arXiv subjects

Zhewei Wei

Publications and source records attributed to Zhewei Wei.

At least 91 records · Page 5Linked to original sources

arXiv2022

Instant Graph Neural Networks for Dynamic Graphs

Graph Neural Networks (GNNs) have been widely used for modeling graph-structured data. With the development of numerous GNN variants, recent years have witnessed groundbreaking results in improving the scalability of GNNs to work on static graphs with millions of nodes. However, how to instantly represent continuous changes of large-scale dynamic graphs with GNNs is still an open problem. Existing dynamic GNNs focus on modeling the periodic evolution of graphs, often on a snapshot basis. Such methods suffer from two drawbacks: first, there is a substantial delay for the changes in the graph to be reflected in the graph representations, resulting in losses on the model's accuracy; second, repeatedly calculating the representation matrix on the entire graph in each snapshot is predominantly time-consuming and severely limits the scalability. In this paper, we propose Instant Graph Neural Network (InstantGNN), an incremental computation approach for the graph representation matrix of dynamic graphs. Set to work with dynamic graphs with the edge-arrival model, our method avoids time-consuming, repetitive computations and allows instant updates on the representation and instant predictions. Graphs with dynamic structures and dynamic attributes are both supported. The upper bounds of time complexity of those updates are also provided. Furthermore, our method provides an adaptive training strategy, which guides the model to retrain at moments when it can make the greatest performance gains. We conduct extensive experiments on several real-world and synthetic datasets. Empirical results demonstrate that our model achieves state-of-the-art accuracy while having orders-of-magnitude higher efficiency than existing methods.

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arXiv2022

Edge-based Local Push for Personalized PageRank

Personalized PageRank (PPR) is a popular node proximity metric in graph mining and network research. Given a graph G=(V,E) and a source node $s \in V$, a single-source PPR (SSPPR) query asks for the PPR value $\vpi(u)$ with respect to s, which represents the relative importance of node u in the context of the source node s. Among existing algorithms for SSPPR queries, LocalPush is a fundamental method which serves as a cornerstone for subsequent algorithms. In LocalPush, a push operation is a crucial primitive operation, which distributes the probability at a node u to ALL u's neighbors via the corresponding edges. Although this push operation works well on unweighted graphs, unfortunately, it can be rather inefficient on weighted graphs. In particular, on unbalanced weighted graphs where only a few of these edges take the majority of the total weight among them, the push operation would have to distribute insignificant probabilities along those edges which just take the minor weights, resulting in expensive overhead. To resolve this issue, we propose the EdgePush algorithm, a novel method for computing SSPPR queries on weighted graphs. EdgePush decomposes the aforementioned push operations in edge-based push, allowing the algorithm to operate at the edge level granularity. Hence, it can flexibly distribute the probabilities according to edge weights. Furthermore, our EdgePush allows a fine-grained termination threshold for each individual edge, leading to a superior complexity over LocalPush. Notably, we prove that EdgePush improves the theoretical query cost of LocalPush by an order of up to O(n) when the graph's weights are unbalanced, both in terms of $\ell_1$-error and normalized additive error. Our experimental results demonstrate that EdgePush significantly outperforms state-of-the-art baselines in terms of query efficiency on large motif-based and real-world weighted graphs.

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arXiv2022

Preformer: Predictive Transformer with Multi-Scale Segment-wise Correlations for Long-Term Time Series Forecasting

Transformer-based methods have shown great potential in long-term time series forecasting. However, most of these methods adopt the standard point-wise self-attention mechanism, which not only becomes intractable for long-term forecasting since its complexity increases quadratically with the length of time series, but also cannot explicitly capture the predictive dependencies from contexts since the corresponding key and value are transformed from the same point. This paper proposes a predictive Transformer-based model called {\em Preformer}. Preformer introduces a novel efficient {\em Multi-Scale Segment-Correlation} mechanism that divides time series into segments and utilizes segment-wise correlation-based attention for encoding time series. A multi-scale structure is developed to aggregate dependencies at different temporal scales and facilitate the selection of segment length. Preformer further designs a predictive paradigm for decoding, where the key and value come from two successive segments rather than the same segment. In this way, if a key segment has a high correlation score with the query segment, its successive segment contributes more to the prediction of the query segment. Extensive experiments demonstrate that our Preformer outperforms other Transformer-based methods.

