Random Fourier Features reduce kernel matrix reconstruction error without dimensionality dependence.
problem Error reduction in kernel matrix reconstruction for high-dimensional data.
method Random Fourier Features with theoretical error bounds.
result Error probability is independent of data dimensionality.
The paper explores how kernel eigenalignments affect generalization in KRR.
problem Achieving robust generalization in kernel methods.
method Direct connection between generalization and matrix eigenvectors/eigenvalues, focusing on finite-sample settings.
result Strong generalization requires increasing eigenvector alignment, eigenvalue magnitude, or gaps between eigenvalues.
Paper develops a novel kernel-based method for MRI data recovery.
problem Reconstructing dynamic MRI data on manifolds.
method Kernel bi-linear modeling in reproducing kernel Hilbert spaces.
result Validated on synthetic dMRI data, the method outperforms state-of-the-art approaches.
New method speeds up kernel-based machine learning for force field reconstruction.
problem Scalability issues in kernel-based machine learning for force field reconstruction.
method Nyström-type methods to construct preconditioners based on low-rank approximations of the kernel matrix.
result Effective preconditioners lead to super-linear convergence in kernel-based machine learning.
In this paper we introduce the deep kernelized autoencoder, a neural network model that allows an explicit approximation of (i) the mapping from an input space to an arbitrary, user-specified kernel space and (ii) the back-projection from such a kernel space to input space. The proposed method is based on traditional a…
Explains various PCA and SPCA methods with theory and applications.
problem No specific problem stated; focuses on explaining methods.
method Explains PCA, SPCA, kernel PCA, and kernel SPCA methods with theory and applications.
result Comprehensive coverage of PCA and SPCA methods with theory and applications.
Framework for joint inference of network topology and interaction types in heterogeneous systems.
problem Joint inference of network topology, multi-type interaction kernels, and latent type assignments in heterogeneous interacting particle systems.
method Three-stage approach: shared structure recovery, discrete interaction type identification, and matrix factorization.
result The method yields accurate reconstruction of underlying dynamics and is robust to noise.
New iterative solvers speed up Gaussian process regression with derivatives.
problem Scaling Gaussian process regression with derivatives for high-dimensional problems and large budgets.
method Iterative solvers using fast matrix-vector multiplications and pivoted Cholesky preconditioning.
result Bayesian optimization with derivatives can now scale to high-dimensional problems and large evaluation budgets.
Enhances autoencoders with kernel alignment for better data representation.
problem Lack of clear properties for autoencoders to capture in data representations.
method Aligns inner products between codes with a kernel matrix to capture topological properties.
result Effective data representations learned, preserving input data similarities.
A new method estimates SDEs using occupation kernels.
problem Learning multivariate stochastic differential equations (SDEs).
method Two-step procedure: estimate drift, then diffusion. Occupation kernels used in RKHS.
result Validated on simulated and real-world data.
This paper reconstructs complex graph signals using kernel methods on manifolds.
problem Reconstructing complex graph signals from samples on graph vertices.
method Kernel methods on complex manifolds, embedding vertices into higher-dimensional spaces.
result Effective reconstruction of complex graph signals, outperforming conventional methods.
Signal processing tasks as fundamental as sampling, reconstruction, minimum mean-square error interpolation and prediction can be viewed under the prism of reproducing kernel Hilbert spaces. Endowing this vantage point with contemporary advances in sparsity-aware modeling and processing, promotes the nonparametric basi…
Kernel Dynamic Mode Decomposition reconstructs dynamical systems using Laplacian kernel.
problem Reconstructing spatial-temporal dynamics of complex systems.
method Kernel Dynamic Mode Decomposition with Laplacian kernel.
result Laplacian kernel allows for the closability of Koopman operators in RKHS, enabling reconstruction.
Single linear solve combines surface reconstruction and uncertainty quantification.
problem Reconstructing surfaces from partial point clouds with uncertainty.
method Geometric Gaussian processes for stochastic surface reconstruction.
result Single linear solve for surface reconstruction with probabilistic capabilities.
