Approximating probability distributions can be a challenging task, particularly when they are supported over regions of high geometrical complexity or exhibit multiple modes. Annealing can be used to facilitate this task which is often combined with constant a priori selected increments in inverse temperature. However, using constant increments limits the computational efficiency due to the inability to adapt to situations where smooth changes in the annealed density could be handled equally well with larger increments. We introduce AdaAnn, an adaptive annealing scheduler that automatically adjusts the temperature increments based on the expected change in the Kullback−Leibler divergence between two distributions with a sufficiently close annealing temperature. AdaAnn is easy to implement and can be integrated into existing sampling approaches such as normalizing flows for variational inference and Markov chain Monte Carlo. We demonstrate the computational efficiency of the AdaAnn scheduler for variational inference with normalizing flows on a number of examples, including posterior estimation of parameters for dynamical systems and probability density approximation in multimodal and high-dimensional settings.

中文翻译：

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AdaAnn：用于概率密度近似的自适应退火调度器

近似概率分布可能是一项具有挑战性的任务，特别是当它们在高几何复杂性区域得到支持或表现出多种模式时。退火可用于促进此任务，该任务通常与恒定的先验选择的逆温度增量相结合。然而，使用恒定增量限制了计算效率，因为无法适应退火密度的平滑变化可以用更大的增量同样好地处理的情况。我们介绍了 AdaAnn，这是一种自适应退火调度程序，它根据退火温度足够接近的两个分布之间的 Kullback−Leibler 散度的预期变化自动调整温度增量。AdaAnn 易于实施，并且可以集成到现有的采样方法中，例如用于变分推理的归一化流和马尔可夫链蒙特卡罗。我们展示了 AdaAnn 调度器的计算效率，用于对许多示例进行归一化流的变分推理，包括动态系统参数的后验估计和多模态和高维设置中的概率密度近似。