Proposes a deep structured generative model for complex scenes.
problem Difficulty in generating images with complicated structures.
method Boosts GANs with structure information encoded by a stochastic and-or graph (sAOG).
result Successfully captures and generates images with complex structures.
The abstract reviews graph clustering models and their extensions.
problem Graph clustering and model-based approaches.
method Different clustering, inference, and topic models for various graph types.
result Comparison of different approaches to graph clustering.
New method solves nonseparable stochastic control problems.
problem Nonseparable and non-monotonic stochastic control problems.
method Scenario-decomposition solution framework using progressive hedging algorithm.
result Extends reach of stochastic optimal control.
The paper tackles drift identification in Lévy α-stable stochastic systems, proposing a Fourier space approach.
problem Estimating the drift field of a stochastic differential equation driven by Lévy α-stable noise.
method Fourier space approach, parameterizing the drift field using Fourier series, minimizing a loss function with gradients computed via the adjoint method.
result The method is capable of learning drift fields in qualitative and/or quantitative agreement with ground truth fields.
Algorithm determines spatial graph isomorphism with vertex, edge colorings and orientations.
problem Algorithmic recognition of spatial graphs with various colorings and orientations.
method Proved existence of an algorithm for isomorphic spatial graphs, decomposed into canonical blocks, and applied Haken and Matveev's result.
result Algorithmic recognition of spatial graphs with colorings and orientations.
Neural network learns causal graph structure from data.
problem Inferring causal graph structure from observational and interventional data.
method Supervised training of a neural network on synthetic graphs.
result Learned model generalizes to new graphs, robust to distribution shifts, and outperforms existing methods.
BCD Nets use variational inference to estimate DAGs with uncertainty.
problem Uncertainty in inferring causal graphs from limited data.
method Variational inference framework for Bayesian DAG estimation.
result BCD Nets outperform maximum-likelihood methods in low data regimes.
Graph Signal Processing (GSP) is a promising framework to analyze multi-dimensional neuroimaging datasets, while taking into account both the spatial and functional dependencies between brain signals. In the present work, we apply dimensionality reduction techniques based on graph representations of the brain to decode…
Neural networks solve SPDEs using Wiener chaos expansion.
problem Solving stochastic partial differential equations (SPDEs) numerically.
method Using neural networks in the truncated Wiener chaos expansion.
result Approximation rates for learning SPDE solutions with noise.
This paper reviews methods for distributed training of machine learning models from high-rate streams.
problem Training machine learning models from high-rate distributed streams in a compute- and bandwidth-limited setting.
method Recently developed methods for large-scale distributed stochastic optimization.
result There exist regimes where systems can learn from distributed, streaming data at order-optimal rates.
Bayesian graph learning improves graph representation accuracy.
problem Inaccurate graph construction from noisy data.
method Non-parametric Bayesian graph model for posterior inference of graph adjacency matrices.
result Model scales well to large graphs and improves node classification, link prediction, and recommendation tasks.
We describe stochastic Newton and stochastic quasi-Newton approaches to efficiently solve large linear least-squares problems where the very large data sets present a significant computational burden (e.g., the size may exceed computer memory or data are collected in real-time). In our proposed framework, stochasticity…
Proposes HBGNN for better recommendation systems using graph neural networks.
problem Sparse structured data in recommendation systems lacking feature richness.
method Hierarchical BiGraph Neural Network (HBGNN) using bigraph framework.
result Competitive performance compared to current methods.
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.
One of the cornerstones of the field of signal processing on graphs are graph filters, direct analogues of classical filters, but intended for signals defined on graphs. This work brings forth new insights on the distributed graph filtering problem. We design a family of autoregressive moving average (ARMA) recursions,…
This paper explains GNNs using graph signal denoising.
problem Understanding how GNNs work for node representation learning.
method Spectral graph convolutional networks and graph attention networks are analyzed from the perspective of graph signal denoising.
result GNNs implicitly solve graph signal denoising problems.
We solve learning mixtures of graphs from epidemic cascades, establishing conditions and algorithms.
problem Learning the weighted edges of a balanced mixture of two undirected graphs from epidemic cascades.
method Established necessary and sufficient conditions for polynomial-time solvability, provided efficient algorithms with optimal sample complexity.
result First rigorous conditions and algorithms for learning graph mixtures from epidemic cascades.
