A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
A novel Gromov-Wasserstein learning framework is proposed to jointly match (align) graphs and learn embedding vectors for the associated graph nodes. Using Gromov-Wasserstein discrepancy, we measure the dissimilarity between two graphs and find their correspondence, according to the learned optimal transport. The node …
The pair-matching problem appears in many applications where one wants to discover good matches between pairs of entities or individuals. Formally, the set of individuals is represented by the nodes of a graph where the edges, unobserved at first, represent the good matches. The algorithm queries pairs of nodes and obs…
We propose a scalable Gromov-Wasserstein learning (S-GWL) method and establish a novel and theoretically-supported paradigm for large-scale graph analysis. The proposed method is based on the fact that Gromov-Wasserstein discrepancy is a pseudometric on graphs. Given two graphs, the optimal transport associated with th…
We introduce a technique to compute probably approximately correct (PAC) bounds on precision and recall for matching algorithms. The bounds require some verified matches, but those matches may be used to develop the algorithms. The bounds can be applied to network reconciliation or entity resolution algorithms, which i…
Graph matching involves combinatorial optimization based on edge-to-edge affinity matrix, which can be generally formulated as Lawler's Quadratic Assignment Problem (QAP). This paper presents a QAP network directly learning with the affinity matrix (equivalently the association graph) whereby the matching problem is tr…
This work presents a two-stage neural architecture for learning and refining structural correspondences between graphs. First, we use localized node embeddings computed by a graph neural network to obtain an initial ranking of soft correspondences between nodes. Secondly, we employ synchronous message passing networks …
A test for comparing networks using stochastic block models.
problem Determining if two network datasets come from the same model.
method Adopting stochastic block models, the study introduces an efficient algorithm to match estimated network parameters and develops a powerful test.
result The test is consistent and asymptotically follows a chi-squared distribution.
Community detection or clustering is a fundamental task in the analysis of network data. Many real networks have a bipartite structure which makes community detection challenging. In this paper, we consider a model which allows for matched communities in the bipartite setting, in addition to node covariates with inform…
We study, to the best of our knowledge, the first Bayesian algorithm for unimodal Multi-Armed Bandit (MAB) problems with graph structure. In this setting, each arm corresponds to a node of a graph and each edge provides a relationship, unknown to the learner, between two nodes in terms of expected reward. Furthermore, …
We propose a consistent polynomial-time method for the unseeded node matching problem for networks with smooth underlying structures. Despite widely conjectured by the research community that the structured graph matching problem to be significantly easier than its worst case counterpart, well-known to be NP-hard, the …
Network complexity has been studied for over half a century and has found a wide range of applications. Many methods have been developed to characterize and estimate the complexity of networks. However, there has been little research with statistical guarantees. In this paper, we develop a statistical theory of graph c…
We give the first efficient algorithm for learning the structure of an Ising model that tolerates independent failures; that is, each entry of the observed sample is missing with some unknown probability p. Our algorithm matches the essentially optimal runtime and sample complexity bounds of recent work for learning Is…
Active search (AS) on graphs focuses on collecting certain labeled nodes (targets) given global knowledge of the network topology and its edge weights under a query budget. However, in most networks, nodes, topology and edge weights are all initially unknown. We introduce selective harvesting, a variant of AS where the…
Graph convolutional network (GCN) provides a powerful means for graph-based semi-supervised tasks. However, as a localized first-order approximation of spectral graph convolution, the classic GCN can not take full advantage of unlabeled data, especially when the unlabeled node is far from labeled ones. To capitalize on…
In this paper, we focus on solving a class of constrained non-convex non-concave saddle point problems in a decentralized manner by a group of nodes in a network. Specifically, we assume that each node has access to a summand of a global objective function and nodes are allowed to exchange information only with their n…
We propose a novel distributed inference algorithm for continuous graphical models, by extending Stein variational gradient descent (SVGD) to leverage the Markov dependency structure of the distribution of interest. Our approach combines SVGD with a set of structured local kernel functions defined on the Markov blanket…
The problem of structure estimation in graphical models with latent variables is considered. We characterize conditions for tractable graph estimation and develop efficient methods with provable guarantees. We consider models where the underlying Markov graph is locally tree-like, and the model is in the regime of corr…