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.
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.
Graphs are naturally sparse objects that are used to study many problems involving networks, for example, distributed learning and graph signal processing. In some cases, the graph is not given, but must be learned from the problem and available data. Often it is desirable to learn sparse graphs. However, making a grap…
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.
Graph neural networks have become increasingly popular in recent years due to their ability to naturally encode relational input data and their ability to scale to large graphs by operating on a sparse representation of graph adjacency matrices. As we look to scale up these models using custom hardware, a natural assum…
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.
We introduce Graph-Sparse Logistic Regression, a new algorithm for classification for the case in which the support should be sparse but connected on a graph. We val- idate this algorithm against synthetic data and benchmark it against L1-regularized Logistic Regression. We then explore our technique in the bioinformat…
NGRs merge sparse graph recovery with PGMs for efficient probabilistic inference.
problem Efficiently recover sparse graphs and learn distributions over variables.
method Integrates sparse graph recovery methods with PGMs using Graph-constrained path norm.
result NGRs can handle multimodal data and perform sparse graph recovery and probabilistic inference.
Random projections help in representing sparse graphs efficiently.
problem Efficiently representing sparse graphs of varying sizes and vertex sets.
method Random projection of adjacency matrices to retain graph functionality and properties.
result Random projections can accurately represent graphs of different sizes and vertex sets in the same space.
SpaPool combines dense and sparse techniques for efficient graph pooling.
problem Efficiently processing large graphs in graph neural networks.
method Adaptive clustering of graph vertices into clusters.
result SpaPool outperforms existing methods on small-scale graphs.
New method estimates graph compatibility from sparse labels.
problem Estimating graph compatibility from sparse labeled data.
method Factorized graph representations and algebraic amplification.
result End-to-end classification accuracy comparable to gold standard.
New model allows sparse graphs with many triangles to be represented.
problem Sparse graphs with many triangles cannot be accurately represented in finite dimensions.
method Infinite-dimensional inner product model with manifold representations.
result Local neighborhoods can be represented in lower dimensions.
New matrix reveals cluster info in sparse directed graphs.
problem Analyzing cluster information in directed graphs.
method Proposed complex non-backtracking matrix integrating Hermitian adjacency matrix and non-backtracking matrix properties.
result The complex non-backtracking matrix holds cluster information, especially for sparse directed graphs.
We propose a method for solving statistical mechanics problems defined on sparse graphs. It extracts a small Feedback Vertex Set (FVS) from the sparse graph, converting the sparse system to a much smaller system with many-body and dense interactions with an effective energy on every configuration of the FVS, then learn…
Graph Convolutional Networks (GCNs) have proven to be successful tools for semi-supervised learning on graph-based datasets. For sparse graphs, linear and polynomial filter functions have yielded impressive results. For large non-sparse graphs, however, network training and evaluation becomes prohibitively expensive. B…
This work introduces a method to compare sparse neural network topologies using graph theory.
problem Comparing and understanding sparse neural network topologies, especially during training.
method Introducing Neural Network Sparse Topology Distance (NNSTD) to measure distances between different sparse neural networks.
result Sparse neural networks can outperform over-parameterized models without further structure optimization.
The paper tackles sparse graph learning under Laplacian-related constraints, improving upon existing methods.
problem Learning a sparse undirected graph from multivariate data under Laplacian-related constraints.
method Modifications to penalized log-likelihood approaches to enforce total positivity and lasso/adaptive lasso penalties using ADMM.
result The proposed constrained adaptive lasso approach significantly outperforms existing Laplacian-based approaches.
Learning the "blocking" structure is a central challenge for high dimensional data (e.g., gene expression data). Recently, a sparse singular value decomposition (SVD) has been used as a biclustering tool to achieve this goal. However, this model ignores the structural information between variables (e.g., gene interacti…
Graph signals offer a very generic and natural representation for data that lives on networks or irregular structures. The actual data structure is however often unknown a priori but can sometimes be estimated from the knowledge of the application domain. If this is not possible, the data structure has to be inferred f…
Linear time algorithm for random walk kernels on sparse graphs.
problem Efficient computation of general random walk kernels for large graphs.
method Sample dependent random walks to compute graph embeddings without direct graph product.
result Up to 27x faster and scalable to 128x larger graphs than previous methods.
Sparse RSP routing improves graph exploration and classification.
problem Optimal randomized routing and distance measures on weighted graphs.
method Tsallis divergence regularization for sparse RSP.
result Sparse random walk converges to least-cost graph as temperature decreases.
HopGAT improves node classification in sparsely labeled graphs by learning from distant neighbors.
problem Classifying nodes in sparsely labeled graphs with limited labeled data.
method Hop-aware supervision mechanism and simulated annealing learning strategy.
result The model achieves high accuracy even with 40% labeled data, reducing performance loss to 3.9%.
New theory for partial disentanglement from sparse graphs.
problem Disentangling latent factors from sparse causal graphs.
method Generalization of disentanglement theory to any graph, using consistency equivalence.
result Partial disentanglement captures expected factor entanglement based on graph structure.
Detecting correlated trees helps align sparse graphs.
problem Detecting correlation between trees for sparse random graphs.
method MPAlign message-passing algorithm for graph alignment.
result MPAlign succeeds in polynomial time for partial alignment.
We compute an approximate Fréchet mean for sets of sparse graphs.
problem Characterizing the location of a set of graphs in a metric space.
method We use the pseudometric defined by the ℓ₂ norm of eigenvalues of adjacency matrices.
result We describe an algorithm to approximate the Fréchet mean of a set of graphs.
