Fabian Bastin

h-index15
2papers
682citations

2 Papers

9.8MLFeb 17, 2023Code
Copula-based transferable models for synthetic population generation

Pascal Jutras-Dubé, Mohammad B. Al-Khasawneh, Zhichao Yang et al.

Population synthesis involves generating synthetic yet realistic representations of a target population of micro-agents for behavioral modeling and simulation. Traditional methods, often reliant on target population samples, such as census data or travel surveys, face limitations due to high costs and small sample sizes, particularly at smaller geographical scales. We propose a novel framework based on copulas to generate synthetic data for target populations where only empirical marginal distributions are known. This method utilizes samples from different populations with similar marginal dependencies, introduces a spatial component into population synthesis, and considers various information sources for more realistic generators. Concretely, the process involves normalizing the data and treating it as realizations of a given copula, and then training a generative model before incorporating the information on the marginals of the target population. Utilizing American Community Survey data, we assess our framework's performance through standardized root mean squared error (SRMSE) and so-called sampled zeros. We focus on its capacity to transfer a model learned from one population to another. Our experiments include transfer tests between regions at the same geographical level as well as to lower geographical levels, hence evaluating the framework's adaptability in varied spatial contexts. We compare Bayesian Networks, Variational Autoencoders, and Generative Adversarial Networks, both individually and combined with our copula framework. Results show that the copula enhances machine learning methods in matching the marginals of the reference data. Furthermore, it consistently surpasses Iterative Proportional Fitting in terms of SRMSE in the transferability experiments, while introducing unique observations not found in the original training sample.

3.5OCJun 29
A survey of trust-region radius update mechanisms. Part I: First-order analysis

Jérémy Rieussec, Fabian Bastin

We isolate three structural conditions on trust-region radius update rules for smooth unconstrained nonlinear optimisation, and study the class of mechanisms they define. The conditions act on the radius directly: a lower bound relative to the gradient norm, a contraction on unsuccessful iterations, and a controlled expansion on successful ones. A mechanism is \emph{weakly admissible} if it satisfies the first two conditions, and \emph{strongly admissible} if it satisfies the lower bound together with the controlled-expansion condition. Under uniformly bounded model Hessians, weak admissibility yields $\lim_{k\to\infty}\|\nabla f(x_k)\|=0$, and strong admissibility yields the optimal worst-case complexity $O(ε^{-2})$ for first-order stationarity. Strong admissibility extends the convergence guarantee to linearly growing model Hessians. We verify admissibility for five mechanism classes: fixed-factor, step-driven, retrospective, criticality-anchored, and gradient-scaled. Along the way, we prove convergence of the retrospective update under linearly growing model Hessians and revisit the framework of Curtis and Scheinberg (2020), and Wang and Yuan (2022): we extend it to three distinct scaling factors with decoupled step acceptance (covering $η= 0$), and specialise its stochastic version to the deterministic gradient-scaled