不用反向传播的新型马尔可夫链蒙特卡洛算法，提升采样效率。
Backpropagation-Free Metropolis-Adjusted Langevin Algorithm
- 用前向自动微分代替反向传播，直接生成梯度方向
- 新算法在多个模型上性能优于或媲美传统MALA
- 适合需要高效贝叶斯推断的复杂模型场景
近期无需反向传播的学习工作表明，可通过前向模式自动微分对可微模型进行优化。前向模式AD需在每次模型前向传播时采样一个切向量，从而得到沿该方向的导数。本文将此切向量采样融入马尔可夫调整拉普拉斯算法（MALA）的提议机制中，首次提出无需反向传播的基于梯度的马尔可夫链蒙特卡洛算法。我们进一步提出一种新颖的、位置相关的前向模式预处理MALA，利用海森矩阵信息。总体提出四种新算法：前向MALA；线性前向MALA；预处理前向MALA，及预处理线性前向MALA。实验显示前向模式采样计算成本更低，且在多种概率模型（包括分层分布与贝叶斯神经网络）上表现优异，部分场景甚至超越原版MALA。
原文摘要 · Abstract (English)
Recent work on backpropagation-free learning has shown that it is possible to use forward-mode automatic differentiation (AD) to perform optimization on differentiable models. Forward-mode AD requires sampling a tangent vector for each forward pass of a model. The result is the model evaluation with the directional derivative along the tangent. In this paper, we illustrate how the sampling of this tangent vector can be incorporated into the proposal mechanism for the Metropolis-Adjusted Langevin Algorithm (MALA). As such, we are the first to introduce a backpropagation-free gradient-based Markov chain Monte Carlo (MCMC) algorithm. We also extend to a novel backpropagation-free position-specific preconditioned forward-mode MALA that leverages Hessian information. Overall, we propose four new algorithms: Forward MALA; Line Forward MALA; Pre-conditioned Forward MALA, and Pre-conditioned Line Forward MALA. We highlight the reduced computational cost of the forward-mode samplers and show that forward-mode is competitive with the original MALA, while even outperforming it depending on the probabilistic model. We include Bayesian inference results on a range of probabilistic models, including hierarchical distributions and Bayesian neural networks.
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