Accurate and Fast Estimation of Temporal Motifs using Path Sampling

Counting the number of small subgraphs, called motifs, is a fundamental problem in social network analysis and graph mining. Many real-world networks are directed and temporal, where edges have timestamps. Motif counting in directed, temporal graphs is especially challenging because there are a plethora of different kinds of patterns. Temporal motif counts reveal much richer information and there is a need for scalable algorithms for motif counting. A major challenge in counting is that there can be trillions of temporal motif matches even with a graph with only millions of vertices. Both the motifs and the input graphs can have multiple edges between two vertices, leading to a combinatorial explosion problem. Counting temporal motifs involving just four vertices is not feasible with current state-of-the-art algorithms. We design an algorithm, TEACUPS, that addresses this problem using a novel technique of temporal path sampling. We combine a path sampling method with carefully designed temporal data structures, to propose an efficient approximate algorithm for temporal motif counting. TEACUPS is an unbiased estimator with provable concentration behavior, which can be used to bound the estimation error. For a Bitcoin graph with hundreds of millions of edges, TEACUPS runs in less than 1 minute, while the exact counting algorithm takes more than a day. We empirically demonstrate the accuracy of TEACUPS on large datasets, showing an average of 30$\times$ speedup (up to 2000$\times$ speedup) compared to existing GPU-based exact counting methods while preserving high count estimation accuracy.

Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methods

Many widely used datasets for graph machine learning tasks have generally been homophilous, where nodes with similar labels connect to each other. Recently, new Graph Neural Networks (GNNs) have been developed that move beyond the homophily regime; however, their evaluation has often been conducted on small graphs with limited application domains. We collect and introduce diverse non-homophilous datasets from a variety of application areas that have up to 384x more nodes and 1398x more edges than prior datasets. We further show that existing scalable graph learning and graph minibatching techniques lead to performance degradation on these non-homophilous datasets, thus highlighting the need for further work on scalable non-homophilous methods. To address these concerns, we introduce LINKX -- a strong simple method that admits straightforward minibatch training and inference. Extensive experimental results with representative simple methods and GNNs across our proposed datasets show that LINKX achieves state-of-the-art performance for learning on non-homophilous graphs. Our codes and data are available at https://github.com/CUAI/Non-Homophily-Large-Scale.

Edge Proposal Sets for Link Prediction

Graphs are a common model for complex relational data such as social networks and protein interactions, and such data can evolve over time (e.g., new friendships) and be noisy (e.g., unmeasured interactions). Link prediction aims to predict future edges or infer missing edges in the graph, and has diverse applications in recommender systems, experimental design, and complex systems. Even though link prediction algorithms strongly depend on the set of edges in the graph, existing approaches typically do not modify the graph topology to improve performance. Here, we demonstrate how simply adding a set of edges, which we call a \emph{proposal set}, to the graph as a pre-processing step can improve the performance of several link prediction algorithms. The underlying idea is that if the edges in the proposal set generally align with the structure of the graph, link prediction algorithms are further guided towards predicting the right edges; in other words, adding a proposal set of edges is a signal-boosting pre-processing step. We show how to use existing link prediction algorithms to generate effective proposal sets and evaluate this approach on various synthetic and empirical datasets. We find that proposal sets meaningfully improve the accuracy of link prediction algorithms based on both neighborhood heuristics and graph neural networks. Code is available at \url{https://github.com/CUAI/Edge-Proposal-Sets}.

DEAP Cache: Deep Eviction Admission and Prefetching for Cache

Recent approaches for learning policies to improve caching, target just one out of the prefetching, admission and eviction processes. In contrast, we propose an end to end pipeline to learn all three policies using machine learning. We also take inspiration from the success of pretraining on large corpora to learn specialized embeddings for the task. We model prefetching as a sequence prediction task based on past misses. Following previous works suggesting that frequency and recency are the two orthogonal fundamental attributes for caching, we use an online reinforcement learning technique to learn the optimal policy distribution between two orthogonal eviction strategies based on them. While previous approaches used the past as an indicator of the future, we instead explicitly model the future frequency and recency in a multi-task fashion with prefetching, leveraging the abilities of deep networks to capture futuristic trends and use them for learning eviction and admission. We also model the distribution of the data in an online fashion using Kernel Density Estimation in our approach, to deal with the problem of caching non-stationary data. We present our approach as a "proof of concept" of learning all three components of cache strategies using machine learning and leave improving practical deployment for future work.