arXiv research

A new method slices and sums radial kernels faster.

RQMC improves QMC by providing practical error bounds for financial applications.

Generative moment matching networks (GMMNs) are introduced for generating quasi-random samples from multivariate models with any underlying copula in order to compute estimates under variance reduction. So far, quasi-random sampling for multivariate distributions required a careful design, exploiting specific propertie…

We consider the problem of improving the efficiency of randomized Fourier feature maps to accelerate training and testing speed of kernel methods on large datasets. These approximate feature maps arise as Monte Carlo approximations to integral representations of shift-invariant kernel functions (e.g., Gaussian kernel).…

Proposes QMC-based QSW for 3D SW distance.

This thesis advances algorithms and software for QMC, GP, and sciML.

Many machine learning problems involve Monte Carlo gradient estimators. As a prominent example, we focus on Monte Carlo variational inference (MCVI) in this paper. The performance of MCVI crucially depends on the variance of its stochastic gradients. We propose variance reduction by means of Quasi-Monte Carlo (QMC) sam…

Deep QMC ansatzes improve variational QMC accuracy.

This study compares MC and QMC methods for derivative pricing, showing QMC's superior convergence rates.

RQMC improves kernel-based learning by reducing deterministic error and offering computational advantages.

QMC and GSA improve option pricing and risk measures efficiency.

This study compares MC and QMC methods for likelihood functions.

We review and apply Quasi Monte Carlo (QMC) and Global Sensitivity Analysis (GSA) techniques to pricing and risk management (greeks) of representative financial instruments of increasing complexity. We compare QMC vs standard Monte Carlo (MC) results in great detail, using high-dimensional Sobol' low discrepancy sequen…

One of the main practical applications of quasi-Monte Carlo (QMC) methods is the valuation of financial derivatives. We aim to give a short introduction into option pricing and show how it is facilitated using QMC. We give some practical examples for illustration.

Deep QMC method accurately computes electronic excited states.

Improves QMC for complex distributions using transport maps.

Optimizes kernel discrepancies by selecting subsets efficiently.

Study compares MC and QMC methods for pricing and risk analysis in a hyperbolic local volatility model.

Large-scale kernel approximation is an important problem in machine learning research. Approaches using random Fourier features have become increasingly popular [Rahimi and Recht, 2007], where kernel approximation is treated as empirical mean estimation via Monte Carlo (MC) or Quasi-Monte Carlo (QMC) integration [Yang …

Quasi-Monte Carlo speeds up option Greeks calculation on GPUs.

Exciton diffusion plays a vital role in the function of many organic semiconducting opto-electronic devices, where an accurate description requires precise control of heterojunctions. This poses a challenging problem because the parameterization of heterojunctions in high-dimensional random space is far beyond the capa…

Deep QMC methods use neural networks to solve quantum chemistry problems.

Effective dimensionality reduction improves accuracy and reduces costs in estimating option Greeks.

We introduce efficient numerical methods for generic HJM equations of interest rate theory by means of high-order weak approximation schemes. These schemes allow for QMC implementations due to the relatively low dimensional integration space. The complexity of the resulting algorithm is considerably lower than the comp…

Many large scale problems in computational fluid dynamics such as uncertainty quantification, Bayesian inversion, data assimilation and PDE constrained optimization are considered very challenging computationally as they require a large number of expensive (forward) numerical solutions of the corresponding PDEs. We pro…

Spin-opstrings from QMC simulations enable ML of quantum phases.

New method smooths integrands for efficient option pricing.

Optimal fund deployment strategy under uncertain deal arrivals.

Data compression speeds up machine learning loss calculations.

Quantum algorithms speed up financial portfolio valuation.

Variational autoencoders (VAEs) are powerful generative models with the salient ability to perform inference. Here, we introduce a quantum variational autoencoder (QVAE): a VAE whose latent generative process is implemented as a quantum Boltzmann machine (QBM). We show that our model can be trained end-to-end by maximi…

In this paper, we introduce a novel and robust approach to Quantized Matrix Completion (QMC). First, we propose a rank minimization problem with constraints induced by quantization bounds. Next, we form an unconstrained optimization problem by regularizing the rank function with Huber loss. Huber loss is leveraged to c…

New model accurately predicts chemical bond breaking.

New method reduces variance in estimating PL model expectations.

The rough Bergomi (rBergomi) model, introduced recently in [5], is a promising rough volatility model in quantitative finance. It is a parsimonious model depending on only three parameters, and yet remarkably fits with empirical implied volatility surfaces. In the absence of analytical European option pricing methods f…

Quantum MC simulations generate financial risk distributions efficiently.

This paper surveys various methods for dimensionality reduction and nearest neighbor search.

The paper studies how norms of random vectors are preserved by random projections.

Orthogonal random features approximate a Bessel kernel, offering sharper bounds than random Fourier features.

New methods improve prediction performance and reduce computation time in boosting and random forest models.

Proposes a method for modeling random objects in metric spaces using random effects.

Enhances random forest performance with exogenous randomness.

New random forest method provides optimal rates and confidence bands.

Much is known about random right-angled Coxeter groups (i.e., right-angled Coxeter groups whose defining graphs are random graphs under the Erdös-Rényi model). In this paper, we extend this model to study random general Coxeter groups and give some results about random Coxeter groups, including some information about t…

Improved random forest proximities capture data geometry.

This work estimates edge weights of edge-reinforced random walks using observed data.

Paper proposes diagnostics for error and variance estimation in randomized matrix computations.

Random forests reduce bias and variance, especially in low SNR settings.