NFM models time-series data directly in the Fourier domain, achieving state-of-the-art performance.
problem Traditional time-series analysis focuses on the time domain, limiting flexibility.
method NFM models time-series data in the Fourier domain, using frequency extrapolation and interpolation.
result NFM achieves state-of-the-art performance on various time-series tasks.
A new SINC method for fast and accurate option pricing.
problem Computing option prices efficiently and accurately.
method SINC approach based on Shannon Sampling Theorem.
result SINC provides the most accurate and fast pricing computation.
DeepPhaseCut uses neural networks to improve Fourier phase retrieval.
problem Fourier phase retrieval from magnitude data.
method Unsupervised feed-forward neural network with cycleGAN training.
result Outperforms existing methods in Fourier phase retrieval.
Improved electrical load forecasting model using Fourier-enhanced RNN.
problem Electrical load time series downscaling with high accuracy and low error.
method Combines recurrent neural network with Fourier seasonal embeddings and self-attention.
result Significantly reduces RMSE across different time horizons compared to existing methods.
Develops Active Fourier Auditor to estimate ML model properties without reconstructing them.
problem Verifying and auditing properties of Machine Learning models in real-world applications.
method A new framework that quantifies ML model properties using Fourier coefficients, without reconstructing the model.
result Active Fourier Auditor (AFA) is more accurate and sample-efficient than baselines for estimating robustness, individual fairness, and group fairness.
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.
A new model captures complex event data using attention and Fourier kernels.
problem Capturing complex non-linear temporal dependencies in discrete event data.
method Integrates attention mechanism into point processes' conditional intensity function and uses Fourier kernel embedding.
result Established theoretical properties and demonstrated competitive performance.
Random Fourier features is one of the most popular techniques for scaling up kernel methods, such as kernel ridge regression. However, despite impressive empirical results, the statistical properties of random Fourier features are still not well understood. In this paper we take steps toward filling this gap. Specifica…
A new method slices and sums radial kernels faster.
problem Fast computation of large kernel sums in kernel methods.
method Random projections to 1D subspaces and QMC for selecting projections.
result QMC-slicing outperforms existing methods on test datasets.
This paper proposes a novel framework to regularize the highly ill-posed and non-linear Fourier ptychography problem using generative models. We demonstrate experimentally that our proposed algorithm, Deep Ptych, outperforms the existing Fourier ptychography techniques, in terms of quality of reconstruction and robustn…
The paper tackles drift identification in Lévy α-stable stochastic systems, proposing a Fourier space approach.
problem Estimating the drift field of a stochastic differential equation driven by Lévy α-stable noise.
method Fourier space approach, parameterizing the drift field using Fourier series, minimizing a loss function with gradients computed via the adjoint method.
result The method is capable of learning drift fields in qualitative and/or quantitative agreement with ground truth fields.
Markov Chain Monte Carlo methods become increasingly popular in applied mathematics as a tool for numerical integration with respect to complex and high-dimensional distributions. However, application of MCMC methods to heavy tailed distributions and distributions with analytically intractable densities turns out to be…
A Fourier-based learning algorithm for multiclass classification.
problem Highly nonlinear multiclass classification problems.
method Smoothing technique with low-pass filters to calculate probability distributions.
result Probabilistic explanation for classification without kernel functions.
We introduce the formalism of generalized Fourier transforms in the context of risk management. We develop a general framework to efficiently compute the most popular risk measures, Value-at-Risk and Expected Shortfall (also known as Conditional Value-at-Risk). The only ingredient required by our approach is the knowle…
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.
Efficiently scales continuous kernels with sparse Fourier domain learning.
problem High computational and memory demands, spectral bias in continuous kernels.
method Sparse learning in the Fourier domain.
result Efficient scaling of continuous kernels, reduced computational and memory requirements, mitigated spectral bias.
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.
A new method computes Greeks for multi-asset options using tensor trains and Fourier transforms.
problem Efficient computation of Greeks for multi-asset options with high accuracy and low sample complexity.
method Tensor train (TT) representations of Fourier-based pricing functions, combined with numerical differentiation or analytical approaches.
result Significant speed-ups of up to 105imes over Monte Carlo simulations while maintaining comparable accuracy. Quantum algorithm for pricing European call options.
problem Accurate valuation of financial derivatives, especially for complex models and options.
method Transforms classical FFT into quantum QFT for pricing European call options.
result Quantum algorithm outperforms classical Monte Carlo simulation in NISQ era.
Random Fourier features improve tabular deep learning convergence.
problem Tabular deep learning convergence issues.
method Random Fourier projections as a pre-processing step, projecting inputs into a fixed feature space.
result Random Fourier pre-processing accelerates tabular deep learning convergence.
FourNet approximates financial transition densities using Fourier transforms.
problem Approximating transition densities in finance with high accuracy.
method FourNet is a novel FFNN with Gaussian activation, learning from characteristic functions.
result FourNet can approximate transition densities arbitrarily well with finite neurons.
As announced in [12], we develop a calculus of Fourier integral G-operators on any Lie groupoid G. For that purpose, we study convolability and invertibility of Lagrangian conic submanifolds of the symplectic groupoid T * G. We also identify those Lagrangian which correspond to equivariant families parametrized by the …
We propose a Fourier-based approach for optimization of several clustering algorithms. Mathematically, clusters data can be described by a density function represented by the Dirac mixture distribution. The density function can be smoothed by applying the Fourier transform and a Gaussian filter. The determination of th…
This work improves Fourier pricing for multi-asset options using RQMC with domain transformation.
problem Efficiently pricing multi-asset options in high dimensions with Fourier methods.
method Randomized quasi-Monte Carlo (RQMC) with domain transformation to handle singularities.
result RQMC with domain transformation provides accurate and scalable Fourier pricing for multi-asset options.
