Novel algorithm compresses ECG signals with preserved R peaks.
problem Efficiently compressing ECG signals while preserving R peak information.
method Blaschke unwinding AFD for faster convergence and higher fidelity.
result The proposed algorithm outperforms state-of-the-art approaches in ECG signal compression.
Proposes a new tensor decomposition method for functional temporal data with adaptive complexity.
problem Challenges in temporal tensor decomposition for general tensor data with continuous indexes.
method Encodes continuous spatial indexes as learnable Fourier features and uses neural ODEs for temporal trajectories. Introduces a sparsity-inducing prior for complexity adaptation.
result Significantly outperforms existing methods in prediction performance and robustness against noise.
New Fourier analysis method for non-uniform Boolean hypercube.
problem Non-uniform probability measures on the Boolean hypercube.
method ANOVA-based decomposition, explicit basis, least squares problem.
result Generalization of Fourier analysis for arbitrary probability measures.
New method uses tensor decompositions to overcome the curse of dimensionality for large-scale learning.
problem Large-scale machine learning problems with kernel methods.
method Deterministic Fourier features combined with low-rank tensor decomposition for tensor product structure.
result Demonstrated consistent performance and superior results compared to random Fourier features.
EFiGP uses Fourier and eigen-decomposition for efficient ODE parameter estimation.
problem Parameter estimation and trajectory reconstruction for noisy, sparse, nonlinear ODE systems.
method EFiGP integrates Fourier transformation and eigen-decomposition into a physics-informed Gaussian Process framework.
result EFiGP efficiently estimates ODE parameters and recovers trajectories from noisy data.
This work proves convergence of adaptive resampling for random Fourier features.
problem Sampling Fourier frequencies well for high-dimensional data.
method Data adaptive resampling of Fourier frequencies, asymptotically optimal.
result Proves convergence of adaptive resampling method for regression and classification problems.
New scalable GP approximation using Fourier series decomposition.
problem Scalability and accuracy in Gaussian process approximations.
method Harmonic kernel decomposition (HKD) to decompose kernels orthogonally.
result Significantly outperforms standard variational methods in scalability and accuracy.
Two ANOVA-based algorithms boost random Fourier feature models for function approximation.
problem Approximating high-dimensional functions with low-order interactions.
method Utilizes ANOVA decomposition to learn low-order functions and index sets of important variables.
result Significantly reduces approximation error compared to existing methods.
Fourier PCA is Principal Component Analysis of a matrix obtained from higher order derivatives of the logarithm of the Fourier transform of a distribution.We make this method algorithmic by developing a tensor decomposition method for a pair of tensors sharing the same vectors in rank-1 decompositions. Our main appli…
KOMET identifies Koopman operators from model parameter trajectories to adapt to evolving data distributions.
problem Adaptation of parametric models to non-stationary environments.
method Data-driven framework using Koopman operator identification and Extended Dynamic Mode Decomposition (EDMD).
result KOMET achieves high autonomous-rollout accuracies of 0.981 to 1.000 over 100 time steps on various drifting datasets.
FNSDA adapts to new dynamics via Fourier space adaptation.
problem Generalizing to unseen dynamical systems with limited data.
method Automatic partitioning of known environments in Fourier modes and adaptation of specific modes for new environments.
result FNSDA achieves superior or competitive generalization performance with reduced parameter cost.
Paper improves tensor completion using unitary transforms.
problem Robust tensor completion for various datasets.
method Transformed tensor SVD with unitary matrices.
result Recovered images have better PSNR than traditional methods.
In this paper we investigate bundles whose structure group is the loop group LU(n). Our main result is to give a necessary and sufficient criterion for there to exist a Fourier type decomposition of such a bundle ξ. This is essentially a decomposition of ξ as ζ⊗LC, where ζ is a finite dimensional…
Enhances DGPs with adaptive RKHS Fourier features for better non-stationary pattern modeling.
problem Capturing complex non-stationary patterns in non-linear dynamical systems.
method Integrates ODE-based RKHS Fourier features into DGPs using convolution operations for adaptive amplitude and phase modulation. Uses a doubly stochastic variational inference framework.
result Improved predictive performance across various regression tasks.
We solve the ANOVA decomposition for categorical inputs.
problem Lack of a closed-form expression for ANOVA decomposition with categorical dependent variables.
method Bridge functional analysis with discrete Fourier analysis to derive a closed-form decomposition.
result Closed-form decomposition for categorical inputs without assumptions.
