Por Renato Assunção (ESRI Inc., USA and Department of Computer Science, Universidade Federal de Minas Gerais, Brazil).
Nos últimos anos, houve um progresso notável nos métodos de simulação de Monte Carlo, impulsionado pela integração de técnicas avançadas de machine learning...
Abstract: Recent years have seen remarkable progress in Monte Carlo simulation methods, driven by the integration of cutting-edge machine learning techniques such as Generative Adversarial Networks (GANs), diffusion models, and normalizing flows. These innovations enable the generation of complex, high-dimensional data, from highly realistic human faces to artistic transformations, such as converting a landscape photo into a Van Gogh-style painting. These breakthroughs, which often make headlines, capture widespread interest but remain challenging to simulate using traditional Monte Carlo techniques. GANs operate by training two networks in a competitive framework, yielding impressive results in high-dimensional sampling. Diffusion models offer a compelling alternative to Monte Carlo sampling by iteratively refining samples, reversing a noise-adding process, and producing smooth transitions critical for many applications. Normalizing flows map simple, tractable distributions (e.g., Gaussians) to complex target distributions through a sequence of invertible transformations, enabling efficient density estimation and sample generation. These advancements significantly expand the scope of Monte Carlo simulations, allowing statisticians and researchers to model more complex and non-standard distributions with greater accuracy and computational efficiency. This talk will explore these transformative methods, highlighting their principles, applications, and potential to redefine simulation in modern statistics and data science.
