This paper studies a curious phenomenon in learning energy-based model (EBM) using MCMC. In each learning iteration, we generate synthesized examples by running a non-convergent, non-mixing, and non-persistent short-run MCMC toward the current model, always starting from the same initial distribution such as uniform noise distribution, and always running a fixed number of MCMC steps. After generating synthesized examples, we then update the model parameters according to the maximum likelihood learning gradient, as if the synthesized examples are fair samples from the current model. We treat this non-convergent short-run MCMC as a learned generator model or a flow model. We provide arguments for treating the learned non-convergent short-run MCMC as a valid model. We show that the learned short-run MCMC is capable of generating realistic images. More interestingly, unlike traditional EBM or MCMC, the learned short-run MCMC is capable of reconstructing observed images and interpolating between images, like generator or flow models. The code can be found in the Appendix.
A Neural Network MCMC sampler that maximizes Proposal Entropy
Redwood Center for theoretical Neuroscience（雷德伍德理论神经科学中心）；Department of Physics（物理系）；University of California Berkeley（加州大学伯克利分校）；Berkeley AI Research（伯克利人工智能研究中心）；Helen Wills Neuroscience Institute（海伦·威尔斯神经科学研究所）
Convergent Stochastic Expectation Maximization algorithm with efficient sampling in high dimension. Application to deformable template model estimation
Spectral divide-and-conquer MCMC for long stationary time series
University of Technology Sydney（悉尼科技大学）；Human Technology Institute, University of Technology Sydney（悉尼科技大学人类技术研究所）；Guanghua School of Management, Peking University（北京大学光华管理学院）；Stockholm University（斯德哥尔摩大学）；University of New South Wales（新南威尔士大学）
Learning Energy-Based Models as Generative ConvNets via Multi-grid Modeling and Sampling
University of California, Los Angeles（加州大学洛杉矶分校）；Amazon（亚马逊）；Zhejiang University（浙江大学）
本文提出了一种用于学习图像的基于能量的生成式ConvNet模型的多重网格方法。对于每个网格，我们学习一个基于能量的概率模型，其中能量函数由自底向上的卷积神经网络（ConvNet或CNN）定义。学习这样的模型需要从模型中生成合成的示例。在我们的学习算法的每次迭代中，对于每个观察到的训练图像，我们通过从训练图像的最小1 x 1版本初始化有限步MCMC采样来在多个网格处生成合成图像。在每个后续网格的合成图像是由有限步MCMC初始化从合成图像生成的前一个粗网格。在得到合成实例后，根据合成实例与观测实例之间的差异，分别和同时更新多个网格处的模型参数。我们证明了这种多重网格方法可以学习现实的基于能量的生成ConvNet模型，并且它优于原始的对比发散（CD）和持久CD。
