringel's conjecture states that every complete graph with 2n+1 nodes can be decomposed into a set of any identical non-overlapping trees of order n. In other words, take any tree with n nodes, place it on the complete graph with 2n+1 nodes, remove the edges your tree covers, and continue with the remaining graph. No matter which tree you have started with, there is a procedure to remove all the edges in a complete graph by placing your tree step by step.

This conjecture was known for 60 years and finally has been proved last month. At last this article makes a good job explaining how it was done.
Reinforcement Learning for Combinatorial Optimization: A Survey

Our new submission to IJCAI survey track. We surveyed all of the literature we found on applying RL methods for combinatorial optimization problems (e.g. TSP, Knapsack, MaxCut).

There are three types of the RL approaches we categorized the papers: Value-based, Policy-based, and Monte-Carlo Tree Search based. This is one of the domains that appeared very recently, a few years ago, and has an increasing number of successful applications to traditional problems each year. I would say it's a good topic for a fresh Ph.D. student to start working on.
Recent approaches to Graph Convolutional Networks, Graph Representation Learning and Reinforcement Learning

Surprisingly discovered a local workshop on GML with strong list of keynote speakers. Free of charge 🤫

https://gcn-grl-rl.sciencesconf.org/
ML and NLP Publications in 2019

One of the reasons why I have this channel is to encourage people do more research in general. And looking at the recent analysis of the number of accepted papers by countries you can understand why.

USA has almost as much publications last year as all other countries combined.

In particular, it's 2.5x > China, 6x > UK, and 100x > Russia.

The reasons are obvious, USA spends more budget on research from both government and industry, but also the culture of doing research is different: making a publication at top conferences is considered a big deal and a lot of efforts is put on this, — which can definitely adopted by other countries.