A new method optimizes Fourier pricing for multi-asset options using adaptive quadrature.
problem Efficiently pricing multi-asset options in Lévy models.
method Optimized damping parameters and hierarchical adaptive quadrature.
result Significant speed-up in computational time for up to six dimensions.
This paper improves sales forecasting on Tmall using Fourier decomposition and Tweedie distribution optimization.
problem Sales forecasting for retailers on Tmall.
method Fourier decomposition for seasonality extraction and Tweedie distribution optimization.
result Improved sales forecasting results using optimized models.
FNN approximates functions and solves PDEs with periodic BCs.
problem Approximating and solving periodic functions and PDEs.
method Fourier neural network architecture with activation and loss functions.
result FNN can solve PDEs with periodic BCs and is interpretable.
Random Fourier features model reconstructs wind fields from sparse measurements.
problem Reconstructing wind fields from limited data.
method Random Fourier features approximating velocity field with adaptive sampling.
result Random Fourier features model outperforms benchmarks.
HFNO enhances interpretability of turbulent flows through parallel wavenumber bin processing.
problem Opaque inner workings of Fourier Neural Operators (FNOs) hinder physical interpretability.
method Introduces HFNO, a novel FNO-based architecture that processes wavenumber bins in parallel, enhancing interpretability.
result HFNO decomposes turbulent flows across various scales, enabling increased interpretability and multiscale modeling.
Developed Taylor series for muscle-finger system analysis.
problem Understanding the complex relationship between muscle activity and finger movement.
method Used Dendrite Net to develop Taylor series and construct relation spectrum.
result Found muscle synergy and coupling in hand movement.
ABO extends RLS for online learning in non-stationary time-series, improving accuracy and speed.
problem Online learning in non-stationary time-series with overparameterized models.
method QR-based exponentially weighted RLS algorithm with orthogonal-triangular updates.
result ABO maintains bounded residuals and stable condition numbers while achieving speed improvements.
Improved sampling strategy reduces Fourier measurements for neural network signals.
problem Efficiently sampling signals from neural networks with random Fourier matrices.
method Model-adapted sampling strategy with improved sample complexity.
result Reduced sample complexity from O(kdnα∞²) to O(kdα²₂) measurements.
The study compares Fourier-based pricing methods, identifying the most efficient and accurate.
problem Comparing CPU effort and pricing biases of Fourier-based implementations.
method Numerical analysis of seven Fourier-based implementations, focusing on truncation and discretization errors.
result The multi-strike version of the COS method is notably faster, and the strike-optimized Carr Madan's formula is both faster and more accurate.
Paper introduces a new method for efficient portfolio risk quantification.
problem Efficiently quantify risk in large portfolios with many trades and few dominant risk factors.
method Combines Fourier-cosine series with tensor decomposition techniques for dimension reduction.
result Achieves relative errors below 0.1% with significant runtime improvement.
Time-subordinated Brownian motion models improve financial market stochastic distribution.
problem Improving stochastic distribution modeling in financial markets.
method Fourier theory and methodology for time-subordinated Brownian motion models, extending real domain to complex plane.
result Characterization and direct study of stochastic time-change from full process.
Sub-Riemannian Selberg trace formulae for compact quotients of SL(2, R)
problem Computing zeta-regularized determinants of sub-Laplacians
method Using Fourier decomposition and Selberg trace formulae
result Compact determinant formula expressed in terms of base hyperbolic surface and relative Selberg product
FEDformer combines Transformer with seasonal-trend decomposition for efficient long-term forecasting.
problem Transformer's inefficiency and inability to capture global time series views.
method Combines seasonal-trend decomposition with Transformer, exploiting Fourier basis for frequency enhancement.
result Reduces prediction error by 14.8% and 22.6% for multivariate and univariate time series, respectively.
This paper improves GANs for 1D data using reparameterizations.
problem Improving GAN performance for 1D data.
method Identifies and uses reparameterizations of Taylor and Fourier series.
result Reparameterized critics outperform standard GANs.
Improved sampling for Diffusion Models by accounting for covariance.
problem Sampling quality degradation in few-step Diffusion Models.
method Covariance-aware sampler using Tweedie's formula and Fourier-space decomposition.
result Consistently superior samples compared to state-of-the-art samplers.
Method transfers label function spectrum between graphs.
problem Domain adaptation with abrupt label function variations.
method Learning aligned graph bases to transfer label function spectrum.
result Improved classification performance compared to existing methods.
A robust method for decomposing spectral peaks robust to distortion and interference.
problem Decomposing spectral peaks in the presence of distortion and interference.
method Optimizing a nonparametric approach using pseudo-symmetric functions with nonincreasing behavior.
result Decomposed spectral peaks show pseudo-orthogonal behavior and power preserving equality.
