DKLM learns adaptive kernels for robust nonlinear subspace clustering.
problem Nonlinear structures in data and challenges with kernel-based clustering.
method Data-driven kernel learning with adaptive weighting and optimal block-diagonal affinity matrix.
result DKLM enhances robustness and preserves manifold structure in nonlinear space.
Kernel approximation via nonlinear random feature maps is widely used in speeding up kernel machines. There are two main challenges for the conventional kernel approximation methods. First, before performing kernel approximation, a good kernel has to be chosen. Picking a good kernel is a very challenging problem in its…
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.
Kernel discriminant analysis uses nonlinear embeddings to improve classification.
problem Limited effectiveness of linear discriminant analysis in capturing nonlinear features.
method Study of nonlinear embeddings in kernel discriminant analysis using polynomial and Gaussian kernels, solving generalized eigenvalue problems.
result Polynomial and Gaussian discriminants capture class differences through population moments and randomized projections.
In this paper, we compare 5 different nonlinear kernels: min-max, RBF, fRBF (folded RBF), acos, and acos-χ2, on a wide range of publicly available datasets. The proposed fRBF kernel performs very similarly to the RBF kernel. Both RBF and fRBF kernels require an important tuning parameter (γ). Interestingly, for a …
SKN learns multi-layer nonlinear features using kernel methods.
problem Limited representational power of classic kernel methods.
method Interleaves layers of nonlinear and linear transformations in a hierarchy of RKHS-based features.
result SKN and SKCN outperform competitive methods on various datasets.
The term "CoRE kernel" stands for correlation-resemblance kernel. In many applications (e.g., vision), the data are often high-dimensional, sparse, and non-binary. We propose two types of (nonlinear) CoRE kernels for non-binary sparse data and demonstrate the effectiveness of the new kernels through a classification ex…
Proposes a new method for nonlinear Bayesian updates using ensemble kernel regression.
problem Nonlinear and non-Gaussian Bayesian updates for complex systems.
method Combines Kalman filtering for observed components and kernel density estimation for unobserved components, with subsampling and clustering.
result Reduces estimation errors in highly nonlinear scenarios compared to standard linear updates.
New method selects variables for nonlinear regression in large datasets.
problem Nonlinear regression with large-scale datasets.
method Kernel-based variable selection with random features.
result Outstanding performance on large-scale synthetic and real datasets.
Kernel VICReg improves SSL in RKHS, capturing nonlinear structures.
problem Limited ability of existing SSL methods to handle nonlinear dependencies.
method Kernel VICReg framework in RKHS, kernelizing VICReg objectives.
result Kernel VICReg mitigates representational collapse and improves performance.
Novel algorithm identifies nonlinear Granger causal relationships using kernel ridge regression.
problem Identification of nonlinear Granger causal relationships.
method Flexible plug-in architecture with kernel ridge regression using radial basis function.
result Kernel ridge regression in mlcausality achieves competitive AUC scores and more finely calibrated p-values.
Develops a framework for learning nonlinear operators using Mercer kernels.
problem Learning nonlinear operators between infinite-dimensional spaces.
method Stochastic approximation framework with Mercer operator-valued kernels.
result Establishes dimension-free polynomial convergence rates for nonlinear operator learning.
Unified kernel-based methods improve nonlinear causal discovery.
problem Identifying nonlinear causal relationships between time series variables.
method Unified Kernel Principal Component Regression (KPCR) and Gaussian Process score-based model with Smooth Information Criterion.
result Improved performance in time series nonlinear causal discovery.
A new method uses multifidelity Gaussian process regression to solve nonlinear PDEs.
problem Efficiently solving nonlinear PDEs using kernel methods.
method Proposes a kernel learning approach based on cokriging for multifidelity simulations.
result Demonstrates improved performance on the Burgers' equation.
Kernel measures similarity of nonlinear causal structures in heterogeneous populations.
problem Learning causal structure in populations with diverse underlying structures.
method Distance covariance-based kernel for measuring similarity of causal structures.
result Kernel enables clustering of homogeneous subpopulations for causal structure learning.