Reconstruction based subspace clustering methods compute a self reconstruction matrix over the samples and use it for spectral clustering to obtain the final clustering result. Their success largely relies on the assumption that the underlying subspaces are independent, which, however, does not always hold in the appli…
Random sinusoidal features are a popular approach for speeding up kernel-based inference in large datasets. Prior to the inference stage, the approach suggests performing dimensionality reduction by first multiplying each data vector by a random Gaussian matrix, and then computing an element-wise sinusoid. Theoretical …
3d-SMRnet speeds up MPI system matrix recovery to 1 minute with high quality.
problem Slow system matrix recovery in MPI due to recalibration.
method 3d-System Matrix Recovery Network using deep learning.
result 3d-SMRnet recovers 3d system matrix with 64x subsampling in 1 minute.
We consider the problem of approximately reconstructing a partially-observed, approximately low-rank matrix. This problem has received much attention lately, mostly using the trace-norm as a surrogate to the rank. Here we study low-rank matrix reconstruction using both the trace-norm, as well as the less-studied max-no…
Graph filtering improves data reconstruction performance.
problem Data reconstruction and dimensionality reduction.
method Formulate data tasks as graph filtering operations, optimize mean-square error cost involving adjacency matrix, update filters via gradient descent.
result Better reconstruction performance of novel method compared to PCA.
Paper develops a graph-based method for reconstructing spatio-temporal signals.
problem Reconstructing space-time varying signals on graphs given limited data.
method Multi-kernel Kriged Kalman Filter combining graph-aware kernels and online selection.
result Superior reconstruction performance compared to existing methods.
This work improves understanding of neural network reconstruction attacks and distillation.
problem Understanding and mitigating reconstruction attacks on neural networks.
method Developed a stronger dataset reconstruction attack and studied its characteristics.
result Reconstruction attacks can recover entire training sets in the infinite width regime.
3-manifold triangulation can be reconstructed from its intersection matrix.
problem Reconstructing the triangulation of 3-manifolds from their intersection matrix.
method Using the intersection matrix of a simplicial complex to determine the triangulation of a 3-manifold up to isomorphism.
result The intersection matrix is sufficient to determine the triangulation of a 3-manifold up to isomorphism.
New method simplifies tomographic reconstruction using RKHS.
problem Tomographic reconstruction challenges.
method RKHS framework for X-ray transform.
result Sharp stability results without Fourier transform.
A1GM method improves efficiency in reconstructing missing data using KL divergence.
problem Efficiently reconstructing missing data in matrices.
method Fast non-gradient-based rank-1 NMF using KL divergence.
result A1GM outperforms gradient methods in efficiency with competitive reconstruction errors.
A new method for accurately reconstructing signals without knowing the kernel or signal regularity.
problem Recovering signals from noisy measurements without prior knowledge of the convolution kernel or signal regularity.
method Parametrizing the convolution kernel and prior length-scales, jointly estimated in the inversion procedure.
result Accurate reconstructions of signals with varying regularity and unknown kernel size.
Designs CNNs for better image reconstruction.
problem Image reconstruction from limited data.
method Parseval convolution operators and chaining of elementary modules.
result CNN-based algorithm yields better results than sparsity-based methods.
We consider fast kernel summations in high dimensions: given a large set of points in d dimensions (with d≫3) and a pair-potential function (the {\em kernel} function), we compute a weighted sum of all pairwise kernel interactions for each point in the set. Direct summation is equivalent to a (dense) matrix-vec…
MKD learns MTS attributes to reconstruct and cluster unseen classes.
problem Reconstructing and clustering unseen multivariate time-series.
method Multiple-kernel dictionary learning (MKD) to learn semantic attributes.
result MKD provides interpretable reconstruction and high clustering performance.
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%.
Two strategies for embedding new data points from proximity data are explored.
problem Embedding new data points using proximity data.
method Two competing strategies: projection and restricted reconstruction.
result Projection and restricted reconstruction can be derived from kernel methods.
Paper proposes a new method for fast matrix completion.
problem Challenges in matrix completion, especially for images with heterogeneous data.
method Sparse reverse of principal component analysis.
result The method efficiently reconstructs matrices with missing data.