Paper proves SHB convergence with biased gradients and approximate step sizes.
problem Establishing convergence of SHB with biased gradients and approximate step sizes.
method Generalizes SHB convergence conditions for biased gradients, approximate step sizes, and block updating.
result Proves convergence of SHB with new conditions for biased gradients and approximate step sizes.
Networks are a useful representation for data on connections between units of interests, but the observed connections are often noisy and/or include missing values. One common approach to network analysis is to treat the network as a realization from a random graph model, and estimate the underlying edge probability ma…
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.
Enhances graph neural networks by creating virtual data examples.
problem Lack of examples to identify optimal graph rationales in graph applications.
method Introduces environment replacement to create virtual data examples and proposes a framework for rationale-environment separation and representation learning.
result Demonstrates the effectiveness and efficiency of the augmentation-based graph rationalization framework on molecular and polymer datasets.
Given a time series of graphs G(t) = (V, E(t)), t = 1, 2, ..., where the fixed vertex set V represents "actors" and an edge between vertex u and vertex v at time t (uv \in E(t)) represents the existence of a communications event between actors u and v during the tth time period, we wish to detect anomalies and/or chang…
Improves deep learning optimization with a new stochastic gradient method.
problem Noisy and sparse gradients in deep learning optimization.
method Proposes a family of double adaptive stochastic gradient methods (DASGrad).
result Analyzes theoretical convergence improvements and empirical validation.
Proposes a method to improve GNN predictions by finding the most predictive subgraph.
problem GNNs aggregate all nodes and edges, making predictions hard to interpret.
method Uses reinforcement learning to find a sparse subgraph that optimizes graph classification performance.
result Our method finds sparser subgraphs that improve interpretability while maintaining performance.
We propose a systematic learning-based approach to the generation of massive quantities of synthetic 3D scenes and arbitrary numbers of photorealistic 2D images thereof, with associated ground truth information, for the purposes of training, benchmarking, and diagnosing learning-based computer vision and robotics algor…
SIGMA model improves graph matching across various applications.
problem Graph matching problem in different domains.
method Stochastic Iterative Graph Matching (SIGMA) model with multi-step refinement and dummy nodes.
result SIGMA produces significantly improved graph matching results compared to state-of-the-art models.
Spectral clustering has become a popular technique due to its high performance in many contexts. It comprises three main steps: create a similarity graph between N objects to cluster, compute the first k eigenvectors of its Laplacian matrix to define a feature vector for each object, and run k-means on these features t…
In many physical, statistical, biological and other investigations it is desirable to approximate a system of points by objects of lower dimension and/or complexity. For this purpose, Karl Pearson invented principal component analysis in 1901 and found 'lines and planes of closest fit to system of points'. The famous k…
FastGAE scales graph AE and VAE to large graphs with millions of nodes.
problem Scalability issues in graph AE and VAE.
method Stochastic subgraph decoding scheme to speed up training.
result Outperforms existing approaches on various real-world graphs.
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.
The paper explores the L1-Liouville property on graphs and its connections to stochastic completeness.
problem Investigating the L1-Liouville property on graphs and its implications. method Characterization of L1-Liouville property in terms of Green function, equivalence with stochastic completeness, and comparison theorems based on inner-outer curvatures. result Equivalence of L1-Liouville property and stochastic completeness on model graphs, and introduction of Dirichlet L1-Liouville property. New adaptive methods solve weakly convex stochastic optimization problems.
problem Solving weakly convex stochastic optimization problems.
method Adaptive first and zeroth-order methods using exponential moving averages.
result Established non-asymptotic convergence rates for nonsmooth and nonconvex problems.
Combines SBMs and graph neural nets for graph embeddings.
problem Discovering community structure and link prediction on graphs.
method Sparse variational autoencoder integrating SBMs and graph neural nets.
result Encouraging link prediction results with interpretable latent structure.
