e-GGPs learn graph vertex transitions over time.
problem Static graph Gaussian Processes cannot handle dynamic graph structures.
method Proposes e-GGPs with a transition function and neighbourhood kernel.
result e-GGPs outperform static GGPs on time-series regression.
Graph Gaussian processes use Matérn models for better function learning.
problem Lack of Gaussian process models for graph input spaces.
method Stochastic partial differential equation characterization of Matérn Gaussian processes.
result Graph Matérn Gaussian processes inherit properties of Euclidean and Riemannian models and can be trained efficiently.
Link prediction aims to reveal missing edges in a graph. We address this task with a Gaussian process that is transformed using simplified graph convolutions to better leverage the inductive bias of the domain. To scale the Gaussian process model to large graphs, we introduce a variational inducing point method that pl…
Gaussian processes classify graphs using vertex and edge features.
problem Graph classification in machine learning.
method Transform graph features into spectral Euclidean features, apply Hodge decomposition.
result Gaussian processes can classify graphs using vertex and edge features.
Proposes a new model for traffic flow on directed graphs.
problem Modeling advection on directed graphs for traffic flow.
method Reformulates graph advection operator as finite difference scheme; proposes DGAMGP model.
result Effective modeling of traffic flow and uncertainty as an advective process.
Proposes a Gaussian process for graph signals using adaptive spectral kernels.
problem Predicting signals on graph nodes with various structures.
method Spectral kernel learning approach that incorporates a polynomial function in the graph spectral domain.
result The model accurately recovers ground truth spectral filters and outperforms in real-world graph data.
Optimizes functions on manifolds using Gaussian processes and graph models.
problem Optimizing functions on unknown manifolds with limited data.
method Graph Gaussian process surrogate model for sequential optimization.
result Established regret bounds for the proposed algorithm.
We propose a novel Bayesian nonparametric method to learn translation-invariant relationships on non-Euclidean domains. The resulting graph convolutional Gaussian processes can be applied to problems in machine learning for which the input observations are functions with domains on general graphs. The structure of thes…
Graph classification improved using spectral features and wavelet filters.
problem Categorizing graphs based on their structure and node attributes.
method Derived spectral features from graph signal processing, designed two Gaussian process models: one simple and one sophisticated.
result Simple and sophisticated Gaussian process models yield competitive performance, including well-calibrated uncertainty estimates.
The paper extends Gaussian processes to model complex interactions in cellular complexes.
problem Capturing topological inductive biases in machine learning models.
method Proposes Gaussian processes on cellular complexes, introducing novel kernels.
result Derives two novel kernels for modeling interactions between cells.
We propose Gaussian processes for signals over graphs (GPG) using the apriori knowledge that the target vectors lie over a graph. We incorporate this information using a graph- Laplacian based regularization which enforces the target vectors to have a specific profile in terms of graph Fourier transform coeffcients, fo…
Proposes Gaussian process priors on graph sets with geometric structure.
problem Defining Gaussian process priors on sets of graphs with geometric structure.
method Defines priors respecting graph geometric structure, analogous to Euclidean isotropic processes.
result Efficient computational technique for evaluating priors' kernels, making them usable in toolboxes.
A method for predicting signals on graphs using Gaussian processes and optimal transport.
problem Predicting signals on complex, graph-based inputs with uncertainty quantification.
method Combining regularized optimal transport, dimension reduction, and Gaussian processes indexed by graphs.
result Efficient prediction of signals on graphs with confidence intervals.
Bayesian optimization on networks using Gaussian process models.
problem Optimizing expensive black-box functions on network structures.
method Developed Bayesian optimization algorithms with Gaussian process surrogates tailored to network geometry.
result Established regret bounds for smooth objective functions and analyzed practical cases.
New kernel speeds up graph regression in physics.
problem Handling large, sparse graphs with continuous node attributes in physics.
method Introduced Sliced Wasserstein Weisfeiler-Lehman (SWWL) graph kernel for Gaussian process regression.
result The SWWL kernel is efficient and positive definite, reducing complexity.
We propose a data-efficient Gaussian process-based Bayesian approach to the semi-supervised learning problem on graphs. The proposed model shows extremely competitive performance when compared to the state-of-the-art graph neural networks on semi-supervised learning benchmark experiments, and outperforms the neural net…
Gaussian processes adapted for non-Euclidean spaces enhance decision-making.
problem Applying Gaussian processes in non-Euclidean spaces.
method Developed pathwise conditioning and Gaussian process models over non-Euclidean spaces.
result Efficient Gaussian process models for non-Euclidean spaces.