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arXiv2022

Learning to be a Statistician: Learned Estimator for Number of Distinct Values

Estimating the number of distinct values (NDV) in a column is useful for many tasks in database systems, such as columnstore compression and data profiling. In this work, we focus on how to derive accurate NDV estimations from random (online/offline) samples. Such efficient estimation is critical for tasks where it is prohibitive to scan the data even once. Existing sample-based estimators typically rely on heuristics or assumptions and do not have robust performance across different datasets as the assumptions on data can easily break. On the other hand, deriving an estimator from a principled formulation such as maximum likelihood estimation is very challenging due to the complex structure of the formulation. We propose to formulate the NDV estimation task in a supervised learning framework, and aim to learn a model as the estimator. To this end, we need to answer several questions: i) how to make the learned model workload agnostic; ii) how to obtain training data; iii) how to perform model training. We derive conditions of the learning framework under which the learned model is workload agnostic, in the sense that the model/estimator can be trained with synthetically generated training data, and then deployed into any data warehouse simply as, e.g., user-defined functions (UDFs), to offer efficient (within microseconds on CPU) and accurate NDV estimations for unseen tables and workloads. We compare the learned estimator with the state-of-the-art sample-based estimators on nine real-world datasets to demonstrate its superior estimation accuracy. We publish our code for training data generation, model training, and the learned estimator online for reproducibility.

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arXiv2022

BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation

Many representative graph neural networks, e.g., GPR-GNN and ChebNet, approximate graph convolutions with graph spectral filters. However, existing work either applies predefined filter weights or learns them without necessary constraints, which may lead to oversimplified or ill-posed filters. To overcome these issues, we propose BernNet, a novel graph neural network with theoretical support that provides a simple but effective scheme for designing and learning arbitrary graph spectral filters. In particular, for any filter over the normalized Laplacian spectrum of a graph, our BernNet estimates it by an order-$K$ Bernstein polynomial approximation and designs its spectral property by setting the coefficients of the Bernstein basis. Moreover, we can learn the coefficients (and the corresponding filter weights) based on observed graphs and their associated signals and thus achieve the BernNet specialized for the data. Our experiments demonstrate that BernNet can learn arbitrary spectral filters, including complicated band-rejection and comb filters, and it achieves superior performance in real-world graph modeling tasks. Code is available at https://github.com/ivam-he/BernNet.

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arXiv2021

Graph Neural Networks Inspired by Classical Iterative Algorithms

Despite the recent success of graph neural networks (GNN), common architectures often exhibit significant limitations, including sensitivity to oversmoothing, long-range dependencies, and spurious edges, e.g., as can occur as a result of graph heterophily or adversarial attacks. To at least partially address these issues within a simple transparent framework, we consider a new family of GNN layers designed to mimic and integrate the update rules of two classical iterative algorithms, namely, proximal gradient descent and iterative reweighted least squares (IRLS). The former defines an extensible base GNN architecture that is immune to oversmoothing while nonetheless capturing long-range dependencies by allowing arbitrary propagation steps. In contrast, the latter produces a novel attention mechanism that is explicitly anchored to an underlying end-to-end energy function, contributing stability with respect to edge uncertainty. When combined we obtain an extremely simple yet robust model that we evaluate across disparate scenarios including standardized benchmarks, adversarially-perturbated graphs, graphs with heterophily, and graphs involving long-range dependencies. In doing so, we compare against SOTA GNN approaches that have been explicitly designed for the respective task, achieving competitive or superior node classification accuracy. Our code is available at https://github.com/FFTYYY/TWIRLS.

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arXiv2021

Approximate Graph Propagation

Efficient computation of node proximity queries such as transition probabilities, Personalized PageRank, and Katz are of fundamental importance in various graph mining and learning tasks. In particular, several recent works leverage fast node proximity computation to improve the scalability of Graph Neural Networks (GNN). However, prior studies on proximity computation and GNN feature propagation are on a case-by-case basis, with each paper focusing on a particular proximity measure. In this paper, we propose Approximate Graph Propagation (AGP), a unified randomized algorithm that computes various proximity queries and GNN feature propagation, including transition probabilities, Personalized PageRank, heat kernel PageRank, Katz, SGC, GDC, and APPNP. Our algorithm provides a theoretical bounded error guarantee and runs in almost optimal time complexity. We conduct an extensive experimental study to demonstrate AGP's effectiveness in two concrete applications: local clustering with heat kernel PageRank and node classification with GNNs. Most notably, we present an empirical study on a billion-edge graph Papers100M, the largest publicly available GNN dataset so far. The results show that AGP can significantly improve various existing GNN models' scalability without sacrificing prediction accuracy.