Vertex clustering in a stochastic blockmodel graph has wide applicability and has been the subject of extensive research. In thispaper, we provide a short proof that the adjacency spectral embedding can be used to obtain perfect clustering for the stochastic blockmodel and the degree-corrected stochastic blockmodel. We…
Study counterfactuals in cyclic systems with shifts and scales.
problem Counterfactual inference in cyclic systems with shifts and scales.
method Shift-scale interventions in cyclic SCMs.
result Valid inference in cyclic systems with shifts and scales.
Simple stochastic Newton and cubic Newton methods with fast convergence.
problem Minimizing large numbers of smooth and strongly convex functions.
method Stochastic Newton and cubic Newton methods with simple local linear-quadratic rates.
result Local linear-quadratic convergence results with fast adaptation to problem's curvature.
FILDNE learns dynamic graph embeddings efficiently.
problem Learning node embeddings on evolving graphs.
method Integrates static graph learning methods into dynamic graphs using convex combination and alignment.
result FILDNE reduces memory and computational costs while improving downstream task performance.
AB-SAGA optimizes distributed optimization over directed graphs using variance reduction and stochastic weights.
problem Optimizing distributed stochastic optimization over directed graphs with stochastic weights.
method AB-SAGA combines variance reduction and network-level gradient tracking, using both row and column stochastic weights.
result AB-SAGA converges linearly to the global optimal with a constant step-size and achieves a linear speed-up over centralized methods.
We extend Dupire's formula for stochastic interest rates and local volatility.
problem Deriving formulas for stochastic interest rates and local volatility.
method Generalizations of Dupire's formula for stochastic drift and local volatility.
result Validated the limits of the generalized Dupire formulae for specific cases.
Paper proves convergence of bi-stochastically normalized graph Laplacian to manifold Laplacian and robustness to outlier noise.
problem Convergence of bi-stochastically normalized graph Laplacian to manifold Laplacian and robustness to outlier noise.
method Proves convergence of bi-stochastically normalized graph Laplacian to manifold Laplacian with rates, and proposes an approximate and constrained matrix scaling problem to achieve the same consistency rate.
result Graph Laplacian consistency rate matches the rate for clean manifold data plus an additional term proportional to the boundedness of the inner-products of the noise vectors.
Spectral clustering for directed graphs using likelihood estimation.
problem Clustering directed graphs with edge directions.
method Maximum likelihood estimation on stochastic block models.
result Significant performance gains over existing methods.
SMP model preserves proximity and permutation in graph neural networks.
problem Challenges in graph mining, such as community and leader finding.
method Stochastic Message Passing (SMP) model that maintains proximity and permutation-equivariance.
result SMP model effectively preserves node proximities and permutation-equivariance.
The study examines convergence of stochastic processes on large graphs and adjacency matrices.
problem Analyzing convergence of stochastic processes on large graphs and adjacency matrices.
method Introduced new metrics on the space of measure-valued graphons and used them to show convergence of random trajectories to deterministic curves.
result The Metropolis chain converges to a deterministic gradient flow curve on the space of graphons under certain conditions.
BayesGrad explains graph convolutional network predictions.
problem Uncertainty in chemical property predictions due to small sample size and label imbalance.
method Bayesian predictive distribution with dropout technique to define node importance.
result BayesGrad successfully visualizes substructures responsible for predictions in small sample size scenarios.
A new algorithm tackles graph-based contextual bandits with efficient regret bounds.
problem Predicting labels on graphs with contextual bandit methods.
method Graph-based contextual bandit algorithm using optimal stochastic bandit techniques.
result Regret bounds for line graphs and trees, and improved bounds for general graphs.
New algorithm updates eigenvectors of evolving graphs efficiently.
problem Updating eigenvectors of dynamic graphs.
method Subspace projection based on Rayleigh-Ritz projections.
result Strong performance in eigenvector approximation and downstream tasks.
Proposes a graph neural network for efficient multi-agent routing.
problem Routing multiple agents in complex, sparsely connected graphs with dynamic traffic.
method Value Iteration Network based on graph neural networks for online coordination.
result Significantly outperforms traditional methods in terms of cost and runtime.
We describe a graph-based semi-supervised learning framework in the context of deep neural networks that uses a graph-based entropic regularizer to favor smooth solutions over a graph induced by the data. The main contribution of this work is a computationally efficient, stochastic graph-regularization technique that u…