Predicting partially observed processes on temporal networks by Dynamics-Aware Node Embeddings (DyANE)

Abstract

Low-dimensional vector representations of network nodes have proven successful to feed graph data to machine learning algorithms and to improve performance across diverse tasks. Most of the embedding techniques, however, have been developed with the goal of achieving dense, low-dimensional encoding of network structure and patterns. Here, we present a node embedding technique aimed at providing low-dimensional feature vectors that are informative of dynamical processes occurring over temporal networks – rather than of the network structure itself – with the goal of enabling prediction tasks related to the evolution and outcome of these processes. We achieve this by using a lossless modified supra-adjacency representation of temporal networks and building on standard embedding techniques for static graphs based on random walks. We show that the resulting embedding vectors are useful for prediction tasks related to paradigmatic dynamical processes, namely epidemic spreading over empirical temporal networks. In particular, we illustrate the performance of our approach for the prediction of nodes’ epidemic states in single instances of a spreading process. We show how framing this task as a supervised multi-label classification task on the embedding vectors allows us to estimate the temporal evolution of the entire system from a partial sampling of nodes at random times, with potential impact for nowcasting infectious disease dynamics.

On the importance of structural equivalence in temporal networks for epidemic forecasting

“…Additionally, in order to reduce the number of nodes that need to be embedded, only active nodes are considered. These are nodes (i, t) where i had at least one contact at time step t. Inactive nodes are deleted and their incoming edges are rerouted to their next active future self, as previously done by Sato et al 21 . Finally, we converted all 24 datasets into supra-adjacency networks as described.…”

Time-varying graph representation learning via higher-order skip-gram with negative sampling

“…We compare our approach with several baseline methods from the literature of time-varying graph embeddings, which learn time-stamped node representations: (1) D y ANE [ 8 ], which learns temporal node embeddings with D eep W alk , mapping a time-varying graph into a supra-adjacency representation; (2) D yn GEM [ 36 ], a deep autoencoder architecture which dynamically reconstructs each graph snapshot initializing model weights with parameters learned in previous time frames; (3) D ynamic T riad [ 47 ], which captures structural information and temporal patterns of nodes, modeling the triadic closure process; (4) D y SAT [ 45 ], a deep neural model that computes node embeddings by a joint self-attention mechanism applied on structural neighborhood and temporal dynamics; (5) ISGNS [ 39 ], an incremental skip-gram embedding model based on D eep W alk . Details about hyper-parameters used in each method can be found in Additional file 1 .…”

“…We simulated 30 realizations of the SIR process on top of each empirical graph with different combinations of parameters . We used similar combinations of epidemic parameters and the same dynamical process to produce SIR states as described in [ 8 ]. Then we set a logistic regression to classify epidemic states S-I-R assigned to each active node during the unfolding of the spreading process.…”

“…Another class of models learn dynamic node representations by recurrent/attention mechanisms [ 43 – 46 ] or by imposing temporal stability among adjacent time intervals [ 47 , 48 ]. D y ANE [ 8 ] and weg 2 vec [ 49 ] project the dynamic graph structure into a static graph, in order to compute embeddings with word 2 vec . Closely related to these ones are [ 50 ] and [ 51 ], which learn node vectors according to time-respecting random walks or spreading trajectory paths.…”

“…[ 7 ]. Time-resolved node embeddings have been shown to yield improved performance for predicting the outcome of dynamical processes over networks, such as information diffusion and disease spreading [ 8 ], providing estimation of infection and contagion risk when used with contact tracing data.…”