DAMNETS: A Deep Autoregressive Model for Generating Markovian Network Time Series

In this work, we introduce DAMNETS, a deep generative model for Markovian network time series. Time series of networks are found in many fields such as trade or payment networks in economics, contact networks in epidemiology or social media posts over time. Generative models of such data are useful for Monte-Carlo estimation and data set expansion, which is of interest for both data privacy and model fitting. Using recent ideas from the Graph Neural Network (GNN) literature, we introduce a novel GNN encoder-decoder structure in which an encoder GNN learns a latent representation of the input graph, and a decoder GNN uses this representation to simulate the network dynamics. We show using synthetic data sets that DAMNETS can replicate features of network topology across time observed in the real world, such as changing community structure and preferential attachment. DAMNETS outperforms competing methods on all of our measures of sample quality over several real and synthetic data sets.

PyTorch Geometric Signed Directed: A Survey and Software on Graph Neural Networks for Signed and Directed Graphs

Signed networks are ubiquitous in many real-world applications (e.g., social networks encoding trust/distrust relationships, correlation networks arising from time series data). While many signed networks are directed, there is a lack of survey papers and software packages on graph neural networks (GNNs) specially designed for directed networks. In this paper, we present PyTorch Geometric Signed Directed, a survey and software on GNNs for signed and directed networks. We review typical tasks, loss functions and evaluation metrics in the analysis of signed and directed networks, discuss data used in related experiments, and provide an overview of methods proposed. The deep learning framework consists of easy-to-use GNN models, synthetic and real-world data, as well as task-specific evaluation metrics and loss functions for signed and directed networks. The software is presented in a modular fashion, so that signed and directed networks can also be treated separately. As an extension library for PyTorch Geometric, our proposed software is maintained with open-source releases, detailed documentation, continuous integration, unit tests and code coverage checks. Our code is publicly available at \url{https://github.com/SherylHYX/pytorch_geometric_signed_directed}.

GNNRank: Learning Global Rankings from Pairwise Comparisons via Directed Graph Neural Networks

Recovering global rankings from pairwise comparisons is an important problem with many applications, ranging from time synchronization to sports team ranking. Pairwise comparisons corresponding to matches in a competition can naturally be construed as edges in a directed graph (digraph), whose nodes represent competitors with an unknown rank or skill strength. However, existing methods addressing the rank estimation problem have thus far not utilized powerful neural network architectures to optimize ranking objectives. Hence, we propose to augment an algorithm with neural network, in particular graph neural network (GNN) for its coherence to the problem at hand. In this paper, we introduce GNNRank, a modeling framework that is compatible with any GNN capable of learning digraph embeddings, and we devise trainable objectives to encode ranking upsets/violations. This framework includes a ranking score estimation approach, and adds a useful inductive bias by unfolding the Fiedler vector computation of the graph constructed from a learnable similarity matrix. Experimental results on a wide range of data sets show that our methods attain competitive and often superior performance compared with existing approaches. It also shows promising transfer ability to new data based on the trained GNN model.

Lead-lag detection and network clustering for multivariate time series with an application to the US equity market

In multivariate time series systems, it has been observed that certain groups of variables partially lead the evolution of the system, while other variables follow this evolution with a time delay; the result is a lead-lag structure amongst the time series variables. In this paper, we propose a method for the detection of lead-lag clusters of time series in multivariate systems. We demonstrate that the web of pairwise lead-lag relationships between time series can be helpfully construed as a directed network, for which there exist suitable algorithms for the detection of pairs of lead-lag clusters with high pairwise imbalance. Within our framework, we consider a number of choices for the pairwise lead-lag metric and directed network clustering components. Our framework is validated on both a synthetic generative model for multivariate lead-lag time series systems and daily real-world US equity prices data. We showcase that our method is able to detect statistically significant lead-lag clusters in the US equity market. We study the nature of these clusters in the context of the empirical finance literature on lead-lag relations and demonstrate how these can be used for the construction of predictive financial signals.

Local2Global: A distributed approach for scaling representation learning on graphs

We propose a decentralised "local2global"' approach to graph representation learning, that one can a-priori use to scale any embedding technique. Our local2global approach proceeds by first dividing the input graph into overlapping subgraphs (or "patches") and training local representations for each patch independently. In a second step, we combine the local representations into a globally consistent representation by estimating the set of rigid motions that best align the local representations using information from the patch overlaps, via group synchronization. A key distinguishing feature of local2global relative to existing work is that patches are trained independently without the need for the often costly parameter synchronization during distributed training. This allows local2global to scale to large-scale industrial applications, where the input graph may not even fit into memory and may be stored in a distributed manner. We apply local2global on data sets of different sizes and show that our approach achieves a good trade-off between scale and accuracy on edge reconstruction and semi-supervised classification. We also consider the downstream task of anomaly detection and show how one can use local2global to highlight anomalies in cybersecurity networks.