Proposes KAR for nonlinear causal discovery using kernel methods.
problem Learning causal relationships in nonlinear settings.
method Kernel anchor regression (KAR) with improved three-stage nonparametric regression.
result KAR outperforms existing methods in nonlinear causal discovery.
Novel adaptive multi-kernel learning scheme for dynamic environments.
problem Learning nonlinear functions in environments with unknown dynamics.
method Random feature approximation and adaptive multi-kernel learning.
result Unique capability to track nonlinear functions in dynamic environments with performance guarantees.
NKI integrates obfuscated datasets using nonlinear kernels for improved data collaboration.
problem Privacy-preserving data collaboration with reduced reconstruction risk.
method Formulates linear kernel integration, kernelizes it, and introduces graph regularization and centering constraints.
result NKI improves classification accuracy over existing linear integration methods under nonlinear dimensionality reduction.
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…
Kernel-based Bayesian filter for nonlinear systems using infinite-dimensional operators.
problem Modeling and predicting nonlinear dynamical systems.
method Functional Bayesian perspective, reproducing kernel Hilbert space, Gaussian kernel.
result Effective approximation and accurate results for nonlinear systems.
This paper introduces Grey Machine Learning and its nonlinear extensions.
problem Developing models for nonlinear data analysis.
method Summarizes grey system models and develops nonlinear extensions using kernels.
result New framework for estimating nonlinear functions using kernels.
Kernel method approximates Koopman operator eigenfunctions.
problem Complexity of computing Koopman operator spectra.
method Kernel-based approach to construct principal eigenfunctions.
result Principal eigenfunctions match linearization eigenvalues.
MC-MCL improves MCL for nonlinear clustering.
problem Nonlinear clustering in data science.
method MC-MCL combines MCL with Minimum Curvilinearity for nonlinear distances.
result MC-MCL outperforms classical MCL and baseline clustering algorithms in nonlinear datasets.
Adapts manifold structure for better clustering performance.
problem Lack of consideration for local manifold structure in existing multiple kernel k-means methods.
method Adopts manifold adaptive kernel to integrate local manifold structure of kernels.
result Proposed method outperforms state-of-the-art methods.
Kernel learning FBSDE filter improves nonlinear filtering efficiency.
problem Nonlinear filtering problem in high-dimensional systems.
method Iterative and adaptive meshfree approach using forward backward SDE and KDE.
result Rigorous convergence analysis provided, supporting empirical results.
New adaptive algorithms improve learning rate and reduce complexity.
problem Nonlinear system identification and prediction with large parameters.
method Data-selective adaptive kernel normalized least-mean square (KNLMS) algorithms.
result Proposed algorithms outperform existing methods in nonlinear system identification and prediction.
This paper develops a fast algorithm for solving nonlinear PDEs using sparse Cholesky factorization.
problem Efficiently solving nonlinear PDEs with Gaussian processes and kernel methods.
method Sparse Cholesky factorization for near-linear complexity.
result Near-linear complexity algorithm for working with kernel matrices of nonlinear PDEs.
A novel adaptive kernel improves RBF neural networks performance.
problem Improving performance of RBF neural networks.
method Adaptive fusion of Euclidean and cosine distance measures using gradient descent.
result The method outperforms manual fusion on three major problems.
Error estimates for nonlinear PDEs using kernel/GP methods.
problem Error analysis of kernel/GP methods for nonlinear and parametric PDEs.
method Sobolev space error estimates based on minimizing norm property of the solution.
result Dimension-benign convergence rates for smooth solutions.
New method clusters data subspaces more accurately.
problem Improving subspace clustering for nonlinear data.
method Introduces nonlinear orthogonal NMF with kernel-based updates.
result Enhanced clustering performance compared to existing methods.
A new deep neural network tackles nonlinear functional regression with improved dimensionality reduction.
problem Nonlinear functional regression in infinite-dimensional functional data analysis.
method Functional deep neural network with adaptive kernel embedding and projection steps.
result Explicit rates of approximating nonlinear smooth functionals are derived, and the network is shown to be effective in both simulated and real datasets.
New LQR kernels improve controller learning from data.
problem Optimal controller design for nonlinear systems from data is challenging.
method Developed LQR kernels for Bayesian optimization.
result LQR kernels lead to superior learning performance on uncertain systems.
