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.
Faster training of neural ODEs using Gauß-Legendre quadrature.
Regularization preserves topological data structure in autoencoders.
Study of contact whirl curves in Sasakian Lorentzian 3-manifolds.
QSurv models survival data without discretization, achieving high accuracy.
This paper applies an algorithm for the convolution of compactly supported Legendre series (the CONLeg method) (cf. Hale and Townsend 2014a), to pricing/hedging European-type, early-exercise and discrete-monitored barrier options under a Levy process. The paper employs Chebfun (cf. Trefethen et al. 2014) in computation…
In this paper we describe how one can obtain Lie group structures on the group of (vertical) bundle automorphisms for a locally convex principal bundle P over the compact manifold M. This is done by first considering Lie group structures on the group of vertical bundle automorphisms Gau(P). Then the full automorphism g…
The study examines Bertrand Legendre curves in the unit tangent bundle over Euclidean plane.
Paper defines curvature equivalence for Legendre curves in a plane.
New quadrature method using randomly pivoted Cholesky outperforms existing techniques.
A geometrization of Schmidt-Legendre transformation of the second order Lagrangians is proposed by building a proper Tulczyjew's triplet. The symplectic relation between Ostrogradsky-Legendre and Schmidt-Legendre transformations is obtained. Several examples are presented.
Legendre transformations link related integrable hierarchies.
The paper characterizes Legendre curves on trans-S-manifolds.
This paper classifies Legendre singularities of sub-Riemannian geodesics on surfaces.
Bayesian quadrature uses probabilistic models for estimating intractable integrals.
Characterizes the Legendre involution on generic frontals.
We consider interpolating sesqui-harmonic Legendre curves in Sasakian space forms. We find the necessary and sufficient conditions for Legendre curves in Sasakian space forms to be interpolating sesqui-harmonic. Finally, we obtain an example for an interpolating sesqui-harmonic Legendre curve in a Sasakian space form.
SOBER optimizes and quadrates efficiently in parallel for diverse tasks.
Introduces Legendre bundle for dually flat manifolds and quantum field theories.
This paper presents a convergence analysis of kernel-based quadrature rules in misspecified settings, focusing on deterministic quadrature in Sobolev spaces. In particular, we deal with misspecified settings where a test integrand is less smooth than a Sobolev RKHS based on which a quadrature rule is constructed. We pr…
Improved Gaussian Process regression using TQFF over RFF and Gaussian QFF.
We study quadrature rules for functions from an RKHS, using nodes sampled from a determinantal point process (DPP). DPPs are parametrized by a kernel, and we use a truncated and saturated version of the RKHS kernel. This link between the two kernels, along with DPP machinery, leads to relatively tight bounds on the qua…
Bayesian quadrature improves integration efficiency with invariant priors.
Herding and kernel herding are deterministic methods of choosing samples which summarise a probability distribution. A related task is choosing samples for estimating integrals using Bayesian quadrature. We show that the criterion minimised when selecting samples in kernel herding is equivalent to the posterior varianc…
Herding and kernel herding are deterministic methods of choosing samples which summarise a probability distribution. A related task is choosing samples for estimating integrals using Bayesian quadrature. We show that the criterion minimised when selecting samples in kernel herding is equivalent to the posterior varianc…
Improved kernel quadrature with convex weights using subsampling.
A new type of quadrature is developed. The Gaussian quadrature, for a given measure, finds optimal values of a function's argument (nodes) and the corresponding weights. In contrast, the Lebesgue quadrature developed in this paper, finds optimal values of function (value-nodes) and the corresponding weights. The Gaussi…
The sigma-point filters, such as the UKF, which exploit numerical quadrature to obtain an additional order of accuracy in the moment transformation step, are popular alternatives to the ubiquitous EKF. The classical quadrature rules used in the sigma-point filters are motivated via polynomial approximation of the integ…
The report analyzes Legendre decomposition for tensor data.
A new family of conformal test martingales based on Legendre polynomials for online exchangeability testing.
The paper studies a flow of Legendre curves, generalizing the inverse curvature flow of regular curves.
In this study, a numerical quadrature for the generalized inverse Gaussian distribution is derived from the Gauss-Hermite quadrature by exploiting its relationship with the normal distribution. The proposed quadrature is not Gaussian, but it exactly integrates the polynomials of both positive and negative orders. Using…
We introduce complex generalizations of the classical Legendre transform, operating on Kähler metrics on a compact complex manifold. These Legendre transforms give explicit local isometric symmetries for the Mabuchi metric on the space of Kähler metrics around any real analytic Kähler metric, answering a question origi…
Paper solves recovery of parametrizations from Legendre data.
Adaptive Bayesian quadrature (ABQ) is a powerful approach to numerical integration that empirically compares favorably with Monte Carlo integration on problems of medium dimensionality (where non-adaptive quadrature is not competitive). Its key ingredient is an acquisition function that changes as a function of previou…
The aim of this article is to design a moment transformation for Student- t distributed random variables, which is able to account for the error in the numerically computed mean. We employ Student-t process quadrature, an instance of Bayesian quadrature, which allows us to treat the integral itself as a random variable…
Legendre curves are smooth plane curves which may have singular points, but still have a well defined smooth normal (and corresponding tangent) vector field. Because of the existence of singular points, the usual curvature concept for regular curves cannot be straightforwardly extended to these curves. However, Fukunag…
Following Burstall and Hertrich-Jeromin we study the Ribaucour transformation of Legendre submanifolds in Lie sphere geometry. We give an explicit parametrization of the resulted Legendre submanifold of a Ribaucour transformation, via a single real function which represents the regular Ribaucour sphere co…
We propose a method for inferring the conditional indepen- dence graph (CIG) of a high-dimensional discrete-time Gaus- sian vector random process from finite-length observations. Our approach does not rely on a parametric model (such as, e.g., an autoregressive model) for the vector random process; rather, it only assu…
We obtain geometric characterizations of isospectral minimal Riemannian Legendre foliations on compact Sasakian manifolds of constant -sectional curvature.
Unified quadrature framework for large-scale kernel machines.
In some previous papers, a Legendre duality between Lagrangian and Hamiltonian Mechanics has been developed. The (ρ,η)-tangent application of the Legendre bundle morphism associated to a Lagrangian L or Hamiltonian H is presented. Using that, a Legendre description of Lagrangian Mechanics and Hamiltonian Mechanics is d…
We present a novel nonnegative tensor decomposition method, called Legendre decomposition, which factorizes an input tensor into a multiplicative combination of parameters. Thanks to the well-developed theory of information geometry, the reconstructed tensor is unique and always minimizes the KL divergence from an inpu…
This paper introduces repulsive Monte Carlo methods for computing the sliced Wasserstein distance.
Novel approach for estimating conditional expectations using Bayesian quadrature.
New Fourier features improve high-precision approximation in large-scale problems.
The Runge-Kutta-Legendre scheme improves pricing American options and other derivatives.
The general framework of Legendre transformation is extended to the case of symplectic groupoids, using an appropriate generalization of the notion of generating function (of a Lagrangian submanifold).
Improved Nyström approximation for kernel quadrature with theoretical guarantees.