SSSNET: Semi-Supervised Signed Network Clustering

Node embeddings are a powerful tool in the analysis of networks; yet, their full potential for the important task of node clustering has not been fully exploited. In particular, most state-of-the-art methods generating node embeddings of signed networks focus on link sign prediction, and those that pertain to node clustering are usually not graph neural network (GNN) methods. Here, we introduce a novel probabilistic balanced normalized cut loss for training nodes in a GNN framework for semi-supervised signed network clustering, called SSSNET. The method is end-to-end in combining embedding generation and clustering without an intermediate step; it has node clustering as main focus, with an emphasis on polarization effects arising in networks. The main novelty of our approach is a new take on the role of social balance theory for signed network embeddings. The standard heuristic for justifying the criteria for the embeddings hinges on the assumption that "an enemy's enemy is a friend". Here, instead, a neutral stance is assumed on whether or not the enemy of an enemy is a friend. Experimental results on various data sets, including a synthetic signed stochastic block model, a polarized version of it, and real-world data at different scales, demonstrate that SSSNET can achieve comparable or better results than state-of-the-art spectral clustering methods, for a wide range of noise and sparsity levels. SSSNET complements existing methods through the possibility of including exogenous information, in the form of node-level features or labels.

Local2Global: Scaling global representation learning on graphs via local training

We propose a decentralised "local2global" approach to graph representation learning, that one can a-priori use to scale any embedding technique. Our local2global approach proceeds by first dividing the input graph into overlapping subgraphs (or "patches") and training local representations for each patch independently. In a second step, we combine the local representations into a globally consistent representation by estimating the set of rigid motions that best align the local representations using information from the patch overlaps, via group synchronization. A key distinguishing feature of local2global relative to existing work is that patches are trained independently without the need for the often costly parameter synchronisation during distributed training. This allows local2global to scale to large-scale industrial applications, where the input graph may not even fit into memory and may be stored in a distributed manner. Preliminary results on medium-scale data sets (up to $\sim$7K nodes and $\sim$200K edges) are promising, with a graph reconstruction performance for local2global that is comparable to that of globally trained embeddings. A thorough evaluation of local2global on large scale data and applications to downstream tasks, such as node classification and link prediction, constitutes ongoing work.

DUKweb: Diachronic word representations from the UK Web Archive corpus

Lexical semantic change (detecting shifts in the meaning and usage of words) is an important task for social and cultural studies as well as for Natural Language Processing applications. Diachronic word embeddings (time-sensitive vector representations of words that preserve their meaning) have become the standard resource for this task. However, given the significant computational resources needed for their generation, very few resources exist that make diachronic word embeddings available to the scientific community. In this paper we present DUKweb, a set of large-scale resources designed for the diachronic analysis of contemporary English. DUKweb was created from the JISC UK Web Domain Dataset (1996-2013), a very large archive which collects resources from the Internet Archive that were hosted on domains ending in `.uk'. DUKweb consists of a series word co-occurrence matrices and two types of word embeddings for each year in the JISC UK Web Domain dataset. We show the reuse potential of DUKweb and its quality standards via a case study on word meaning change detection.

DIGRAC: Digraph Clustering with Flow Imbalance

Node clustering is a powerful tool in the analysis of networks. Here, we introduce a graph neural network framework with a novel scalable Directed Mixed Path Aggregation(DIMPA) scheme to obtain node embeddings for directed networks in a self-supervised manner, including a novel probabilistic imbalance loss. The method is end-to-end in combining embedding generation and clustering without an intermediate step. In contrast to standard approaches in the literature, in this paper, directionality is not treated as a nuisance, but rather contains the main signal. In particular, we leverage the recently introduced cut flow imbalance measure, which is tightly related to directionality; cut flow imbalance is optimized without resorting to spectral methods or cluster labels. Experimental results on synthetic data, in the form of directed stochastic block models and real-world data at different scales, demonstrate that our method attains state-of-the-art results on directed clustering, for a wide range of noise and sparsity levels, as well as graph structures.

An extension of the angular synchronization problem to the heterogeneous setting

Given an undirected measurement graph $G = ([n], E)$, the classical angular synchronization problem consists of recovering unknown angles $\theta_1,\dots,\theta_n$ from a collection of noisy pairwise measurements of the form $(\theta_i - \theta_j) \mod 2\pi$, for each $\{i,j\} \in E$. This problem arises in a variety of applications, including computer vision, time synchronization of distributed networks, and ranking from preference relationships. In this paper, we consider a generalization to the setting where there exist $k$ unknown groups of angles $\theta_{l,1}, \dots,\theta_{l,n}$, for $l=1,\dots,k$. For each $ \{i,j\} \in E$, we are given noisy pairwise measurements of the form $\theta_{\ell,i} - \theta_{\ell,j}$ for an unknown $\ell \in \{1,2,\ldots,k\}$. This can be thought of as a natural extension of the angular synchronization problem to the heterogeneous setting of multiple groups of angles, where the measurement graph has an unknown edge-disjoint decomposition $G = G_1 \cup G_2 \ldots \cup G_k$, where the $G_i$'s denote the subgraphs of edges corresponding to each group. We propose a probabilistic generative model for this problem, along with a spectral algorithm for which we provide a detailed theoretical analysis in terms of robustness against both sampling sparsity and noise. The theoretical findings are complemented by a comprehensive set of numerical experiments, showcasing the efficacy of our algorithm under various parameter regimes. Finally, we consider an application of bi-synchronization to the graph realization problem, and provide along the way an iterative graph disentangling procedure that uncovers the subgraphs $G_i$, $i=1,\ldots,k$ which is of independent interest, as it is shown to improve the final recovery accuracy across all the experiments considered.