Graph-structured data arise in wide applications, such as computer vision, bioinformatics, and social networks. Quantifying similarities among graphs is a fundamental problem. In this paper, we develop a framework for computing graph kernels, based on return probabilities of random walks. The advantages of our proposed…
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48 results for “kernel-based random graphs”
We develop a multi-kernel based regression method for graph signal processing where the target signal is assumed to be smooth over a graph. In multi-kernel regression, an effective kernel function is expressed as a linear combination of many basis kernel functions. We estimate the linear weights to learn the effective …
Unified view on random walk and Weisfeiler-Leman kernels, improving accuracy.
problem Improving graph kernel methods for better classification accuracy.
method Define and analyze walk-based node refinement methods, relate to Weisfeiler-Leman test, and introduce new walk-based kernels.
result Walk-based kernels are as expressive as Weisfeiler-Leman subtree kernel but support non-strict neighborhood comparison.
Graph kernels have become an established and widely-used technique for solving classification tasks on graphs. This survey gives a comprehensive overview of techniques for kernel-based graph classification developed in the past 15 years. We describe and categorize graph kernels based on properties inherent to their des…
We propose graph kernels based on subgraph matchings, i.e. structure-preserving bijections between subgraphs. While recently proposed kernels based on common subgraphs (Wale et al., 2008; Shervashidze et al., 2009) in general can not be applied to attributed graphs, our approach allows to rate mappings of subgraphs by …
Kernel-based test detects differences between two conditional distributions efficiently.
problem Detecting differences between two conditional distributions efficiently.
method Kernel-based measure using nearest-neighbor graphs, consistent estimate with Gaussian limit.
result Asymptotic level control and universal consistency for detecting differences.
New theoretical tools simplify kernel-based tests analysis.
problem Asymptotic behavior of kernel-based tests in various scenarios.
method Avoids complex expansions and limit theorems, works directly with Hilbert spaces random functionals.
result Framework leads to simpler analysis with minimal regularity conditions.
We present a new paradigm for speeding up randomized computations of several frequently used functions in machine learning. In particular, our paradigm can be applied for improving computations of kernels based on random embeddings. Above that, the presented framework covers multivariate randomized functions. As a bypr…
Approximate Kernel-based Conditional Independence Tests for Fast Non-Parametric Causal Discoverystat.ME
Constraint-based causal discovery (CCD) algorithms require fast and accurate conditional independence (CI) testing. The Kernel Conditional Independence Test (KCIT) is currently one of the most popular CI tests in the non-parametric setting, but many investigators cannot use KCIT with large datasets because the test sca…
In this paper, we propose an outlier-robust regularized kernel-based method for linear system identification. The unknown impulse response is modeled as a zero-mean Gaussian process whose covariance (kernel) is given by the recently proposed stable spline kernel, which encodes information on regularity and exponential …
A new kernel for ranked data tackles computational challenges.
problem Complex geometric structure and partial rankings make existing algorithms infeasible for real-world applications.
method Derives a graph cut kernel that combines submodular optimization and kernel-based methods.
result The graph cut kernel efficiently handles large-scale ranked data.
End-to-end graph SVM with graph convolutions and RKHS.
problem Graph classification with complex feature spaces.
method End-to-end training of graph convolutions, kernel function, and SVM parameters.
result Outperforms existing deep learning models on graph classification tasks.
Graph-based methods pervade the inference toolkits of numerous disciplines including sociology, biology, neuroscience, physics, chemistry, and engineering. A challenging problem encountered in this context pertains to determining the attributes of a set of vertices given those of another subset at possibly different ti…
A new algorithm identifies interpretable network representations via subgraph count statistics.
problem Interpreting network-valued data samples.
method Principal Component Analysis for Networks (PCAN) and its fast sampling-based version (sPCAN).
result The PCAN and sPCAN methods provide informative and discriminatory features for network samples.
New method improves Gaussian kernel approximations for high-frequency data.
problem Limited scalability of kernel-based models to large data sets.
method Local random feature approximations using Maclaurin expansions and polynomial sketches.
result Significant improvement in kernel approximations and downstream performance for high-frequency data.