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arXiv2021

Scalable Graph Neural Networks via Bidirectional Propagation

Graph Neural Networks (GNN) is an emerging field for learning on non-Euclidean data. Recently, there has been increased interest in designing GNN that scales to large graphs. Most existing methods use "graph sampling" or "layer-wise sampling" techniques to reduce training time. However, these methods still suffer from degrading performance and scalability problems when applying to graphs with billions of edges. This paper presents GBP, a scalable GNN that utilizes a localized bidirectional propagation process from both the feature vectors and the training/testing nodes. Theoretical analysis shows that GBP is the first method that achieves sub-linear time complexity for both the precomputation and the training phases. An extensive empirical study demonstrates that GBP achieves state-of-the-art performance with significantly less training/testing time. Most notably, GBP can deliver superior performance on a graph with over 60 million nodes and 1.8 billion edges in less than half an hour on a single machine. The codes of GBP can be found at https://github.com/chennnM/GBP .

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arXiv2021

Unifying the Global and Local Approaches: An Efficient Power Iteration with Forward Push

Personalized PageRank (PPR) is a critical measure of the importance of a node t to a source node s in a graph. The Single-Source PPR (SSPPR) query computes the PPR's of all the nodes with respect to s on a directed graph $G$ with $n$ nodes and $m$ edges, and it is an essential operation widely used in graph applications. In this paper, we propose novel algorithms for solving two variants of SSPPR: (i) high-precision queries and (ii) approximate queries. For high-precision queries, Power Iteration (PowItr) and Forward Push (FwdPush) are two fundamental approaches. Given an absolute error threshold $λ$, the only known bound of FwdPush is $O(\frac{m}λ)$, much worse than the $O(m \log \frac{1}λ)$-bound of PowItr. Whether FwdPush can achieve the same running time bound as PowItr does still remains an open question in the research community. We give a positive answer to this question by showing that the running time of a common implementation of FwdPush is actually bounded by $O(m \cdot \log \frac{1}λ)$.Based on this finding, we propose a new algorithm, called Power Iteration with Forward Push (PowerPush), which incorporates the strengths of both PowItr and FwdPush. For approximate queries (with a relative error $ε$), we propose a new algorithm, called SpeedPPR, with overall expected time bounded by $O(n \cdot \log n \cdot \log \frac{1}ε)$ on scale-free graphs. This bound greatly improves the $O(\frac{n \cdot \log n}ε)$ bound of a state-of-the-art algorithm FORA.

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arXiv2021

FlashP: An Analytical Pipeline for Real-time Forecasting of Time-Series Relational Data

Interactive response time is important in analytical pipelines for users to explore a sufficient number of possibilities and make informed business decisions. We consider a forecasting pipeline with large volumes of high-dimensional time series data. Real-time forecasting can be conducted in two steps. First, we specify the part of data to be focused on and the measure to be predicted by slicing, dicing, and aggregating the data. Second, a forecasting model is trained on the aggregated results to predict the trend of the specified measure. While there are a number of forecasting models available, the first step is the performance bottleneck. A natural idea is to utilize sampling to obtain approximate aggregations in real time as the input to train the forecasting model. Our scalable real-time forecasting system FlashP (Flash Prediction) is built based on this idea, with two major challenges to be resolved in this paper: first, we need to figure out how approximate aggregations affect the fitting of forecasting models, and forecasting results; and second, accordingly, what sampling algorithms we should use to obtain these approximate aggregations and how large the samples are. We introduce a new sampling scheme, called GSW sampling, and analyze error bounds for estimating aggregations using GSW samples. We introduce how to construct compact GSW samples with the existence of multiple measures to be analyzed. We conduct experiments to evaluate our solution and compare it with alternatives on real data.

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arXiv2020

Simple and Deep Graph Convolutional Networks

Graph convolutional networks (GCNs) are a powerful deep learning approach for graph-structured data. Recently, GCNs and subsequent variants have shown superior performance in various application areas on real-world datasets. Despite their success, most of the current GCN models are shallow, due to the {\em over-smoothing} problem. In this paper, we study the problem of designing and analyzing deep graph convolutional networks. We propose the GCNII, an extension of the vanilla GCN model with two simple yet effective techniques: {\em Initial residual} and {\em Identity mapping}. We provide theoretical and empirical evidence that the two techniques effectively relieves the problem of over-smoothing. Our experiments show that the deep GCNII model outperforms the state-of-the-art methods on various semi- and full-supervised tasks. Code is available at https://github.com/chennnM/GCNII .

