q-Paths：使用幂平均推广几何退火路径
q-Paths: Generalizing the Geometric Annealing Path using Power Means
摘要：
许多常见的机器学习方法涉及几何退火路径，即使用几何平均值构造的两个感兴趣分布之间的中间密度序列。虽然诸如力矩平均路径之类的替代方案在某些设置中已经证明了性能增益，但其实际适用性仍然受到指数族端点假设和缺乏封闭形式能量函数的限制。在这项工作中，我们介绍了$q$ -路径，这是一个家庭的路径是来自一个广义的概念的平均值，包括几何和算术的混合物作为特殊情况下，并承认一个简单的封闭形式涉及变形对数函数从非广延热力学。根据先前的几何路径的分析，我们解释我们的$q$ -路径对应于一个$q$ -指数分布族，并提供了一个变分表示的中间密度最小化混合物的$α$ -分歧的端点。我们发现，小的偏差远离几何路径产生经验收益贝叶斯推断使用顺序蒙特卡罗和生成模型评估使用退火重要性采样。
英文摘要：
Many common machine learning methods involve the geometric annealing path, a sequence of intermediate densities between two distributions of interest constructed using the geometric average. While alternatives such as the moment-averaging path have demonstrated performance gains in some settings, their practical applicability remains limited by exponential family endpoint assumptions and a lack of closed form energy function. In this work, we introduce $q$-paths, a family of paths which is derived from a generalized notion of the mean, includes the geometric and arithmetic mixtures as special cases, and admits a simple closed form involving the deformed logarithm function from nonextensive thermodynamics. Following previous analysis of the geometric path, we interpret our $q$-paths as corresponding to a $q$-exponential family of distributions, and provide a variational representation of intermediate densities as minimizing a mixture of $α$-divergences to the endpoints. We show that small deviations away from the geometric path yield empirical gains for Bayesian inference using Sequential Monte Carlo and generative model evaluation using Annealed Importance Sampling.
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