arXiv research

Deep QMC ansatzes improve variational QMC accuracy.

Deep QMC method accurately computes electronic excited states.

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

A new method slices and sums radial kernels faster.

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

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…

Proposes QMC-based QSW for 3D SW distance.

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…

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.

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…

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.

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.

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…

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…

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.

New model accurately predicts chemical bond breaking.

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…

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 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.

Probabilistic deep learning uses neural networks and models to handle uncertainty.

Improves deep learning robustness by considering task and model.

Deep-RLS uses deep learning to improve PCA for better source separation.

How to understand deep learning systems remains an open problem. In this paper we propose that the answer may lie in the geometrization of deep networks. Geometrization is a bridge to connect physics, geometry, deep network and quantum computation and this may result in a new scheme to reveal the rule of the physical w…

Deep SSMs use neural networks to identify complex systems.

This paper presents a basic property of region dividing of ReLU (rectified linear unit) deep learning when new layers are successively added, by which two new perspectives of interpreting deep learning are given. The first is related to decision trees and forests; we construct a deep learning structure equivalent to a …

The great success of deep learning shows that its technology contains profound truth, and understanding its internal mechanism not only has important implications for the development of its technology and effective application in various fields, but also provides meaningful insights into the understanding of human brai…

Bayesian methods enhance deep learning models by improving reliability and uncertainty.

Deep residual networks (ResNets) have demonstrated better generalization performance than deep feedforward networks (FFNets). However, the theory behind such a phenomenon is still largely unknown. This paper studies this fundamental problem in deep learning from a so-called "neural tangent kernel" perspective. Specific…

NeurIPS 2020 competition seeks to predict deep learning generalization.

This paper analyzes generalization issues in deep reinforcement learning.

This paper provides an overview of deep semi-supervised learning methods.