Data-driven prediction of molecular properties presents unique challenges to the design of machine learning methods concerning data structure/dimensionality, symmetry adaption, and confidence management. In this paper, we present a kernel-based pipeline that can learn and predict the atomization energy of molecules wit…
The study of networks has witnessed an explosive growth over the past decades with several ground-breaking methods introduced. A particularly interesting -- and prevalent in several fields of study -- problem is that of inferring a function defined over the nodes of a network. This work presents a versatile kernel-base…
Algorithm optimizes collaborative learning among distributed clients using kernel-based bandits.
problem Optimizing personalized objectives in a distributed system with limited global information.
method Kernel-based bandit framework with surrogate Gaussian process models, sparse approximations.
result Order-optimal regret performance (up to polylogarithmic factors) and reduced communication overhead.
Independent component analysis (ICA) is a method for recovering statistically independent signals from observations of unknown linear combinations of the sources. Some of the most accurate ICA decomposition methods require searching for the inverse transformation which minimizes different approximations of the Mutual I…
Inference of space-time varying signals on graphs emerges naturally in a plethora of network science related applications. A frequently encountered challenge pertains to reconstructing such dynamic processes, given their values over a subset of vertices and time instants. The present paper develops a graph-aware kernel…
RQMC improves kernel-based learning by reducing deterministic error and offering computational advantages.
problem Improving kernel-based learning methods to reduce deterministic error and computational complexity.
method Randomized quasi-Monte Carlo (RQMC) methods applied to random feature approximations.
result RQMC methods improve deterministic approximation error bound from to , matching QMC methods.
Non-linear kernel methods can be approximated by fast linear ones using suitable explicit feature maps allowing their application to large scale problems. We investigate how convolution kernels for structured data are composed from base kernels and construct corresponding feature maps. On this basis we propose exact an…
A new graph kernel uses LCS and Wasserstein distance for better graph comparisons.
problem Graph learning methods can be limited by information from distant vertices and path length constraints.
method Proposes a Graph Kernel based on LCS similarity and Wasserstein distance in a novel metric space.
result The new kernel emphasizes comparisons between similar paths and reduces information loss.
Random feature method approximates operators with theoretical guarantees and reduced computation.
problem Approximating operators between infinite dimensional Banach spaces using machine learning.
method Random feature operator learning method with theoretical guarantees and error bounds.
result The random feature method can achieve similar or better test errors than kernel-based methods and neural networks with significantly reduced training times.
Kernel-based estimation for partially functional linear model: Minimax rates and randomized sketchesmath.ST
Paper develops a method for estimating PFLM with minimized rates in high dimensions.
problem Estimating PFLM with minimized rates in high dimensions.
method Least square approach with mixed regularizations of function-norm and ℓ1-norm.
result Established optimal minimax rates of estimation for PFLM.
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.
Recent developments in system identification have brought attention to regularized kernel-based methods. This type of approach has been proven to compare favorably with classic parametric methods. However, current formulations are not robust with respect to outliers. In this paper, we introduce a novel method to robust…
Paper proposes an efficient causal discovery method with linear computational complexity.
problem Identifying causal relationships efficiently in large datasets.
method Approximate kernel-based generalized score function with low-rank technique and sampling algorithms.
result Significantly reduces computational costs while maintaining comparable accuracy.
A number of applications in engineering, social sciences, physics, and biology involve inference over networks. In this context, graph signals are widely encountered as descriptors of vertex attributes or features in graph-structured data. Estimating such signals in all vertices given noisy observations of their values…
We show that kernel-based quadrature rules for computing integrals can be seen as a special case of random feature expansions for positive definite kernels, for a particular decomposition that always exists for such kernels. We provide a theoretical analysis of the number of required samples for a given approximation e…
Develops a new method for learning non-parametric DAGs using RKHS.
problem Challenges of learning non-parametric causal models with large combinatorial search space.
method Uses reproducing kernel Hilbert spaces (RKHS) and sparsity-inducing regularization terms based on partial derivatives to enforce acyclicity.
result Shows improved performance through simulations and data analyses.
Aggregates predictions from multiple regression models using random projections and kernel methods.
problem Combining predictions from multiple regression models to improve accuracy.
method Random projection of high-dimensional feature space, followed by kernel-based consensual aggregation.
result The aggregation scheme performs similarly to using the original high-dimensional features, with high probability.