Proposes RBGP framework for efficient block sparse neural networks.
problem Efficiently exploit structured sparsity patterns for sparse neural networks on GPU.
method Uses Ramanujan Bipartite Graph Product to generate structured multi-level block sparse neural networks.
result Achieves 5-9x and 2-5x runtime gains over unstructured and block sparsity patterns respectively, while maintaining accuracy.
Graph neural networks improve AMG convergence for sparse systems.
problem Efficiently constructing algebraic multigrid prolongation operators for sparse linear systems.
method Train a graph neural network to learn prolongation operators from matrix classes, using an unsupervised loss function.
result Improved convergence rates compared to classical AMG methods.
New method handles structural uncertainty in graphs better than existing models.
problem Handling heterophily and structural noise in semi-supervised learning on graphs.
method Sparse signed message passing network that models a posterior distribution over signed adjacency matrices.
result Our method outperforms strong baseline models on heterophilic benchmarks under both synthetic and real-world structural noise.
We introduce a nonlinear method for directly embedding large, sparse, stochastic graphs into low-dimensional spaces, without requiring vertex features to reside in, or be transformed into, a metric space. Graph data and models are prevalent in real-world applications. Direct graph embedding is fundamental to many graph…
Network Lasso clusters sparse graph clusters efficiently.
problem Local graph clustering of sparse and chain-like clusters.
method Network Lasso minimizes total variation of cluster indicator signals.
result Network Lasso handles sparse clusters difficult for spectral clustering.
Originally designed to model text, topic modeling has become a powerful tool for uncovering latent structure in domains including medicine, finance, and vision. The goals for the model vary depending on the application: in some cases, the discovered topics may be used for prediction or some other downstream task. In ot…
MFCNs use sparse graphs to approximate manifold convergence.
problem Understanding manifold neural networks (MNNs).
method Sparse graph approximation for manifold convergence.
result Method converges to continuum limit as data points increase.
Graph Neural Networks (GNNs) have proved to be an effective representation learning framework for graph-structured data, and have achieved state-of-the-art performance on many practical predictive tasks, such as node classification, link prediction and graph classification. Among the variants of GNNs, Graph Attention N…
Chromatic Learning reduces feature dimensions for sparse datasets.
problem Sparse, high-dimensional data challenges traditional learning methods.
method Graph coloring over co-occurrence graph to create dense feature representation.
result Compresses sparse datasets significantly while maintaining model accuracy.
Proposes a method for coarse graph alignment using sparse partial least squares.
problem Aligning graphs with community structures when there's no natural one-to-one mapping.
method Sparse partial least squares method incorporating observed graph structures and imposing sparsity.
result Demonstrates effectiveness in simulations.
This supplementary material includes three parts: some preliminary results, four examples, an experiment, three new algorithms, and all proofs of the results in the paper "Reversible MCMC on Markov equivalence classes of sparse directed acyclic graphs".
A new method reduces memory requirements for Graph Transformers by sparsely training a network.
problem Quadratic memory complexity in Graph Transformers limits their scalability to large graphs.
method Spexphormer: trains a narrow network on augmented graph, then uses only active connections in a wider network.
result Spexphormer achieves good performance with drastically reduced memory requirements.
New algorithms detect communities in sparse graphs with labeled data.
problem Detecting communities in sparse graphs with limited labeled data.
method Introduces two algorithms: combinatorial and optimization-based, to integrate labeled data with graph structures.
result Detection of communities is feasible throughout the parameter domain with arbitrary labeled data.
New method discovers causal relationships in sparse linear data.
problem Discovering cause-effect relationships in sparse linear data.
method Uses structural matrix to reconstruct data and identify causal structures without independence tests.
result Outperforms existing methods in sparse causal structure recovery.
We present a supervised-learning algorithm from graph data (a set of graphs) for arbitrary twice-differentiable loss functions and sparse linear models over all possible subgraph features. To date, it has been shown that under all possible subgraph features, several types of sparse learning, such as Adaboost, LPBoost, …
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 …
Sparse graph learning for dependent time series using ADMM.
problem Inferring conditional independence graph of sparse, high-dimensional stationary multivariate Gaussian time series.
method Sparse-group lasso-based frequency-domain formulation and alternating direction method of multipliers (ADMM) optimization.
result Convergence of inverse PSD estimators to true value under certain conditions.
Sparse hypergraph neural networks improve reasoning in large knowledge graphs.
problem Reasoning about relationships in large, real-world domains using sparse and local inferences.
method Sparse and local hypergraph neural networks (SpaLoc) exploiting relational inferences that are usually local and sparse.
result State-of-the-art performance on real-world knowledge graph reasoning benchmarks.
In sparse signal representation, the choice of a dictionary often involves a tradeoff between two desirable properties -- the ability to adapt to specific signal data and a fast implementation of the dictionary. To sparsely represent signals residing on weighted graphs, an additional design challenge is to incorporate …
Efficiently discovers causal DAG permutations without additional assumptions.
problem Learning a DAG up to Markov equivalence.
method Utilizing DAG-specific problem structure, introduces an efficient algorithm for sparse permutations.
result Significant improvement in permutation discovery compared to existing algorithms.
BiGG model efficiently generates sparse graphs with reduced complexity.
problem Challenges in scalable deep learning for sparse graphs.
method BiGG model, an autoregressive model that leverages graph sparsity.
result Graph generation time complexity reduced from O(n2) to O((n+m)logn). uGLAD recovers sparse graphs from data using deep unrolled networks.
problem Sparse graph recovery from complex data.
method Optimizing deep unrolled networks to learn precision matrices.
result uGLAD outperforms existing algorithms in sparsity optimization and robustly handles missing data.
Recovering sparse conditional independence graphs from data is a fundamental problem in machine learning with wide applications. A popular formulation of the problem is an ℓ1 regularized maximum likelihood estimation. Many convex optimization algorithms have been designed to solve this formulation to recover the …