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.
Kernel methods are powerful and flexible approach to solve many problems in machine learning. Due to the pairwise evaluations in kernel methods, the complexity of kernel computation grows as the data size increases; thus the applicability of kernel methods is limited for large scale datasets. Random Fourier Features (R…
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.
Periodicity is often studied in timeseries modelling with autoregressive methods but is less popular in the kernel literature, particularly for higher dimensional problems such as in textures, crystallography, and quantum mechanics. Large datasets often make modelling periodicity untenable for otherwise powerful non-pa…
Scalable kernel methods for large datasets using Fourier representations and NUFFT.
problem Cubic complexity in kernel methods limits their use on large-scale datasets.
method Fourier representation of kernels combined with NUFFT for O(n log n) complexity.
result Achieves minimax convergence rates and processes up to tens of billions of samples.
New method uses machine learning to optimize Fourier pricing methods.
problem Difficulty in tuning parameters for Fourier pricing methods.
method Learning tuning parameters of Fourier methods using machine learning.
result Very fast algorithms with full error control.
Improved numerical solution for BSDEs with reduced boundary errors.
problem Boundary errors in numerical solution of BSDEs.
method Modified damping and shifting schemes to transform target function into a bounded periodic function, applying Fourier transforms.
result Significant reduction in boundary errors with improved accuracy and convergence.
Online change detection algorithm using random Fourier features.
problem Online non-parametric change point detection in multivariate data streams.
method Sequential testing procedure based on random Fourier features.
result The algorithm has optimal detection delay in the minimax sense.
New Fourier transform method handles missing data and asynchronous observations.
problem Volatility inference with missing or asynchronous data.
method Spectral framework using Fourier transforms.
result Consistent volatility functional estimation with limit distributions.
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.
A new method integrates Fourier basis expansion and mapping for improved time series forecasting.
problem Inconsistent starting cycles and series length issues in Fourier-based methods.
method Fourier Basis Mapping (FBM) method that integrates time-frequency features through Fourier basis expansion and mapping.
result FBM addresses inconsistencies and preserves temporal characteristics, achieving SOTA performance.
This paper develops a bootstrap method to estimate errors in Random Fourier Features.
problem Inability to estimate the error of Random Fourier Features approximations.
method Develops a bootstrap approach to numerically estimate the errors of RFF approximations.
result Specific, flexible, and adaptive error estimates for RFF approximations.
The square root of Fredholm determinants causes numerical instabilities in option pricing models.
problem Numerical instabilities in Fourier-based option pricing for the Volterra Stein-Stein model.
method Characterization of determinant crossing behavior, derivation of transform to handle crossings, efficient algorithms.
result Significant improvement in accuracy and reduction in computational cost for Fourier-based pricing.
Paper variates Navier-Stokes-Fourier system for thermodynamic consistency.
problem Modeling compressible fluid dynamics with thermodynamic constraints.
method Variational discretization with discrete exterior calculus.
result Derives a nonholonomic variational integrator for NSF system.
Hybrid models forecast EPEC energy spot prices.
problem Forecasting energy spot prices in EPEC markets.
method Combining Naive, Fourier, ARMA/GARCH, mean-reversion, jump-diffusion, and RNN models.
result Improved accuracy in forecasting compared to individual models.
Paper proves Fourier transform for valuations, simplifying previous work.
problem Existence of isomorphism for translation-invariant smooth valuations.
method Directly describes Alesker's isomorphism in terms of Fourier transform on functions.
result Simple proofs of Alesker's Fourier transform properties, including a previously conjectured result.
Proposes a differentiable STFT for more efficient optimization of hop length.
problem Efficient optimization of hop length in STFT for better temporal control.
method Introduces a differentiable version of STFT with continuous hop length.
result Improves optimization methods like gradient descent for STFT.
In this paper we consider the problem of calculating the quantiles of a risky position, the dynamic of which is described as a continuous time regime-switching jump-diffusion, by using Fourier Transform methods. Furthermore, we study a classical option-based portfolio strategy which minimizes the Value-at-Risk of the h…
This paper compares hedging strategies for pegged FX markets using a RS model.
problem Hedging performance in pegged foreign exchange markets.
method Regime switching model, Fourier approach for calibration, exact and approximated delta hedging.
result Approximated RS delta hedge is a viable alternative to the exact RS delta hedge and significantly faster.
New Fourier features improve high-precision approximation in large-scale problems.
problem Designing scalable, high-precision Fourier features for large-scale kernel methods.
method Introducing a new family of quadrature rules that accurately approximate the Gaussian measure in higher dimensions.
result Improved approximation bounds with new Fourier features.
In this paper we propose a scalable version of a state-of-the-art deterministic time-invariant feature extraction approach based on consecutive changes of basis and nonlinearities, namely, the scattering network. The first focus of the paper is to extend the scattering network to allow the use of higher order nonlinear…
Spread options are a fundamental class of derivative contract written on multiple assets, and are widely used in a range of financial markets. There is a long history of approximation methods for computing such products, but as yet there is no preferred approach that is accurate, efficient and flexible enough to apply …
New algorithms learn sparse set functions in non-orthogonal Fourier bases.
problem Learning sparse set functions in non-orthogonal Fourier bases.
method Novel algorithms using non-orthogonal Fourier transforms.
result At most nk−klog2k+k queries for k non-zero Fourier coefficients. RFFNet scales kernel methods to large datasets by learning kernel relevance.
problem Scaling kernel methods to large datasets while maintaining interpretability.
method Designs random Fourier features for ARD kernels and uses first-order stochastic optimization for learning kernel relevances.
result RFFNet achieves low prediction error and identifies relevant features, leading to more interpretable solutions.