arXiv research

Deep QMC ansatzes improve variational QMC accuracy.

Deep QMC method accurately computes electronic excited states.

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…

A new method slices and sums radial kernels faster.

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

QMC and GSA improve option pricing and risk measures efficiency.

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…

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…

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…

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.

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

Improves QMC for complex distributions using transport maps.

Optimizes kernel discrepancies by selecting subsets efficiently.

Proposes QMC-based QSW for 3D SW distance.

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

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

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).…

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

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

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.

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

Optimal fund deployment strategy under uncertain deal arrivals.

Data compression speeds up machine learning loss calculations.

Quantum algorithms speed up financial portfolio valuation.

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…

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 …

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

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.

New variational principle found for non-variational differential equations.

Derives Lagrangian for minimal surfaces, proving tangential variations vanish.

Improved Bayesian uncertainty quantification using variational bagging.

This work improves variational inference by reducing gradient variance.

Adaptive variational Bayes framework improves inference adaptively.

A new EVI framework improves ParVI methods by maintaining variational structure and reducing KL-divergence.

We propose a family of variational approximations to Bayesian posterior distributions, called $α$-VB, with provable statistical guarantees. The standard variational approximation is a special case of $α$-VB with $α=1$. When $α\in(0,1]$, a novel class of variational inequalities are developed for linking the Bayes risk …

New examples of variational bivectors found that are not Poissonian.

Variational Prediction simplifies Bayesian inference without test time costs.

Improved VAE estimation from incomplete data using variational mixtures.

In the paper "On Truncated Variation of Brownian Motion with Drift" (Bull. Pol. Acad. Sci. Math. 56 (2008), no.4, 267 - 281) we defined truncated variation of Brownian motion with drift, $W_t = B_t + μt, t\geq 0,$ where $(B_t)$ is a standard Brownian motion. Truncated variation differs from regular variation by neglect…

Semi-Implicit Variational Inference (SIVI) is improved with SIVI-SM using score matching.