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.
Revisits stochastic collocation with exponential splines for option pricing.
Combines spline interpolation and ARIMA for stock market forecasting.
Cubic spline smoothing improves interpolation between irregularly sampled data.
Paper finds maximum curvature of Bézier-spline curves.
This paper presents an efficient algorithm for evolving point cloud data on smooth manifolds using B-Splines.
A new method evolves point clouds using B-splines for smooth surfaces.
The paper proposes a new method for density estimation using spline quasi-interpolation for clustering.
This paper develops a new method for constructing splines on Lie groups using Poisson equation solutions.
This paper constructs PH spline curves with prescribed arc lengths.
This note is the updated outline of the article "Interpolational properties of planar spiral curves", Fund. and Applied Math., 2001, Vol.7, N.2, 441-463, published in Russian. The main result establishes boundary regions for spiral and piecewise spiral splines, matching given data. The width of such region can serve as…
Paper proves regularity and existence of Riemannian splines.
Cubic spline interpolation on Euclidean space is a standard topic in numerical analysis, with countless applications in science and technology. In several emerging fields, for example computer vision and quantum control, there is a growing need for spline interpolation on curved, non-Euclidean space. The generalization…
A comprehensive methodology is provided for smoothing noisy, irregularly sampled data with non-Gaussian noise using smoothing splines. We demonstrate how the spline order and tension parameter can be chosen a priori from physical reasoning. We also show how to allow for non-Gaussian noise and outliers which are typical…
A new method optimizes knot selection for spline dimensional decomposition in stochastic dynamic analysis.
Study reconstructs Faber-Schauder coefficients from antiderivative observations.
We present a theoretical and empirical study of the gradient dynamics of overparameterized shallow ReLU networks with one-dimensional input, solving least-squares interpolation. We show that the gradient dynamics of such networks are determined by the gradient flow in a non-redundant parameterization of the network fun…
We propose a novel method to determine the dissimilarity between subjects for functional data clustering. Spline smoothing or interpolation is common to deal with data of such type. Instead of estimating the best-representing curve for each subject as fixed during clustering, we measure the dissimilarity between subjec…
Approximates nonlocal curvature of curves using splines.
Neural networks require a careful design in order to perform properly on a given task. In particular, selecting a good activation function (possibly in a data-dependent fashion) is a crucial step, which remains an open problem in the research community. Despite a large amount of investigations, most current implementat…
Gradient descent training of neural networks leads to solutions close to natural cubic splines.
In this paper, we consider one dimensional (shallow) ReLU neural networks in which weights are chosen randomly and only the terminal layer is trained. First, we mathematically show that for such networks L2-regularized regression corresponds in function space to regularizing the estimate's second derivative for fairly …
NQE uses quantile regression for fast SBI with cubic Hermite splines.
Piecewise polynomial interpolation-based gradient descent reduces oracle complexity for smooth loss functions.
For a wide range of clinical applications, such as adaptive treatment planning or intraoperative image update, feature-based deformable registration (FDR) approaches are widely employed because of their simplicity and low computational complexity. FDR algorithms estimate a dense displacement field by interpolating a sp…
There is a vast literature on numerical valuation of exotic options using Monte Carlo, binomial and trinomial trees, and finite difference methods. When transition density of the underlying asset or its moments are known in closed form, it can be convenient and more efficient to utilize direct integration methods to ca…
{\em Riemannian cubics} are curves in a manifold that satisfy a variational condition appropriate for interpolation problems. When is the rotation group SO(3), Riemannian cubics are track-summands of {\em Riemannian cubic splines}, used for motion planning of rigid bodies. Partial integrability results are know…
New boundary and point constraints for controlling conformal surfaces.
This research uses DPPs to improve semi-parametric regression models.
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…
Kolmogorov-Arnold Networks promise scalable performance in high dimensions.
In this paper, we review pricing of variable annuity living and death guarantees offered to retail investors in many countries. Investors purchase these products to take advantage of market growth and protect savings. We present pricing of these products via an optimal stochastic control framework, and review the exist…
Kronecker trend filtering improves lattice data smoothing.
Proposes a model to handle mobile health data with irregular measurements.
We consider the question of what functions can be captured by ReLU networks with an unbounded number of units (infinite width), but where the overall network Euclidean norm (sum of squares of all weights in the system, except for an unregularized bias term for each unit) is bounded; or equivalently what is the minimal …
Improves spline quality and accuracy in computational microscopy.
This paper studies the application of machine learning in extracting the market implied features from historical risk neutral corporate bond yields. We consider the example of a hypothetical illiquid fixed income market. After choosing a surrogate liquid market, we apply the Denoising Autoencoder algorithm from the fie…
Sig-Splines model uses signatures and splines for time series data, achieving universality and convexity.
Deep learning improves model discovery from sparse sensor data.
We extend the adaptive regression spline model by incorporating saturation, the natural requirement that a function extend as a constant outside a certain range. We fit saturating splines to data using a convex optimization problem over a space of measures, which we solve using an efficient algorithm based on the condi…
With the renewed and growing interest in geometric continuity in mind, this article gives a general definition of geometrically continuous polygonal surfaces and geometrically continuous spline functions on them. Polynomial splines defined by G1 gluing data in terms of rational functions are analyzed further. A general…
Sinh-acceleration speeds up B-spline option pricing.
A new nonparametric approach for system identification has been recently proposed where the impulse response is seen as the realization of a zero--mean Gaussian process whose covariance, the so--called stable spline kernel, guarantees that the impulse response is almost surely stable. Maximum entropy properties of the …
A new spline method for manifold learning using Hessian-based curvature penalties.
Locally-verifiable conditions ensure exactness of spline discrete de Rham complex.
We use splines and the Sasaki metric to analyze and compare manifold-valued trajectories.
We reparametrize ReLU NNs as splines to understand their learning dynamics.
Smoothing splines provide a powerful and flexible means for nonparametric estimation and inference. With a cubic time complexity, fitting smoothing spline models to large data is computationally prohibitive. In this paper, we use the theoretical optimal eigenspace to derive a low rank approximation of the smoothing spl…
Forecast stock return distributions using neural networks.