Improved particle-flow event reconstruction with scalable neural networks for current and future particle detectorsphysics.data-an
Improved particle-flow event reconstruction for future colliders using scalable neural networks.
problem Efficient and accurate particle reconstruction in future particle detectors.
method Comparative study of scalable machine learning models (graph neural network and kernel-based transformer) for event reconstruction.
result Graph neural network model improves jet transverse momentum resolution by up to 50%.
The approximation of nonlinear kernels via linear feature maps has recently gained interest due to their applications in reducing the training and testing time of kernel-based learning algorithms. Current random projection methods avoid the curse of dimensionality by embedding the nonlinear feature space into a low dim…
Graph kernels for metric graphs using tropical algebra.
problem Comparing graphs representing different metric spaces.
method Purely based on geometry and topology, invariant under edge subdivision.
result Capture complementary geometric and topological information.
Most state-of-the-art graph kernels only take local graph properties into account, i.e., the kernel is computed with regard to properties of the neighborhood of vertices or other small substructures. On the other hand, kernels that do take global graph propertiesinto account may not scale well to large graph databases.…
Unified analysis for nonlinear parametric models in Bayesian optimization.
problem Limited theoretical guarantees for nonlinear parametric models in Bayesian optimization.
method Kernel-based framework for analyzing regularized nonlinear parametric models trained on adaptively collected data.
result Unified convergence guarantees for nonlinear acquisition and surrogate models.
New kernel improves graph learning with fewer labeled data.
problem Limited kernels for node-level problems on graphs.
method Derived from a regularization framework, transductive kernel for graphs with node features.
result Improved learning on fewer training points and non-Euclidean data.
Study spectral properties of graph Laplacian for manifold data.
problem Understanding spectral properties of graph Laplacian for manifold data.
method Non-asymptotic error bounds on spectral properties of empirical graph Laplacian.
result Eigenvalues and eigenspaces of empirical graph Laplacian are close to Laplace-Beltrami operator of manifold.
Performing exact posterior inference in complex generative models is often difficult or impossible due to an expensive to evaluate or intractable likelihood function. Approximate Bayesian computation (ABC) is an inference framework that constructs an approximation to the true likelihood based on the similarity between …
Graph-based clustering has shown promising performance in many tasks. A key step of graph-based approach is the similarity graph construction. In general, learning graph in kernel space can enhance clustering accuracy due to the incorporation of nonlinearity. However, most existing kernel-based graph learning mechanism…
Enhances graph comparison by incorporating edge features using Fused Gromov-Wasserstein distance.
problem Graph distances overlook edge attributes, limiting their effectiveness.
method Introduced Fused Gromov-Wasserstein distance for graph comparison with edge features. Proposed algorithms for distance and barycenter computation.
result Empirically validated the effectiveness of the novel distance in graph learning tasks.
Online Centralized Non-parametric Change-point Detection via Graph-based Likelihood-ratio Estimationstat.ML
Paper detects changes in graph-based data streams using likelihood-ratios.
problem Detecting changes in synchronized graph-based data streams.
method Kernel-based likelihood-ratio estimation over graph nodes.
result Effective detection and localization of change-points.
We identify conditional parity as a general notion of non-discrimination in machine learning. In fact, several recently proposed notions of non-discrimination, including a few counterfactual notions, are instances of conditional parity. We show that conditional parity is amenable to statistical analysis by studying ran…
We propose a new method for input variable selection in nonlinear regression. The method is embedded into a kernel regression machine that can model general nonlinear functions, not being a priori limited to additive models. This is the first kernel-based variable selection method applicable to large datasets. It sides…
Kernel-based mean-field games use MMD penalties for interaction and target costs.
problem Optimizing mean-field games with specific cost functions.
method Kernel structure, random Fourier U-statistics, neural network training.
result Sample-level convergence theorem and rate of convergence proved.
Approximating non-linear kernels using feature maps has gained a lot of interest in recent years due to applications in reducing training and testing times of SVM classifiers and other kernel based learning algorithms. We extend this line of work and present low distortion embeddings for dot product kernels into linear…
New method for faster graph parameter inference from large random Kronecker graphs.
problem Efficiently infer graph parameters from large random Kronecker graphs.
method Decompose adjacency matrix into signal and noise components, then use denoising and solving approach.
result Proposed method achieves comparable or better performance than existing methods at lower computational cost.