Quasi-random Monte Carlo application in CGE systematic sensitivity analysis

The uncertainty and robustness of Computable General Equilibrium models can be assessed by conducting a Systematic Sensitivity Analysis. Different methods have been used in the literature for SSA of CGE models such as Gaussian Quadrature and Monte Carlo methods. This paper explores the use of Quasi-random Monte Carlo methods based on the Halton and Sobol' sequences as means to improve the efficiency over regular Monte Carlo SSA, thus reducing the computational requirements of the SSA. The findings suggest that by using low-discrepancy sequences, the number of simulations required by the regular MC SSA methods can be notably reduced, hence lowering the computational time required for SSA of CGE models.Comment: 7 pages, 6 figures, Submitte

Application of Sequential Quasi-Monte Carlo to Autonomous Positioning

Sequential Monte Carlo algorithms (also known as particle filters) are popular methods to approximate filtering (and related) distributions of state-space models. However, they converge at the slow $1/\sqrt{N}$ rate, which may be an issue in real-time data-intensive scenarios. We give a brief outline of SQMC (Sequential Quasi-Monte Carlo), a variant of SMC based on low-discrepancy point sets proposed by Gerber and Chopin (2015), which converges at a faster rate, and we illustrate the greater performance of SQMC on autonomous positioning problems.Comment: 5 pages, 4 figure

Quasi-Monte Carlo Algorithms (not only) for Graphics Software

Quasi-Monte Carlo methods have become the industry standard in computer graphics. For that purpose, efficient algorithms for low discrepancy sequences are discussed. In addition, numerical pitfalls encountered in practice are revealed. We then take a look at massively parallel quasi-Monte Carlo integro-approximation for image synthesis by light transport simulation. Beyond superior uniformity, low discrepancy points may be optimized with respect to additional criteria, such as noise characteristics at low sampling rates or the quality of low-dimensional projections

A Tool for Custom Construction of QMC and RQMC Point Sets

We present LatNet Builder, a software tool to find good parameters for lattice rules, polynomial lattice rules, and digital nets in base 2, for quasi-Monte Carlo (QMC) and randomized quasi-Monte Carlo (RQMC) sampling over the s-dimensional unit hypercube. The selection criteria are figures of merit that give different weights to different subsets of coordinates. They are upper bounds on the worst-case error (for QMC) or variance (for RQMC) for integrands rescaled to have a norm of at most one in certain Hilbert spaces of functions. We summarize what are the various Hilbert spaces, discrepancies, types of weights, figures of merit, types of constructions, and search methods supported by LatNet Builder. We briefly discuss its organization and we provide simple illustrations of what it can do.NSERC Discovery Grant, IVADO Grant, Corps des Mines Stipend, ERDF, ESF, EXP. 2019/0043

Surrogate time series

Before we apply nonlinear techniques, for example those inspired by chaos theory, to dynamical phenomena occurring in nature, it is necessary to first ask if the use of such advanced techniques is justified "by the data". While many processes in nature seem very unlikely a priori to be linear, the possible nonlinear nature might not be evident in specific aspects of their dynamics. The method of surrogate data has become a very popular tool to address such a question. However, while it was meant to provide a statistically rigorous, foolproof framework, some limitations and caveats have shown up in its practical use. In this paper, recent efforts to understand the caveats, avoid the pitfalls, and to overcome some of the limitations, are reviewed and augmented by new material. In particular, we will discuss specific as well as more general approaches to constrained randomisation, providing a full range of examples. New algorithms will be introduced for unevenly sampled and multivariate data and for surrogate spike trains. The main limitation, which lies in the interpretability of the test results, will be illustrated through instructive case studies. We will also discuss some implementational aspects of the realisation of these methods in the TISEAN (http://www.mpipks-dresden.mpg.de/~tisean) software package.Comment: 28 pages, 23 figures, software at http://www.mpipks-dresden.mpg.de/~tisea

Simulation-free Schr\"odinger bridges via score and flow matching

We present simulation-free score and flow matching ([SF]$^2$M), a simulation-free objective for inferring stochastic dynamics given unpaired source and target samples drawn from arbitrary distributions. Our method generalizes both the score-matching loss used in the training of diffusion models and the recently proposed flow matching loss used in the training of continuous normalizing flows. [SF]$^2$M interprets continuous-time stochastic generative modeling as a Schr\"odinger bridge (SB) problem. It relies on static entropy-regularized optimal transport, or a minibatch approximation, to efficiently learn the SB without simulating the learned stochastic process. We find that [SF]$^2$M is more efficient and gives more accurate solutions to the SB problem than simulation-based methods from prior work. Finally, we apply [SF]$^2$M to the problem of learning cell dynamics from snapshot data. Notably, [SF]$^2$M is the first method to accurately model cell dynamics in high dimensions and can recover known gene regulatory networks from simulated data.Comment: A version of this paper appeared in the New Frontiers in Learning, Control, and Dynamical Systems workshop at ICML 2023. Code: https://github.com/atong01/conditional-flow-matchin