The paper explains practical insights for sparse network modeling.
problem Resolving pathologies in traditional network modeling, focusing on sparsity.
method Sparse exchangeable graphs, network subsampling, test-train dataset splitting, mean field variational inference.
result Practical insights and methods for sparse network modeling.
We propose a novel statistical model for sparse networks with overlapping community structure. The model is based on representing the graph as an exchangeable point process, and naturally generalizes existing probabilistic models with overlapping block-structure to the sparse regime. Our construction builds on vectors …
Many popular network models rely on the assumption of (vertex) exchangeability, in which the distribution of the graph is invariant to relabelings of the vertices. However, the Aldous-Hoover theorem guarantees that these graphs are dense or empty with probability one, whereas many real-world graphs are sparse. We prese…
Statistical network modeling has focused on representing the graph as a discrete structure, namely the adjacency matrix, and considering the exchangeability of this array. In such cases, the Aldous-Hoover representation theorem (Aldous, 1981;Hoover, 1979} applies and informs us that the graph is necessarily either dens…
Dynamic model clusters interactions over time, improving prediction.
problem Sparse, evolving interaction graphs with temporal dynamics.
method Structured, nonparametric edge-exchangeable model for dynamic clustering.
result Improved predictive performance compared to static models.
We study a simple exchange model in which price is fixed and the amount of a good transferred between actors depends only on the actors' respective budgets and the existence of a link between transacting actors. The model induces a simply-connected but possibly multi-component bipartite graph. A trading session on a fi…
New models generate power law exponents from 0.5 to 2.5, enabling inference.
problem Inference difficulty in models generating power laws with exponents > 2.
method Design and implement inference algorithms for a new class of models.
result Inference possible for models generating power laws with exponents from 0.5 to 2.5.
The paper shows exchanging estimates over networks is effective for learning sparse signals.
problem Learning sparse signals over networks with limited communication.
method Iterative algorithm exchanging intermediate estimates over a network, with theoretical and simulation analysis.
result The iterative algorithm provides competitive performance in learning sparse signals.
A known failing of many popular random graph models is that the Aldous-Hoover Theorem guarantees these graphs are dense with probability one; that is, the number of edges grows quadratically with the number of nodes. This behavior is considered unrealistic in observed graphs. We define a notion of edge exchangeability …
Directed graphs occur throughout statistical modeling of networks, and exchangeability is a natural assumption when the ordering of vertices does not matter. There is a deep structural theory for exchangeable undirected graphs, which extends to the directed case via measurable objects known as digraphons. Using digraph…
New algorithm tackles multi-agent bandits with heavy-tailed data.
problem Maximizing system performance in multi-agent settings with heavy-tailed data.
method Algorithm exploits hub-like structures and synchronization among clients.
result Regret bound of O(M1−α1logT) for homogeneous settings, O(MlogT) for heterogeneous. New model captures sparse, evolving multigraph structures.
problem Understanding sparse, evolving multigraph structures in dynamic interaction data.
method Dynamic nonparametric Bayesian model combining sparsity and clustering.
result Improved held-out likelihood and predictive performance.
Study uses graph techniques to understand meromorphic quadratic differential strata.
problem Understanding the topology of meromorphic quadratic differential strata.
method Exchange graph techniques to study fundamental groups; generalizes relations for mixed-angulations.
result Explicit presentations of fundamental groups in genus-zero case with four singularities.
It is assumed that under suitable economic and information-theoretic conditions, market exchange rates are free from arbitrage. Commodity markets in which trades occur over a complete graph are shown to be trivial. We therefore examine the vector space of no-arbitrage exchange rate ensembles over an arbitrary connected…
Enhances understanding of stability conditions on surfaces.
problem Understanding stability conditions on surfaces.
method Introduces cluster exchange groupoid and uses triangulation covering graphs.
result Space of stability conditions is simply connected.
Graph learning improves FXRP and FXSA with significant statistical arbitrage gains.
problem Improving FXRP and FXSA with complex multi-currency and interest rate relationships.
method Two-step graph learning approach: first, edge-level regression on spatiotemporal graph; second, stochastic optimization with constraints and risk-adjusted return maximization.
result Graph-learning method achieves higher information and Sortino ratios than benchmarks.
