论文标题
快速计算机模型使用退火和转化的变分推断
Fast Computer Model Calibration using Annealed and Transformed Variational Inference
论文作者
论文摘要
计算机模型在众多科学和工程领域中起着至关重要的作用。为了确保模拟的准确性，必须通过统计推断正确校准这些模型的输入参数。虽然贝叶斯推断是该任务的标准方法，但采用马尔可夫链蒙特卡洛方法通常会遇到计算障碍，因为对似然函数的昂贵评估和缓慢的混合速率。尽管各变化推理（VI）可以是传统贝叶斯方法的快速替代方法，但由于边界问题和本地最佳问题，VI的适用性有限。为了应对这些挑战，我们提出了基于深层生成模型的灵活VI方法，这些方法不需要关于变异分布的参数假设。我们在框架中嵌入了冲流性转换，以避免边界的后截断。此外，我们提供了保证算法成功的理论条件。此外，我们的温度退火方案可以防止通过一系列中间后期被困在局部优点中。我们将我们的方法应用于传染病模型和地球物理模型，这说明该方法与竞争对手相比可以提供快速准确的推断。
Computer models play a crucial role in numerous scientific and engineering domains. To ensure the accuracy of simulations, it is essential to properly calibrate the input parameters of these models through statistical inference. While Bayesian inference is the standard approach for this task, employing Markov Chain Monte Carlo methods often encounters computational hurdles due to the costly evaluation of likelihood functions and slow mixing rates. Although variational inference (VI) can be a fast alternative to traditional Bayesian approaches, VI has limited applicability due to boundary issues and local optima problems. To address these challenges, we propose flexible VI methods based on deep generative models that do not require parametric assumptions on the variational distribution. We embed a surjective transformation in our framework to avoid posterior truncation at the boundary. Additionally, we provide theoretical conditions that guarantee the success of the algorithm. Furthermore, our temperature annealing scheme can prevent being trapped in local optima through a series of intermediate posteriors. We apply our method to infectious disease models and a geophysical model, illustrating that the proposed method can provide fast and accurate inference compared to its competitors.
