An official website of the United States government
Given a sequence of random graphs, we address the problem of online monitoring and detection of changes in the underlying data distribution. To this end, we adopt the Random Dot Product Graph (RDPG) model which postulates each node has an associated latent vector, and inner products between these vectors dictate the edge formation probabilities. Existing approaches for graph change-point detection (CPD) rely either on extensive computation, or they store and process the entire observed time series. In this paper we consider the cumulative sum of a judicious monitoring function, which quantifies the discrepancy between the streaming graph observations and the nominal model. This reference distribution is inferred via spectral embeddings of the first few graphs in the sequence, and the monitoring function can be updated in an efficient, online fashion. We characterize the distribution of this running statistic, allowing us to select appropriate thresholding parameters that guarantee error-rate control. The end result is a lightweight online CPD algorithm, with a proven capability to flag distribution shifts in the arriving graphs. The novel method is tested on both synthetic and real network data, corroborating its effectiveness in quickly detecting changes in the input graph sequence.
more »
« less
Change Point Detection in Weighted and Directed Random Dot Product Graphs
Given a sequence of possibly correlated randomly generated graphs, we address the problem of detecting changes on their underlying distribution. To this end, we will consider Random Dot Product Graphs (RDPGs), a simple yet rich family of random graphs that subsume Erdös-Rényi and Stochastic Block Model ensembles as particular cases. In RDPGs each node has an associated latent vector and inner products between these vectors dictate the edge existence probabilities. Previous works have mostly focused on the undirected and unweighted graph case, a gap we aim to close here. We first extend the RDPG model to accommodate directed and weighted graphs, a contribution whose interest transcends change-point detection (CPD). A statistic derived from the nodes' estimated latent vectors (i.e., embeddings) facilitates adoption of scalable geometric CPD techniques. The resulting algorithm yields interpretable results and facilitates pinpointing which (and when) nodes are acting differently. Numerical tests on simulated data as well as on a real dataset of graphs stemming from a Wi-Fi network corroborate the effectiveness of the proposed CPD method.
more »
« less
- PAR ID:
- 10321466
- Date Published:
- Journal Name:
- 2021 29th European Signal Processing Conference (EUSIPCO)
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
The popular Random Dot Product Graph (RDPG) generative model postulates that each node has an associated (latent) vector, and the probability of existence of an edge between two nodes is their inner-product (with variants to consider directed and weighted graphs). In any case, the latent vectors may be estimated through a spectral decomposition of the adjacency matrix, the so-called Adjacency Spectral Embedding (ASE). Assume we are monitoring a stream of graphs and the objective is to track the latent vectors. Examples include recommender systems or monitoring of a wireless network. It is clear that performing the ASE of each graph separately may result in a prohibitive computation load. Furthermore, the invariance to rotations of the inner product complicates comparing the latent vectors at different time-steps. By considering the minimization problem underlying ASE, we develop an iterative algorithm that updates the latent vectors' estimation as new graphs from the stream arrive. Differently to other proposals, our method does not accumulate errors and thus does not requires periodically re-computing the spectral decomposition. Furthermore, the pragmatic setting where nodes leave or join the graph (e.g. a new product in the recommender system) can be accommodated as well. Our code is available at https://github.com/marfiori/efficient-ASEmore » « less
-
Statistical inference for exponential-family models of random graphs with dependent edges is challenging. We stress the importance of additional structure and show that additional structure facilitates statistical inference. A simple example of a random graph with additional structure is a random graph with neighborhoods and local dependence within neighborhoods. We develop the first concentration and consistency results for maximum likelihood and M-estimators of a wide range of canonical and curved exponentialfamily models of random graphs with local dependence. All results are nonasymptotic and applicable to random graphs with finite populations of nodes, although asymptotic consistency results can be obtained as well. In addition, we show that additional structure can facilitate subgraph-to-graph estimation, and present concentration results for subgraph-to-graph estimators. As an application, we consider popular curved exponential-family models of random graphs, with local dependence induced by transitivity and parameter vectors whose dimensions depend on the number of nodes.more » « less
-
In this paper, we propose a novel representation learning framework, namely HIN2Vec, for heterogeneous information networks (HINs). The core of the proposed framework is a neural network model, also called HIN2Vec, designed to capture the rich semantics embedded in HINs by exploiting different types of relationships among nodes. Given a set of relationships specified in forms of meta-paths in an HIN, HIN2Vec carries out multiple prediction training tasks jointly based on a target set of relationships to learn latent vectors of nodes and meta-paths in the HIN. In addition to model design, several issues unique to HIN2Vec, including regularization of meta-path vectors, node type selection in negative sampling, and cycles in random walks, are examined. To validate our ideas, we learn latent vectors of nodes using four large-scale real HIN datasets, including Blogcatalog, Yelp, DBLP and U.S. Patents, and use them as features for multi-label node classification and link prediction applications on those networks. Empirical results show that HIN2Vec soundly outperforms the state-of-the-art representation learning models for network data, including DeepWalk, LINE, node2vec, PTE, HINE and ESim, by 6.6% to 23.8% ofmicro-f1 in multi-label node classification and 5% to 70.8% of MAP in link prediction.more » « less
-
The Random Dot Product Graph (RDPG) is a popular generative graph model for relational data. RDPGs postulate there exist latent positions for each node, and specifies the edge formation probabilities via the inner product of the corresponding latent vectors. The embedding task of estimating these latent positions from observed graphs is usually posed as a non-convex matrix factorization problem. The workhorse Adjacency Spectral Embedding offers an approximate solution obtained via the eigendecomposition of the adjacency matrix, which enjoys solid statistical guarantees but can be computationally intensive and is formally solving a surrogate problem. In this paper, we bring to bear recent non-convex optimization advances and demonstrate their impact to RDPG inference. We develop first-order gradient descent methods to better solve the original optimization problem, and to accommodate broader network embedding applications in an organic way. The effectiveness of the resulting graph representation learning framework is demonstrated on both synthetic and real data. We show the algorithms are scalable, robust to missing network data, and can track the latent positions over time when the graphs are acquired in a streaming fashion.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.23919/EUSIPCO54536.2021.9616036