Proposes a method to learn a low-rank kernel matrix for graph-based clustering.
problem Challenges in learning an optimal kernel matrix for graph-based clustering.
method Unified framework for graph construction and kernel learning, focusing on a low-rank kernel matrix.
result Efficacy of the proposed method validated through extensive experiments.
A well-recognized limitation of kernel learning is the requirement to handle a kernel matrix, whose size is quadratic in the number of training examples. Many methods have been proposed to reduce this computational cost, mostly by using a subset of the kernel matrix entries, or some form of low-rank matrix approximatio…
New method reconstructs network topology from node-dynamics data.
problem Reconstructing network topology from time-resolved observations of node-dynamics.
method Feature ranking using Random forest and RReliefF to rank node importance.
result Method is robust to various system parameters and depends on dynamical regime.
Boosts neural network performance by improving weight separability.
problem Improving the separability of weight vectors in neural networks.
method Proposes a new evaluation metric and feed-backward reconstruction loss to encourage weight separability.
result Improves visual recognition performance across various tasks.
Paper proposes a new method to learn similarity from data.
problem Learning similarity from data without losing manifold structure.
method Minimizing reconstruction error of kernel matrices.
result Significant improvements in clustering tasks compared to state-of-the-art methods.
We develop a method to factorize symmetric sparse Boolean matrices efficiently.
problem Finding a symmetric factorization of a given matrix into a sparse, Boolean matrix.
method Polynomial-time algorithm based on bootstrapping higher-order information and tensor decomposition.
result A matrix with full column rank can be recovered with high probability when the matrix size is sufficiently large.
We consider the problem of reconstructing a low rank matrix from a subset of its entries and analyze two variants of the so-called Alternating Minimization algorithm, which has been proposed in the past. We establish that when the underlying matrix has rank r=1, has positive bounded entries, and the graph $\mathcal{G…
New PCA method detects faults using occupation kernels.
problem Fault detection in dynamical systems.
method Occupation kernel PCA for irregularly sampled data.
result Validation of reconstruction error approach for fault detection.
We give a new, very general, formulation of the compressed sensing problem in terms of coordinate projections of an analytic variety, and derive sufficient sampling rates for signal reconstruction. Our bounds are linear in the coherence of the signal space, a geometric parameter independent of the specific signal and m…
We develop latent variable models for Bayesian learning based low-rank matrix completion and reconstruction from linear measurements. For under-determined systems, the developed methods are shown to reconstruct low-rank matrices when neither the rank nor the noise power is known a-priori. We derive relations between th…
Memory-efficient algorithms reduce kernel matrix size for machine learning.
problem Efficiently handling large kernel matrices in machine learning.
method Hierarchical matrix approximations and clustering techniques.
result Compression improves efficiency without sacrificing prediction accuracy.
Accelerated RPCholesky speeds up kernel matrix approximations.
problem Efficiently approximating large kernel matrices.
method Accelerated randomly pivoted Cholesky (RPCholesky) with block matrix computations and rejection sampling.
result Approximates kernel matrices up to 40 times faster.
Paper proposes an algorithm to reconstruct optimal model structure from graph adjacency matrix.
problem Optimal model structure reconstruction from weighted colored graph adjacency matrix.
method Uses prize-collecting Steiner tree algorithm to reconstruct minimum spanning tree.
result Demonstrates the effectiveness of the prize-collecting Steiner tree algorithm for model structure reconstruction.
New methods complete multiple incomplete kernel matrices while controlling model flexibility.
problem Incomplete data in multiple kernel learning.
method Parameterized model matrix with restrictions on model covariance and use of LogDet divergence to ensure positive definiteness.
result Proposed methods yield significant improvements in generalization performance.
MKPN predicts varying-sized kernels for burst image denoising.
problem Denoising burst images corrupted by noise.
method Deep neural network (MKPN) predicts and fuses kernels of varying sizes.
result MKPN outperforms state-of-the-art on synthetic datasets.
A determinantal point process (DPP) is a probabilistic model of set diversity compactly parameterized by a positive semi-definite kernel matrix. To fit a DPP to a given task, we would like to learn the entries of its kernel matrix by maximizing the log-likelihood of the available data. However, log-likelihood is non-co…
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…