Textual network embedding aims to learn low-dimensional representations of text-annotated nodes in a graph. Prior work in this area has typically focused on fixed graph structures; however, real-world networks are often dynamic. We address this challenge with a novel end-to-end node-embedding model, called Dynamic Embe…
New graph kernels capture spatio-temporal interactions.
problem Lack of justified spatio-temporal graph kernels for graph problems.
method Derive graph kernels via SPDEs for spatio-temporal modelling.
result Non-separable spatio-temporal graph kernels outperform existing ones.
Stochastic gradient descent improves Gaussian process regression.
problem Efficiently solving large linear systems in Gaussian process regression.
method Developed a stochastic dual descent algorithm using insights from optimisation and kernel communities.
result Stochastic gradient descent is highly effective when done right.
The paper proposes a semi-parametric Bayesian network model using Gaussian Processes and Horseshoe priors.
problem Learning semi-parametric relationships in Expert Bayesian Networks with minimal nonlinear components.
method Uses Gaussian Processes and Horseshoe priors to model relationships, prioritizes modifying expert graphs, and generates diverse graphs.
result Models outperform state-of-the-art semi-parametric Bayesian Network models in synthetic and real-world datasets.
Graph-based kernels improve GP performance on graph data.
problem Improving Gaussian process performance on graph-structured data.
method Introduced graph neural network-inspired kernels into Gaussian processes.
result Graph convolutional networks are equivalent to certain GP kernels when infinitely wide.
A scalable GP model for online uncertainty quantification over graphs.
problem Scalable uncertainty quantification over graphs with dynamic data.
method Graph-aware parametric Gaussian process model using random features and online conformal prediction.
result Improved coverage and efficient prediction sets over existing methods.
Deep Gaussian Processes model functions on DAGs with partially observed data.
problem Reconstructing and inferring from partially observed functions on DAGs with noisy measurements.
method Place priors over functions on DAGs, theoretically study prior-collapse behavior, and offer a structured variational approximation.
result Almost-sure lower bounds on the preservation of input distinctions and interpretability of simulator hierarchies.
Convolutional neural networks (CNNs) can be applied to graph similarity matching, in which case they are called graph CNNs. Graph CNNs are attracting increasing attention due to their effectiveness and efficiency. However, the existing convolution approaches focus only on regular data forms and require the transfer of …
fCBO optimizes interventions in causal graphs using Gaussian processes.
problem Optimizing interventions in known causal graphs.
method Functional causal Bayesian optimization (fCBO) using Gaussian processes and expected improvement acquisition.
result Functional interventions can lead to better target effects and optimal conditional effects.
cCBO optimizes interventions in causal graphs under constraints.
problem Finding optimal interventions in causal graphs with constraints.
method Exploits graph structure, uses Gaussian processes, and sequentially selects interventions.
result Successful trade-off between fast convergence and feasibility of interventions.
Statistical physics approaches can be used to derive accurate predictions for the performance of inference methods learning from potentially noisy data, as quantified by the learning curve defined as the average error versus number of training examples. We analyse a challenging problem in the area of non-parametric inf…
New method predicts dynamic relationships in terrorist networks.
problem Dynamic co-evolution of multiplex graphs and nodal attributes in terrorism networks.
method Time-varying stochastic latent factor models with neural network Gaussian processes.
result Superior performance in predicting unobserved dynamic relationships.
New GL-GP models learn covariance respecting domain geometry.
problem Suboptimal results from nonparametric regression on restricted domains.
method Graph Laplacian based Gaussian Processes (GL-GPs) with Nyström extension.
result Performance gains in various applications.
Paper learns Cartesian product graphs with Laplacian constraints.
problem Learning Cartesian product graphs from Laplacian constraints.
method Penalized maximum likelihood estimation (MLE) and efficient algorithm.
result Statistical consistency for Cartesian product Laplacian estimation.
Method learns Dirichlet-to-Neumann maps on graphs using Gaussian processes.
problem Coupling multiphysics simulations on graphs with conservation constraints.
method Gaussian processes combined with discrete exterior calculus and maximum likelihood estimation.
result Data-driven predictions with uncertainty quantification on entire graph.