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arXiv2020

Personalized PageRank to a Target Node, Revisited

Personalized PageRank (PPR) is a widely used node proximity measure in graph mining and network analysis. Given a source node $s$ and a target node $t$, the PPR value $π(s,t)$ represents the probability that a random walk from $s$ terminates at $t$, and thus indicates the bidirectional importance between $s$ and $t$. The majority of the existing work focuses on the single-source queries, which asks for the PPR value of a given source node $s$ and every node $t \in V$. However, the single-source query only reflects the importance of each node $t$ with respect to $s$. In this paper, we consider the {\em single-target PPR query}, which measures the opposite direction of importance for PPR. Given a target node $t$, the single-target PPR query asks for the PPR value of every node $s\in V$ to a given target node $t$. We propose RBS, a novel algorithm that answers approximate single-target queries with optimal computational complexity. We show that RBS improves three concrete applications: heavy hitters PPR query, single-source SimRank computation, and scalable graph neural networks. We conduct experiments to demonstrate that RBS outperforms the state-of-the-art algorithms in terms of both efficiency and precision on real-world benchmark datasets.

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arXiv2020

Exact Single-Source SimRank Computation on Large Graphs

SimRank is a popular measurement for evaluating the node-to-node similarities based on the graph topology. In recent years, single-source and top-$k$ SimRank queries have received increasing attention due to their applications in web mining, social network analysis, and spam detection. However, a fundamental obstacle in studying SimRank has been the lack of ground truths. The only exact algorithm, Power Method, is computationally infeasible on graphs with more than $10^6$ nodes. Consequently, no existing work has evaluated the actual trade-offs between query time and accuracy on large real-world graphs. In this paper, we present ExactSim, the first algorithm that computes the exact single-source and top-$k$ SimRank results on large graphs. With high probability, this algorithm produces ground truths with a rigorous theoretical guarantee. We conduct extensive experiments on real-world datasets to demonstrate the efficiency of ExactSim. The results show that ExactSim provides the ground truth for any single-source SimRank query with a precision up to 7 decimal places within a reasonable query time.

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arXiv2019

Efficient Algorithms for Approximate Single-Source Personalized PageRank Queries

Given a graph $G$, a source node $s$ and a target node $t$, the personalized PageRank (PPR) of $t$ with respect to $s$ is the probability that a random walk starting from $s$ terminates at $t$. An important variant of the PPR query is single-source PPR (SSPPR), which enumerates all nodes in $G$, and returns the top-$k$ nodes with the highest PPR values with respect to a given source $s$. PPR in general and SSPPR in particular have important applications in web search and social networks, e.g., in Twitter's Who-To-Follow recommendation service. However, PPR computation is known to be expensive on large graphs, and resistant to indexing. Consequently, previous solutions either use heuristics, which do not guarantee result quality, or rely on the strong computing power of modern data centers, which is costly. Motivated by this, we propose effective index-free and index-based algorithms for approximate PPR processing, with rigorous guarantees on result quality. We first present FORA, an approximate SSPPR solution that combines two existing methods Forward Push (which is fast but does not guarantee quality) and Monte Carlo Random Walk (accurate but slow) in a simple and yet non-trivial way, leading to both high accuracy and efficiency. Further, FORA includes a simple and effective indexing scheme, as well as a module for top-$k$ selection with high pruning power. Extensive experiments demonstrate that the proposed solutions are orders of magnitude more efficient than their respective competitors. Notably, on a billion-edge Twitter dataset, FORA answers a top-500 approximate SSPPR query within 1 second, using a single commodity server.

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arXiv2019

Scalable Graph Embeddings via Sparse Transpose Proximities

Graph embedding learns low-dimensional representations for nodes in a graph and effectively preserves the graph structure. Recently, a significant amount of progress has been made toward this emerging research area. However, there are several fundamental problems that remain open. First, existing methods fail to preserve the out-degree distributions on directed graphs. Second, many existing methods employ random walk based proximities and thus suffer from conflicting optimization goals on undirected graphs. Finally, existing factorization methods are unable to achieve scalability and non-linearity simultaneously. This paper presents an in-depth study on graph embedding techniques on both directed and undirected graphs. We analyze the fundamental reasons that lead to the distortion of out-degree distributions and to the conflicting optimization goals. We propose {\em transpose proximity}, a unified approach that solves both problems. Based on the concept of transpose proximity, we design \strap, a factorization based graph embedding algorithm that achieves scalability and non-linearity simultaneously. \strap makes use of the {\em backward push} algorithm to efficiently compute the sparse {\em Personalized PageRank (PPR)} as its transpose proximities. By imposing the sparsity constraint, we are able to apply non-linear operations to the proximity matrix and perform efficient matrix factorization to derive the embedding vectors. Finally, we present an extensive experimental study that evaluates the effectiveness of various graph embedding algorithms, and we show that \strap outperforms the state-of-the-art methods in terms of effectiveness and scalability.