We say that a graph is intrinsically knotted or completely 3-linked if every embedding of the graph into the 3-sphere contains a nontrivial knot or a 3-component link any of whose 2-component sublink is nonsplittable. We show that a graph obtained from the complete graph on seven vertices by a finite sequence of $\tria…
The paper extends and applies a new shrinkage prior in Bayesian factor analysis.
problem Estimating the number of factors in sparse Bayesian factor analysis.
method Introduces and extends a generalized cumulative shrinkage process (CUSP) prior.
result Exchangeable spike-and-slab shrinkage priors imply increasing shrinkage as the column index increases.
A new model predicts sparse temporal network links better than existing models.
problem Capturing sparse connections in real temporal networks.
method Dynamic edge exchangeable model that accounts for social influence and sparsity.
result The model achieves superior link prediction accuracy and interpretable community structures.
We construct an infinitely exchangeable process on the set $\cate$ of subsets of the power set of the natural numbers N via a Poisson point process with mean measure Λ on the power set of N. Each $E\in\cate$ has a least monotone cover in $\catf$, the collection of monotone subsets of $\cate$, an…
Graph-Sparse Logistic Regression for sparse and connected support classification.
problem Sparse and connected support classification problems.
method Introduces Graph-Sparse Logistic Regression algorithm.
result Validated and benchmarked against L1-regularized Logistic Regression.
Proposes methods for selecting sparse variables in linear regression.
problem Selecting sparse variables in linear regression models.
method K-sparse exhaustive search (ES-K) and K-sparse approximate exhaustive search (AES-K) methods.
result AES-K method effectively reconstructs density of states for large problems.
The paper explores graphons of line graphs from sparse finite graphs.
problem Estimating graph limits from sparse finite graphs.
method Mapping finite graphs to their line graphs and analyzing graphs with the square-degree property.
result Graphons of line graphs can distinguish between sparse graphs like star graphs and superlinear preferential attachment graphs.
Connectedness constraint for sparse graph learning.
problem Learning sparse graphs often results in disconnected components.
method Formulated connectedness as a convex constraint.
result Connected sparse graphs can be learned from data.
New model generates clusters with sublinear growth, useful for sparse multigraphs.
problem Cluster sizes grow linearly with sample size, limiting applicability in some cases.
method Non-exchangeable random partition models based on completely random measures and Poisson embedding.
result Model generates partitions with sublinearly growing cluster sizes, controlled by parameters.
Enhances graph neural networks with Relational Pooling for better graph classification.
problem Improving graph neural networks for better graph classification.
method Relational Pooling (RP) based on finite partial exchangeability theory.
result Improved performance on graph classification tasks.
A new method for generating sets and graphs without requiring exchangeability.
problem Generating exchangeable distributions for sets and graphs is challenging.
method Top-n creation, a differentiable generation mechanism that selects relevant points from a latent vector.
result Top-n method outperforms i.i.d. generation in various tasks.
Researchers analyze tagging patterns on Stack Exchange communities.
problem Understanding the structure and evolution of tags in Q&A platforms.
method Empirical analysis and development of a generative model for tag co-occurrence.
result The model can reproduce statistical properties of co-tagging graphs.
New method speeds up sparse graph neural networks training on dense hardware.
problem Training sparse graph neural networks is slow on custom hardware.
method Inspired by sparse matrix optimization, developed techniques for dense hardware.
result Sparse graph neural networks trained in 13 minutes on 512-core TPUv2 Pod.
Conway-Gordon proved that for every spatial complete graph on 6 vertices, the sum of the linking numbers over all of the constituent 2-component links is congruent to 1 modulo 2, and for every spatial complete graph on 7 vertices, the sum of the Arf invariants over all of the Hamiltonian knots is also congruent to 1 mo…
New neural model processes 2D data with long-range dependencies efficiently.
problem Limited receptive field of convolutions for complex 2D tasks.
method Proposes Matrix Shuffle-Exchange network with O(logn) layers and O(n2logn) complexity. result Exceeds convolutional and graph neural network baselines in long-range dependency modeling.
The paper infers graph structure from sparse signal observations.
problem Inferring graph structure from sparse signal observations.
method Formulates a non-convex graph learning problem and solves it via alternating signal sparse coding and graph update steps.
result The method generally outperforms other network inference algorithms in graph recovery.
LG algorithm finds profitable trading paths in decentralized exchanges.
problem Identifying optimal trading paths in decentralized exchanges.
method Line-graph-based algorithm (LG) for efficient route discovery.
result LG consistently identifies more profitable paths than DFS with comparable costs.