G-FuNK learns solutions for nonlinear PDEs on multiple domains and parameters.
problem Predicting time-dependent dynamics of complex systems governed by nonlinear PDEs with varying parameters and domains.
method Graph Fourier Neural Kernels combining domain-adapted and transferable components for non-diffusive and diffusive terms.
result G-FuNK achieves low relative errors on unseen domains and fiber fields, significantly accelerating predictions.
X-ray transform on H-type groups solved, revealing function injectivity.
problem Injectivity in sub-Riemannian geometry.
method Fourier Slice Theorem adapted to H-type groups.
result Integrable functions on H-type groups are uniquely determined by their integrals over geodesics.
Graph-based denoising framework for smooth manifolds.
problem Denoising of signals on smooth manifolds.
method Spectral Graph Wavelet transform applied to the graph Fourier frequency domain.
result Significantly outperforms state-of-the-art denoising methods.
ATOMO reduces communication in distributed learning by sparsifying gradients.
problem Communication overheads in distributed model training.
method ATOMO framework for atomic sparsification of stochastic gradients.
result Sparsifying singular value decomposition can lead to faster distributed training.
Quantum-assisted Gaussian process speeds up data regression.
problem High computational complexity of Gaussian process regression for large datasets.
method Quantum-assisted sparse Gaussian process regression using random Fourier features.
result Achieves polynomial-order computational speedup compared to classical methods.
We consider the representation space of a compact surface, that is the space of morphisms from the fundamental group to SU(2) up to conjugation. We show that the trace functions associated to multicurves on the surface are linearly independent as functions on the representation space. The proof relies on the Fourier de…
Paper derives option pricing formula for SVJ models with jumps.
problem Option pricing for models with finite activity jumps.
method Generic decomposition and explicit approximation formulas for SVJ models.
result Improved computation efficiency and insight into volatility smiles.
New model learns relative importance of multiple seasonal patterns in time series data.
problem Complex seasonal patterns in business time series data.
method Mixed hierarchical seasonality (MHS) model using Stan.
result Significant improvements in prediction error and predictive density compared to existing models.
Adaptive tensor modeling preserves continuity in multidimensional data.
problem Discretization of continuous multidimensional data loses important information.
method Functional Tucker decomposition (FTD) with RKHS modeling.
result FTD enables adaptive and expressive tensor modeling.
Quantum method improves neural density estimation in high dimensions.
problem High-dimensional density estimation with poor performance and high computational complexity.
method Adaptive Fourier features based on quantum density matrices, integrated with neural networks.
result Competitive performance compared to state-of-the-art methods in various datasets.
Proposes a Gradient Boosting method for learning adaptive kernel functions.
problem Learning a versatile ensemble of kernel functions for better performance.
method Approximates kernel functions as a weighted sum of Random Fourier Features and optimizes their barycenter at each iteration.
result Shows improved performance compared to Boosting-based and kernel-learning methods.
ARFF reduces spectral bias in SGD-trained neural networks.
problem Spectral bias in two-layer neural networks.
method Comparison of SGD and ARFF on spectral bias and robustness.
result ARFF yields a closer to zero spectral bias compared to SGD.
No-trick kernel adaptive filtering uses deterministic features for scalability and robustness.
problem Scalability issues in kernel methods for large datasets.
method Deterministic feature-map construction using polynomial-exact solutions.
result Deterministic features outperform random Fourier features in performance and scalability.
The paper proves the consistency and efficiency of a volatility estimator in noisy data.
problem Proving the consistency and efficiency of a volatility estimator in the presence of microstructure noise.
method Proves asymptotic normality using Central Limit Theorem for Fourier spot volatility estimator.
result Proves consistency and asymptotic efficiency of the Fourier spot volatility estimator in noisy data.
RP-GFRFT unifies fractional order and rotation control for graph signals.
problem Lack of rotation-based spectral control in GFRFT and zero-angle degeneracy in AGFT.
method Rotation-parameterized graph fractional Fourier transform (RP-GFRFT) with degeneracy preserving rotation matrix.
result RP-GFRFT improves spectral filtering performance over existing methods.
SASE improves attributed graph clustering for large graphs with linear time and space complexity.
problem Challenges in clustering large attributed graphs due to high computational and memory costs.
method SASE combines node features smoothing, scalable spectral clustering, and adaptive order selection.
result SASE achieves a 6.9% improvement in ACC and a 5.87x speedup on the ArXiv dataset.