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arXiv2019

PRSim: Sublinear Time SimRank Computation on Large Power-Law Graphs

{\it SimRank} is a classic measure of the similarities of nodes in a graph. Given a node $u$ in graph $G =(V, E)$, a {\em single-source SimRank query} returns the SimRank similarities $s(u, v)$ between node $u$ and each node $v \in V$. This type of queries has numerous applications in web search and social networks analysis, such as link prediction, web mining, and spam detection. Existing methods for single-source SimRank queries, however, incur query cost at least linear to the number of nodes $n$, which renders them inapplicable for real-time and interactive analysis. { This paper proposes \prsim, an algorithm that exploits the structure of graphs to efficiently answer single-source SimRank queries. \prsim uses an index of size $O(m)$, where $m$ is the number of edges in the graph, and guarantees a query time that depends on the {\em reverse PageRank} distribution of the input graph. In particular, we prove that \prsim runs in sub-linear time if the degree distribution of the input graph follows the power-law distribution, a property possessed by many real-world graphs. Based on the theoretical analysis, we show that the empirical query time of all existing SimRank algorithms also depends on the reverse PageRank distribution of the graph.} Finally, we present the first experimental study that evaluates the absolute errors of various SimRank algorithms on large graphs, and we show that \prsim outperforms the state of the art in terms of query time, accuracy, index size, and scalability.

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arXiv2019

Efficient Estimation of Heat Kernel PageRank for Local Clustering

Given an undirected graph G and a seed node s, the local clustering problem aims to identify a high-quality cluster containing s in time roughly proportional to the size of the cluster, regardless of the size of G. This problem finds numerous applications on large-scale graphs. Recently, heat kernel PageRank (HKPR), which is a measure of the proximity of nodes in graphs, is applied to this problem and found to be more efficient compared with prior methods. However, existing solutions for computing HKPR either are prohibitively expensive or provide unsatisfactory error approximation on HKPR values, rendering them impractical especially on billion-edge graphs. In this paper, we present TEA and TEA+, two novel local graph clustering algorithms based on HKPR, to address the aforementioned limitations. Specifically, these algorithms provide non-trivial theoretical guarantees in relative error of HKPR values and the time complexity. The basic idea is to utilize deterministic graph traversal to produce a rough estimation of exact HKPR vector, and then exploit Monte-Carlo random walks to refine the results in an optimized and non-trivial way. In particular, TEA+ offers practical efficiency and effectiveness due to non-trivial optimizations. Extensive experiments on real-world datasets demonstrate that TEA+ outperforms the state-of-the-art algorithm by more than four times on most benchmark datasets in terms of computational time when achieving the same clustering quality, and in particular, is an order of magnitude faster on large graphs including the widely studied Twitter and Friendster datasets.

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arXiv2018

ProbeSim: Scalable Single-Source and Top-k SimRank Computations on Dynamic Graphs

Single-source and top-$k$ SimRank queries are two important types of similarity search in graphs with numerous applications in web mining, social network analysis, spam detection, etc. A plethora of techniques have been proposed for these two types of queries, but very few can efficiently support similarity search over large dynamic graphs, due to either significant preprocessing time or large space overheads. This paper presents ProbeSim, an index-free algorithm for single-source and top-$k$ SimRank queries that provides a non-trivial theoretical guarantee in the absolute error of query results. ProbeSim estimates SimRank similarities without precomputing any indexing structures, and thus can naturally support real-time SimRank queries on dynamic graphs. Besides the theoretical guarantee, ProbeSim also offers satisfying practical efficiency and effectiveness due to several non-trivial optimizations. We conduct extensive experiments on a number of benchmark datasets, which demonstrate that our solutions significantly outperform the existing methods in terms of efficiency and effectiveness. Notably, our experiments include the first empirical study that evaluates the effectiveness of SimRank algorithms on graphs with billion edges, using the idea of pooling.

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