Reconstructing Graph Diffusion History from a Single Snapshot

Diffusion on graphs is ubiquitous with numerous high-impact applications. In these applications, complete diffusion histories play an essential role in terms of identifying dynamical patterns, reflecting on precaution actions, and forecasting intervention effects. Despite their importance, complete diffusion histories are rarely available and are highly challenging to reconstruct due to ill-posedness, explosive search space, and scarcity of training data. To date, few methods exist for diffusion history reconstruction. They are exclusively based on the maximum likelihood estimation (MLE) formulation and require to know true diffusion parameters. In this paper, we study an even harder problem, namely reconstructing Diffusion history from A single SnapsHot} (DASH), where we seek to reconstruct the history from only the final snapshot without knowing true diffusion parameters. We start with theoretical analyses that reveal a fundamental limitation of the MLE formulation. We prove: (a) estimation error of diffusion parameters is unavoidable due to NP-hardness of diffusion parameter estimation, and (b) the MLE formulation is sensitive to estimation error of diffusion parameters. To overcome the inherent limitation of the MLE formulation, we propose a novel barycenter formulation: finding the barycenter of the posterior distribution of histories, which is provably stable against the estimation error of diffusion parameters. We further develop an effective solver named DIffusion hiTting Times with Optimal proposal (DITTO) by reducing the problem to estimating posterior expected hitting times via the Metropolis--Hastings Markov chain Monte Carlo method (M--H MCMC) and employing an unsupervised graph neural network to learn an optimal proposal to accelerate the convergence of M--H MCMC. We conduct extensive experiments to demonstrate the efficacy of the proposed method.Comment: Full version of the KDD 2023 paper. Our code is available at https://github.com/q-rz/KDD23-DITT

Networked Time Series Imputation via Position-aware Graph Enhanced Variational Autoencoders

Multivariate time series (MTS) imputation is a widely studied problem in recent years. Existing methods can be divided into two main groups, including (1) deep recurrent or generative models that primarily focus on time series features, and (2) graph neural networks (GNNs) based models that utilize the topological information from the inherent graph structure of MTS as relational inductive bias for imputation. Nevertheless, these methods either neglect topological information or assume the graph structure is fixed and accurately known. Thus, they fail to fully utilize the graph dynamics for precise imputation in more challenging MTS data such as networked time series (NTS), where the underlying graph is constantly changing and might have missing edges. In this paper, we propose a novel approach to overcome these limitations. First, we define the problem of imputation over NTS which contains missing values in both node time series features and graph structures. Then, we design a new model named PoGeVon which leverages variational autoencoder (VAE) to predict missing values over both node time series features and graph structures. In particular, we propose a new node position embedding based on random walk with restart (RWR) in the encoder with provable higher expressive power compared with message-passing based graph neural networks (GNNs). We further design a decoder with 3-stage predictions from the perspective of multi-task learning to impute missing values in both time series and graph structures reciprocally. Experiment results demonstrate the effectiveness of our model over baselines.Comment: KDD 202

Extended Target Echo Detection Based on KLD and Wigner Matrices

With the development of airborne radar radio frequency stealth (RFS) technology, the method of improving the RFS performance of airborne radar by optimizing target detection performance has been extensively studied. However, for wideband radar signals, the traditional point target model appears as an extended target model in the range-dimension, which is unfavorable to the detection of target echoes. To overcome the existing drawbacks, this paper devises an efficient echo detection algorithm from the perspective of information theory and random matrix. Firstly, aperiodic agile wideband radar signals are utilized to observe targets. Then, one frame of echo signals in the same range gate is reconstructed into a data form conforming to the Wigner matrix spectral decomposition. Finally, according to the signal detection theory, Kullback-Leibler Divergence (KLD) is used as the test statistic to complete the echo detection of the stealthy extended targets. By statistical analysis and comparison with other established echo detection algorithms, simulation results manifest that the proposed algorithm has superior detection performance and strong robustness, which not only makes up for the deficiency of traditional narrowband radar detection algorithms, but also increases the detection probability of radar system when it is faced with stealthy extended targets