标题： 通过约化MCMC核的渐近精确变分流 显示英文标题

标题： Asymptotically exact variational flows via involutive MCMC kernels

摘要： 最富有表现力的变分族——如归一化流——缺乏实际的收敛保证，因为它们的理论保证通常仅在难以处理的全局最优值下成立。 在本工作中，我们提出了一种通用的方法，从对合MCMC核构建无需调整、渐近精确的变分流，适用于任意状态空间。 核心方法组件是将一般对合MCMC核表示为可逆的、测度保持的迭代随机函数系统，这作为我们变分流的流映射。 这导致了三种具有可证明总变分收敛的新变分族。 我们的框架解决了具有类似保证的现有变分族的关键实际限制（例如，MixFlows），同时需要明显较弱的理论假设。 最后，我们在后验近似、蒙特卡洛估计和归一化常数估计等任务中展示了我们流的竞争力，其性能优于或匹配No-U-Turn采样器（NUTS）和黑盒归一化流。 显示英文摘要

摘要： Most expressive variational families -- such as normalizing flows -- lack practical convergence guarantees, as their theoretical assurances typically hold only at the intractable global optimum. In this work, we present a general recipe for constructing tuning-free, asymptotically exact variational flows on arbitrary state spaces from involutive MCMC kernels. The core methodological component is a novel representation of general involutive MCMC kernels as invertible, measurepreserving iterated random function systems, which act as the flow maps of our variational flows. This leads to three new variational families with provable total variation convergence. Our framework resolves key practical limitations of existing variational families with similar guarantees (e.g., MixFlows), while requiring substantially weaker theoretical assumptions. Finally, we demonstrate the competitive performance of our flows across tasks including posterior approximation, Monte Carlo estimates, and normalization constant estimation, outperforming or matching No-U-Turn sampler (NUTS) and black-box normalizing flows.