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.
Unified quadrature framework for large-scale kernel machines.
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…
New Fourier features improve high-precision approximation in large-scale problems.
Improved Gaussian Process regression using TQFF over RFF and Gaussian QFF.
Improved kernel quadrature with convex weights using subsampling.
Improved kernel herding algorithm for faster quadrature rule convergence.
New quadrature method using randomly pivoted Cholesky outperforms existing techniques.
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…
Kernel-based quadrature rules are becoming important in machine learning and statistics, as they achieve super- convergence rates in numerical integration, and thus provide alternatives to Monte Carlo integration in challenging settings where integrands are expensive to evaluate or where integrands are high d…
Combines control variates and adaptive importance sampling for Monte Carlo integration.
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…
Computation of moments of transformed random variables is a problem appearing in many engineering applications. The current methods for moment transformation are mostly based on the classical quadrature rules which cannot account for the approximation errors. Our aim is to design a method for moment transformation for …
A new method optimizes Fourier pricing for multi-asset options using adaptive quadrature.
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…
This article is concerned with Gaussian process quadratures, which are numerical integration methods based on Gaussian process regression methods, and sigma-point methods, which are used in advanced non-linear Kalman filtering and smoothing algorithms. We show that many sigma-point methods can be interpreted as Gaussia…
We propose and analyze numerical methods for the Heath-Jarrow-Morton (HJM) model. To construct the methods, we first discretize the infinite dimensional HJM equation in maturity time variable using quadrature rules for approximating the arbitrage-free drift. This results in a finite dimensional system of stochastic dif…
We propose an offline-online procedure for Fourier transform based option pricing. The method supports the acceleration of such essential tasks of mathematical finance as model calibration, real-time pricing, and, more generally, risk assessment and parameter risk estimation. We adapt the empirical magic point interpol…
Efficiently approximates kernel mean embeddings using Nyström method.
Adaptive quadrature improves Bayesian inference through active learning.
We show that kernel-based quadrature rules for computing integrals can be seen as a special case of random feature expansions for positive definite kernels, for a particular decomposition that always exists for such kernels. We provide a theoretical analysis of the number of required samples for a given approximation e…
The paper explores how control variates can reduce variance in Monte Carlo simulations, especially for Sobolev functions.
New methods for Bayesian inference using mean shift particle systems.
Factor graphs have recently gained increasing attention as a unified framework for representing and constructing algorithms for signal processing, estimation, and control. One capability that does not seem to be well explored within the factor graph tool kit is the ability to handle deterministic nonlinear transformati…
With the aid of concrete examples, we consider the question of whether, in the presence of conformal curvature, a conformal geodesic can become trapped in smaller and smaller sets, or phrased informally: are spirals possible? We do not arrive at a definitive answer, but we are able to find situations where this behavio…
Bayesian quadrature uses probabilistic models for estimating intractable integrals.
Efficiently calculates privacy guarantees for 2020 Census data.
This work learns models for population dynamics using variational methods and higher-order quadrature.
SOBER optimizes and quadrates efficiently in parallel for diverse tasks.
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…
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…
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…
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…
The Artificial Prediction Market is a recent machine learning technique for multi-class classification, inspired from the financial markets. It involves a number of trained market participants that bet on the possible outcomes and are rewarded if they predict correctly. This paper generalizes the scope of the Artificia…
This paper introduces repulsive Monte Carlo methods for computing the sliced Wasserstein distance.
Novel approach for estimating conditional expectations using Bayesian quadrature.
Improved Nyström approximation for kernel quadrature with theoretical guarantees.
Parallelized Bayesian quadrature improves sample efficiency and inference.
A new method slices and sums radial kernels faster.
New approach improves computational efficiency of Bass Local Volatility model.
A new method calculates accurate SABR model option prices and deltas.
DBQPG improves policy gradient estimation with fewer samples.
Bayesian quadrature improves conformal prediction for better risk assessment.
Efficiently marginalizes over Gaussian Process kernels for better model flexibility and uncertainty.
The paper improves error bounds for Bayesian quadrature in noisy settings.
Bayesian Quadrature improves ensembling for neural networks with dispersed likelihood peaks.
Developed a monotone numerical method for MV portfolio optimization under jump-diffusion models.