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 spline method for manifold learning using Hessian-based curvature penalties.
Generative networks are analyzed using spline operators to understand their properties and limitations.
In this article, we start to recall the inversion formula for the convolution with the Box spline. The equivariant cohomology and the equivariant K-theory with respect to a compact torus G of various spaces associated to a linear action of G in a vector space M can be both described using some vector spaces of distribu…
The aim of this paper is to propose an operational two-dimensional parametric adjustment for laws of maintenance in disability. The method suggested rests on splines in dimension 2; it is applied to a real data set, and the scale of reserving which results from it is compared with the scale of reference of the BCAC.
We build a rigorous bridge between deep networks (DNs) and approximation theory via spline functions and operators. Our key result is that a large class of DNs can be written as a composition of max-affine spline operators (MASOs), which provide a powerful portal through which to view and analyze their inner workings. …
Prediction of dynamical time series with additive noise using support vector machines or kernel based regression has been proved to be consistent for certain classes of discrete dynamical systems. Consistency implies that these methods are effective at computing the expected value of a point at a future time given the …
Paper finds maximum curvature of Bézier-spline curves.
Revisits stochastic collocation with exponential splines for option pricing.
Kronecker trend filtering improves lattice data smoothing.
Paper proves regularity and existence of Riemannian splines.
Improves spline quality and accuracy in computational microscopy.
New method speeds up sparse Gaussian processes for large datasets.
This paper develops a new method for constructing splines on Lie groups using Poisson equation solutions.
Sig-Splines model uses signatures and splines for time series data, achieving universality and convexity.
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…
New method adds interactions to interpretable models for large-scale data.
Sinh-acceleration speeds up B-spline option pricing.
Combines spline interpolation and ARIMA for stock market forecasting.
A new method evolves point clouds using B-splines for smooth surfaces.
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 …
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.
Cubic spline smoothing improves interpolation between irregularly sampled data.
We reparametrize ReLU NNs as splines to understand their learning dynamics.
We will discuss the equivariant cohomology of a manifold endowed with the action of a Lie group. Localization formulae for equivariant integrals are explained by a vanishing theorem for equivariant cohomology with generalized coefficients. We then give applications to integration of characteristic classes on symplectic…
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…
This paper is devoted to the application of B-splines to volatility modeling, specifically the calibration of the leverage function in stochastic local volatility models and the parameterization of an arbitrage-free implied volatility surface calibrated to sparse option data. We use an extension of classical B-splines …
This paper introduces a spline-based method for nonparametric ADVI that handles complex posterior distributions.
The paper introduces a spline-based method for calibrating neural networks.
Multivariate splines linked to infinitely-wide neural networks with improved numerical performance.
Let G be a connected compact Lie group acting on a manifold M and let D be a transversally elliptic operator on M. The multiplicity of the index of D is a function on the set of irreducible representations of G. Let T be a maximal torus of G with Lie algebra Lie(T). We construct a finite number of piecewise polynomial …
Quantum walks blend patterns into splines when averaged.
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…
Regularized least-squares approaches have been successfully applied to linear system identification. Recent approaches use quadratic penalty terms on the unknown impulse response defined by stable spline kernels, which control model space complexity by leveraging regularity and bounded-input bounded-output stability. T…
We study Tikhonov regularization for solving ill--posed operator equations where the solutions are functions defined on surfaces. One contribution of this paper is an error analysis of Tikhonov regularization which takes into account perturbations of the surfaces, in particular when the surfaces are approximated by spl…
A new modeling framework CSN simplifies and interprets machine learning models.
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…
This paper presents an efficient algorithm for evolving point cloud data on smooth manifolds using B-Splines.
Cardiac motion modeling using LDDMM and shape splines.
Gaussian processes are the leading class of distributions on random functions, but they suffer from well known issues including difficulty scaling and inflexibility with respect to certain shape constraints (such as nonnegativity). Here we propose Deep Random Splines, a flexible class of random functions obtained by tr…
Improves BN graph learning with splines for scalability.
Bayesian nonparametric LABS model adapts to function smoothness in Besov spaces.
Researchers modify distance to handle long, thin splines.
Deep neural networks (DNNs) generate much richer function spaces than shallow networks. Since the function spaces induced by shallow networks have several approximation theoretic drawbacks, this explains, however, not necessarily the success of deep networks. In this article we take another route by comparing the expre…
The paper addresses optimal control on Riemannian manifolds, introducing biased splines for robotic systems.
We study trend filtering, a recently proposed tool of Kim et al. [SIAM Rev. 51 (2009) 339-360] for nonparametric regression. The trend filtering estimate is defined as the minimizer of a penalized least squares criterion, in which the penalty term sums the absolute th order discrete derivatives over the input points…
A normalizing flow models a complex probability density as an invertible transformation of a simple base density. Flows based on either coupling or autoregressive transforms both offer exact density evaluation and sampling, but rely on the parameterization of an easily invertible elementwise transformation, whose choic…