A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
A new density model using Fourier basis achieves better approximations and compression.
A new method integrates Fourier basis expansion and mapping for improved time series forecasting.
Derives representations invariant under crystallographic groups for functions.
New Fourier analysis method for non-uniform Boolean hypercube.
Enhances Fourier estimator performance for asynchronous event-data.
It is a known fact that training recurrent neural networks for tasks that have long term dependencies is challenging. One of the main reasons is the vanishing or exploding gradient problem, which prevents gradient information from propagating to early layers. In this paper we propose a simple recurrent architecture, th…
New method embeds correlation networks to reveal underlying time series patterns.
We develop Fourier methods to expand translation-invariant kernels.
We introduce a novel harmonic analysis for functions defined on the vertices of a strongly connected directed graph of which the random walk operator is the cornerstone. As a first step, we consider the set of eigenvectors of the random walk operator as a non-orthogonal Fourier-type basis for functions over directed gr…
We study estimation of (semi-)inner products between two nonparametric probability distributions, given IID samples from each distribution. These products include relatively well-studied classical and Sobolev inner products, as well as those induced by translation-invariant reproducing kernels, for whic…
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…
This paper analyzes SHAP values using Fourier expansions for model interpretability.
New method uses tensor decompositions to overcome the curse of dimensionality for large-scale learning.
New method combines spectral and sparse methods for Gaussian processes.
Stochastic control problems in finance often involve complex controls at discrete times. As a result numerically solving such problems, for example using methods based on partial differential or integro-differential equations, inevitably give rise to low order accuracy, usually at most second order. In many cases one c…
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…
RP-GFRFT unifies fractional order and rotation control for graph signals.
Proposes a framework to predict stock movements by integrating multi-order and internal dynamics.
Localized signal representation on graph bundles using Fourier analysis.
We introduce a multiple curve framework that combines tractable dynamics and semi-analytic pricing formulas with positive interest rates and basis spreads. Negatives rates and positive spreads can also be accommodated in this framework. The dynamics of OIS and LIBOR rates are specified following the methodology of the …
New algorithm trains deep neural networks without global optimization.
Study bounds Rademacher complexity of Fourier neural operators.
This paper has proposed a new baseline deep learning model of more benefits for image classification. Different from the convolutional neural network(CNN) practice where filters are trained by back propagation to represent different patterns of an image, we are inspired by a method called "PCANet" in "PCANet: A Simple …
We propose Absum, which is a regularization method for improving adversarial robustness of convolutional neural networks (CNNs). Although CNNs can accurately recognize images, recent studies have shown that the convolution operations in CNNs commonly have structural sensitivity to specific noise composed of Fourier bas…
Subspace recovery from corrupted and missing data is crucial for various applications in signal processing and information theory. To complete missing values and detect column corruptions, existing robust Matrix Completion (MC) methods mostly concentrate on recovering a low-rank matrix from few corrupted coefficients w…
Spectral methods predict long-term signals from linear and nonlinear systems.
Reconstruction of density functions and their characteristic functions by radial basis functions with scattered data points is a popular topic in the theory of pricing of basket options. Such functions are usually entire or admit an analytic extension into an appropriate tube and "bell-shaped" with rapidly decaying tai…
We study the problem of independence testing given independent and identically distributed pairs taking values in a -finite, separable measure space. Defining a natural measure of dependence as the squared -distance between a joint density and the product of its marginals, we first show that there is…
A machine learning method selects optimal orthonormal bases for functional data analysis.
mcanalysis quantifies menstrual cycle effects in health data.
Paper integrates real data into probabilistic models using Fourier transform.
FMMNN combines sine activations with multi-component, multi-layer structure for high-frequency function approximation.
A common assumption in semi-supervised learning with graph models is that the class label function varies smoothly on the data graph, resulting in the rather strict prior that the label function has low-frequency content. Meanwhile, in many classification problems, the label function may vary abruptly in certain graph …
We introduce the convolutional spectral kernel (CSK), a novel family of non-stationary, nonparametric covariance kernels for Gaussian process (GP) models, derived from the convolution between two imaginary radial basis functions. We present a principled framework to interpret CSK, as well as other deep probabilistic mo…
Model forecasts natural gas consumption with Fourier series and feedback.
Compressive sensing (CS) has been studied and applied in structural health monitoring for wireless data acquisition and transmission, structural modal identification, and spare damage identification. The key issue in CS is finding the optimal solution for sparse optimization. In the past years, many algorithms have bee…
Introduces a neural network-based method for efficient state and parameter estimation in complex systems.
FEDformer combines Transformer with seasonal-trend decomposition for efficient long-term forecasting.
Unified diffusion framework enhances generative models flexibility.
We study the geometry of infinitely presented groups satisfying the small cancelation condition C'(1/8), and define a standard decomposition (called the criss-cross decomposition) for the elements of such groups. We use it to prove the Rapid Decay property for groups with the stronger small cancelation property C'(1/10…
Recent deep learning approaches have achieved impressive performance on speech enhancement and separation tasks. However, these approaches have not been investigated for separating mixtures of arbitrary sounds of different types, a task we refer to as universal sound separation, and it is unknown how performance on spe…
Paper proves Fourier transform for valuations, simplifying previous work.
New algorithms learn sparse set functions in non-orthogonal Fourier bases.
Improved SVM classification with interpretable features from scattered data.
New Hilbert bundles with ends defined from indexed bases.
A new algorithm computes Fourier coefficients for a specified range efficiently.
Enhances privacy in federated learning with Laplacian smoothing.
Establish a unified framework for negative results in Fourier analysis.