A new method for efficient nonlinear process monitoring using random Bernoulli features.
problem High computational demands and real-time responsiveness in online monitoring systems.
method Random Bernoulli principal component analysis to capture nonlinear patterns efficiently.
result The proposed methods offer excellent scalability and reduced computational complexity.
KRCD detects unobserved confounders in nonlinear observational data.
problem Detecting unobserved confounders in nonlinear observational studies.
method Kernel Regression Confounder Detection (KRCD) using reproducing kernel Hilbert spaces.
result KRCD outperforms existing methods and achieves superior computational efficiency.
Enhances kernel regression with network data for better predictions.
problem Improving predictive power in high-dimensional data.
method Combines kernel regression with network cohesion data to model nonlinearities.
result Significantly better predictive performances in high-dimensional data.
Extends linear classification framework to nonlinear SVM-based ranking problems.
problem Maximizing performance on relevant samples in ranking problems.
method Dualization, kernel addition, componentwise dual ascent method.
result General framework for nonlinear classifiers in ranking problems.
The paper studies how neural networks evolve representations, finding a unique fixed point for nonlinear activations.
problem Understanding how neural networks transform input data across layers.
method Theoretical framework for the evolution of the kernel sequence, using mean-field regime and Hermite polynomials.
result For nonlinear activations, the kernel sequence converges globally to a unique fixed point.
We propose a general matrix-valued multiple kernel learning framework for high-dimensional nonlinear multivariate regression problems. This framework allows a broad class of mixed norm regularizers, including those that induce sparsity, to be imposed on a dictionary of vector-valued Reproducing Kernel Hilbert Spaces. W…
We propose a general matrix-valued multiple kernel learning framework for high-dimensional nonlinear multivariate regression problems. This framework allows a broad class of mixed norm regularizers, including those that induce sparsity, to be imposed on a dictionary of vector-valued Reproducing Kernel Hilbert Spaces. W…
We consider a stochastic control problem for a class of nonlinear kernels. More precisely, our problem of interest consists in the optimisation, over a set of possibly non-dominated probability measures, of solutions of backward stochastic differential equations (BSDEs). Since BSDEs are nonlinear generalisations of the…
The paper introduces a fast algorithm for learning and forecasting nonlinear dynamics from noisy time series data.
problem Challenges in capturing nonlinear dynamics from noisy time series data.
method A projected nonlinear state-space model with kernel functions applied to projected lines.
result The model effectively learns and forecasts complex nonlinear dynamics with computational efficiency.
We introduce a data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves linearly when lifted into a high (or infinite) dimensional feature space where ba…
We introduce a novel data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves linearly when lifted into a high (or infinite) dimensional feature space wh…
The paper develops a robust test for nonlinear effects using Gaussian processes.
problem Detecting nonlinear interactions between continuous features.
method Hypothesis test based on Gaussian processes, robust to kernel mis-specification, and using ensemble estimators.
result Demonstrates interesting connections between machine learning and statistical inference.
Deep DPP model uses neural networks to learn kernel matrices for DPPs.
problem Limitations of DPPs in capturing nonlinear interactions and incorporating item metadata.
method Integrates a deep feed-forward neural network to learn the kernel matrix of DPPs.
result Deep DPP model improves predictive performance and outperforms baselines.
A new method for complex-valued signals improves convergence and performance.
problem Nonlinear channel equalization and complex-valued signals with different properties.
method Generalized complex kernel least-mean-square (gCKLMS) algorithm.
result The gCKLMS algorithm converges faster and performs better than previous methods.
Nonlinear kernel regression models are often used in statistics and machine learning because they are more accurate than linear models. Variable selection for kernel regression models is a challenge partly because, unlike the linear regression setting, there is no clear concept of an effect size for regression coeffici…
CDSSL improves representation quality by integrating linear and nonlinear dependencies.
problem Scarcity of labeled data and neglect of nonlinear dependencies in SSL.
method CDSSL combines linear correlations and nonlinear dependencies using HSIC in RKHS.
result CDSSL enhances representation quality on diverse benchmarks.