Graph transformers outperform graph convolutions by preserving community information.
problem Understanding why graph transformers perform well in node-level prediction tasks.
method Analyzing the Gaussian process limits of graph transformers with infinite width and infinite heads.
result Graph transformers maintain discriminative node representations even in deep layers, preventing oversmoothing.
Graph convolutional neural networks~(GCNs) have recently demonstrated promising results on graph-based semi-supervised classification, but little work has been done to explore their theoretical properties. Recently, several deep neural networks, e.g., fully connected and convolutional neural networks, with infinite hid…
The construction of a meaningful graph plays a crucial role in the success of many graph-based representations and algorithms for handling structured data, especially in the emerging field of graph signal processing. However, a meaningful graph is not always readily available from the data, nor easy to define depending…
Surveying joint Gaussian graphical models to identify shared structures across domains.
problem Estimating shared structures across different data sources.
method Statistical inference of joint Gaussian graphical models.
result Improved estimation power for high-dimensional data.
We study learning problems in which the conditional distribution of the output given the input varies as a function of additional task variables. In varying-coefficient models with Gaussian process priors, a Gaussian process generates the functional relationship between the task variables and the parameters of this con…
Paper proposes a method to improve graph clustering by integrating node textual metadata with node signals in GGMs.
problem Graph learning in Gaussian Graphical Models with auxiliary node metadata.
method Laplacian-constrained Gaussian Graphical Models with majorization-minimization algorithm.
result The proposed method outperforms state-of-the-art approaches that use either signals or metadata alone.
We consider learning on graphs, guided by kernels that encode similarity between vertices. Our focus is on random walk kernels, the analogues of squared exponential kernels in Euclidean spaces. We show that on large, locally treelike, graphs these have some counter-intuitive properties, specifically in the limit of lar…
Scalable machine learning with path signatures for time series and graphs.
problem Challenges in real-world time series and graph data.
method Combines rough path theory with probabilistic, deep, and kernel methods.
result Scalable models for time series and graph data.
A novel GPUM constructs Gaussian Processes for unknown manifolds with probabilistic metrics.
problem High-dimensional data on unknown manifolds with non-Euclidean geometry.
method Bayesian Gaussian Processes latent variable models (BGPLVM), Riemannian geometry, probabilistic metric tensor, Brownian Motion.
result GPUM provides more accurate predictions on unknown manifolds compared to traditional methods.
Reciprocal processes are acausal generalizations of Markov processes introduced by Bernstein in 1932. In the literature, a significant amount of attention has been focused on developing dynamical models for reciprocal processes. Recently, probabilistic graphical models for reciprocal processes have been provided. This …
Framework for completing computational graphs using Gaussian Processes.
problem Completing computational graphs from incomplete data.
method Using Gaussian Processes to approximate unknown functions and recover unobserved variables.
result Efficiently completes computational graphs with fewer data points.
SGPA calibrates transformer uncertainty for safety-critical tasks.
problem Uncertainty estimation in transformer models for safety-critical domains.
method Bayesian inference in transformer's output space using sparse Gaussian processes.
result SGPA-based Transformers improve in-distribution calibration and out-of-distribution robustness.
Gaussian Belief Propagation (BP) algorithm is one of the most important distributed algorithms in signal processing and statistical learning involving Markov networks. It is well known that the algorithm correctly computes marginal density functions from a high dimensional joint density function over a Markov network i…
In this paper, we introduce a new directed graphical model from Gaussian data: the Gaussian graphical interaction model (GGIM). The development of this model comes from considering stationary Gaussian processes on graphs, and leveraging the equations between the resulting steady-state covariance matrix and the Laplacia…
Distributed Thompson sampling improves regret convergence in constrained communication networks.
problem Maximizing a black-box function with multi-agent Bayesian optimization under communication constraints.
method Distributed Thompson sampling using Gaussian processes, with theoretical bounds on regret convergence.
result Theoretical bounds on Bayesian average and simple regret depend on communication graph structure and are applicable in constrained networks.
Neighborhood sampling affects graph neural network training outcomes.
problem Understanding the impact of neighborhood sampling on graph neural network training.
method Theoretical analysis using neural tangent kernels and Gaussian processes.
result Posterior covariance differs for different neighborhood sampling approaches, indicating no dominant approach.