Decentralized learning of personalized models and collaboration graphs without central coordination.
problem Training personalized models and collaboration graphs in a decentralized manner without a central coordinator.
method Alternates between training models given the graph and updating the graph given the models, using peer-to-peer exchanges.
result Communication-efficient approach that avoids exchanging personal data, with benefits demonstrated on synthetic and real datasets.
Graphs from van der Corput sequence embed into Chamanara surface.
problem Embedding graphs from van der Corput sequence into surfaces.
method Constructed 4-regular graphs from van der Corput sequence and Kronecker sequence, embedded into torus and Chamanara surface. result Graphs from van der Corput sequence embed into Chamanara surface with one edge removal.
This paper introduces cluster exchange groupoids for Coxeter-Dynkin diagrams and finds their fundamental groups are braid groups.
problem Understanding the fundamental groups of cluster exchange groupoids for Coxeter-Dynkin diagrams.
method Introduced cluster exchange groupoids for Coxeter-Dynkin diagrams and showed the fundamental group isomorphic to braid groups.
result The fundamental group of the exchange groupoid for a Coxeter-Dynkin diagram is the braid group associated with the diagram.
Improved GCNs for non-sparse graphs with low-rank filters.
problem Training and evaluation of GCNs on large non-sparse graphs is computationally expensive.
method Introduced low-rank filters and a reduced-order GCN architecture.
result Significant runtime acceleration and improved accuracy achieved.
Paper uses GNNs to efficiently detect profitable triangular arbitrage opportunities.
problem Detecting profitable triangular arbitrage opportunities in dynamic markets.
method Formulate the problem as a graph-based optimization task and use a GNN architecture to capture complex relationships.
result GNN-based method achieves higher average yield with reduced computational time compared to traditional methods.
This paper proposes a method to reveal task relationships in multi-task learning models using sparse graphs.
problem Understanding the underlying task relationships in multi-task learning models.
method Proposes a bilevel formulation of multi-task learning that induces sparse graphs.
result The method improves interpretability of multi-task learning models without sacrificing generalization performance.
Generative model captures hubs and dense communities in social networks.
problem Capturing both hubs and dense communities in social networks.
method Graphon mixture model with a new condition on sparse graphs.
result Estimation of hub normalized degree and graphon for sparse components.
The paper gives bounds for how long it takes for gossip protocols to spread information in networks.
problem Understanding the diffusion time in asynchronous gossip protocols.
method Provides non-asymptotic bounds for the number of messages needed for consensus in asynchronous gossip protocols.
result Explicit formula and approximation for the number of messages needed for consensus in different types of graphs.
This paper detects market manipulation in Mt. Gox's Bitcoin exchange transactions.
problem Detecting market manipulation in cryptocurrency exchanges.
method Mining Mt. Gox's transaction history, categorizing accounts, constructing graphs, and using SVD for analysis.
result Identifies serious market manipulation in Mt. Gox exchange and recommends stronger market supervision.
A new method embeds sparse stochastic graphs into low dimensions.
problem Embedding large, sparse, stochastic graphs into low-dimensional spaces.
method Spaceland Embedding (SG-t-SNE) inspired by t-SNE, leveraging modern computing techniques.
result Effective embedding results on synthetic and real-world graphs.
Derives formulae for general permutation equivariant layers and presents a second order graph variational encoder.
problem Tackles the limitation of previous equivariant neural networks by considering permutations of matrices.
method Derives formulae for general permutation equivariant layers, including matrix permutations. Presents a second order graph variational encoder.
result Latent distribution of equivariant generative models must be exchangeable.
Method learns sparse graph for multivariate data prediction efficiently.
problem Prediction of multivariate data processes using sparse graph models.
method Recursive learning of sparse partial correlation graph without cross-validation or tuning.
result Significant performance gains in prediction compared to existing graphs.
Method converts sparse systems to dense ones for statistical mechanics problems.
problem Statistical mechanics on sparse graphs
method Extracts a Feedback Vertex Set, learns variational distribution, estimates free energy.
result More accurate and faster than existing methods for sparse systems.
Graph-Dictionary model for sparse multivariate signal representation.
problem Capturing complex relational information in multivariate signals.
method Graph dictionaries and bilinear primal-dual splitting algorithm.
result Graph-dictionary model outperforms baselines in signal reconstruction and classification.
Paper detects anomalous edges in social networks using edge exchangeability.
problem Detecting anomalous edges in directed social networks.
method Exploits edge exchangeability and uses conformal prediction theory.
result Proposed anomaly detector has a guaranteed upper bound for false positives.