论文标题
用于离散分布的langevin样采样器
A Langevin-like Sampler for Discrete Distributions
论文作者
论文摘要
我们提出了离散的Langevin提案（DLP），这是一种简单且可扩展的基于梯度的建议，用于对复杂的高维离散分布进行采样。与基于Gibbs采样的方法相反，DLP能够单个步骤并行更新所有坐标，并且更改的幅度由步骤尺寸控制。这允许在高维且密切相关的变量的空间中进行廉价，高效的探索。我们通过证明其固定分布的渐近偏置对于对数季节分布而言是零，并且对于接近对数季度的分布而言，我们证明了DLP的效率为零。使用DLP，我们开发了几种采样算法的变体，包括未经调整的，大都市调整后的，随机和预处理版本。 DLP在各种任务上都优于许多流行的替代方案，包括Ising模型，受限的玻尔兹曼机器，基于深层的基于能量的模型，二进制神经网络和语言生成。
We propose discrete Langevin proposal (DLP), a simple and scalable gradient-based proposal for sampling complex high-dimensional discrete distributions. In contrast to Gibbs sampling-based methods, DLP is able to update all coordinates in parallel in a single step and the magnitude of changes is controlled by a stepsize. This allows a cheap and efficient exploration in the space of high-dimensional and strongly correlated variables. We prove the efficiency of DLP by showing that the asymptotic bias of its stationary distribution is zero for log-quadratic distributions, and is small for distributions that are close to being log-quadratic. With DLP, we develop several variants of sampling algorithms, including unadjusted, Metropolis-adjusted, stochastic and preconditioned versions. DLP outperforms many popular alternatives on a wide variety of tasks, including Ising models, restricted Boltzmann machines, deep energy-based models, binary neural networks and language generation.
