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.
New Krylov subspace methods speed up mixed-effects models with crossed random effects.
We analyze the Hessian spectra of large models up to 100B parameters.
HessFormer enables distributed Hessian computation for large models.
Unified quadrature framework for large-scale kernel machines.
New insights into learning rates and batch sizes for neural networks using random matrix theory.
For applications as varied as Bayesian neural networks, determinantal point processes, elliptical graphical models, and kernel learning for Gaussian processes (GPs), one must compute a log determinant of an positive definite matrix, and its derivatives - leading to prohibitive computatio…
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…
A new method calculates accurate SABR model option prices and deltas.
New filters improve radar target inference in complex scenarios.
Efficiently differentiate functions of large matrices using new adjoint systems.
Botnet, a group of coordinated bots, is becoming the main platform of malicious Internet activities like DDOS, click fraud, web scraping, spam/rumor distribution, etc. This paper focuses on design and experiment of a new approach for botnet detection from streaming web server logs, motivated by its wide applicability, …
Principal component analysis (PCA) is one of the most powerful tools in machine learning. The simplest method for PCA, the power iteration, requires full-data passes to recover the principal component of a matrix with eigen-gap . Lanczos, a significantly more complex method, achieves an accelerated…
We propose the Lanczos network (LanczosNet), which uses the Lanczos algorithm to construct low rank approximations of the graph Laplacian for graph convolution. Relying on the tridiagonal decomposition of the Lanczos algorithm, we not only efficiently exploit multi-scale information via fast approximated computation of…
Efficient method for lookback option pricing under Markov models.
A new method tackles bilevel optimization using Lanczos process for efficient hyper-gradient computation.
Combines control variates and adaptive importance sampling for Monte Carlo integration.
This work learns models for population dynamics using variational methods and higher-order quadrature.
Improved option pricing for SABR model using Gauss-Hermite quadrature.
New quadrature method using randomly pivoted Cholesky outperforms existing techniques.
Bayesian quadrature uses probabilistic models for estimating intractable integrals.
SOBER optimizes and quadrates efficiently in parallel for diverse tasks.
The study examines algebraic structures of specific tensor forms in four-dimensional spacetimes.
The paper addresses numerical integration issues in SV models, proposing a fast regime switching algorithm.
One of the most compelling features of Gaussian process (GP) regression is its ability to provide well-calibrated posterior distributions. Recent advances in inducing point methods have sped up GP marginal likelihood and posterior mean computations, leaving posterior covariance estimation and sampling as the remaining …
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.
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…
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…
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…
New recommendations improve Gaussian process accuracy and stability.
The runtime for Kernel Partial Least Squares (KPLS) to compute the fit is quadratic in the number of examples. However, the necessity of obtaining sensitivity measures as degrees of freedom for model selection or confidence intervals for more detailed analysis requires cubic runtime, and thus constitutes a computationa…
New method smooths integrands for efficient option pricing.
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…
The paper analyzes contraction rates for GP regression approximations.
Deep Curvature Suite offers a PyTorch package for neural network curvature analysis.
This paper introduces repulsive Monte Carlo methods for computing the sliced Wasserstein distance.
The purpose if this master's thesis is to study and develop a new algorithmic framework for Collaborative Filtering to produce recommendations in the top-N recommendation problem. Thus, we propose Lanczos Latent Factor Recommender (LLFR); a novel "big data friendly" collaborative filtering algorithm for top-N recommend…
Novel approach for estimating conditional expectations using Bayesian quadrature.
New Fourier features improve high-precision approximation in large-scale problems.
Improved Nyström approximation for kernel quadrature with theoretical guarantees.
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 …
Parallelized Bayesian quadrature improves sample efficiency and inference.