论文标题

使用有偏见的蒙特卡洛抽样学习受限制的玻尔兹曼机器

Learning a Restricted Boltzmann Machine using biased Monte Carlo sampling

论文作者

Béreux, Nicolas, Decelle, Aurélien, Furtlehner, Cyril, Seoane, Beatriz

论文摘要

受限的玻尔兹曼机器是简单而强大的生成模型,可以编码任何复杂的数据集。尽管他们有所有优势,但实际上,培训通常是不稳定的,并且很难评估其质量,因为动态受到极慢的时间依赖性的影响。当处理低维聚类数据集时,这种情况变得至关重要,在这种数据集中,训练有素的模型在计算上进行了训练有素的测试所需的时间。在这项工作中,我们表明,蒙特卡洛混合时间的这种差异与相共存的现象有关,类似于在一阶相变附近物理中发生的现象。我们表明,使用Markov链蒙特卡洛方法对平衡分布进行采样,当使用偏置采样技术,尤其是束缚的蒙特卡洛(TMC)方法时,可以显着加速。这种抽样技术有效地解决了评估给定训练模型的质量并在合理时间内生成新样本的问题。此外,我们表明,这种采样技术也可以用于改善训练过程中对数类样梯度的计算,从而通过人工聚类数据集对训练RBM进行巨大改进。在实际的低维数据集上,这种新的训练方法适合与标准PCD食谱获得的RBM模型更快的放松动力学。我们还表明,TMC采样可用于恢复RBM的自由能曲线。事实证明,这对于计算给定模型的概率分布并改善了慢速PCD训练模型中新的非相关样品的生成非常有用。

Restricted Boltzmann Machines are simple and powerful generative models that can encode any complex dataset. Despite all their advantages, in practice the trainings are often unstable and it is difficult to assess their quality because the dynamics are affected by extremely slow time dependencies. This situation becomes critical when dealing with low-dimensional clustered datasets, where the time required to sample ergodically the trained models becomes computationally prohibitive. In this work, we show that this divergence of Monte Carlo mixing times is related to a phenomenon of phase coexistence, similar to that which occurs in physics near a first-order phase transition. We show that sampling the equilibrium distribution using the Markov chain Monte Carlo method can be dramatically accelerated when using biased sampling techniques, in particular the Tethered Monte Carlo (TMC) method. This sampling technique efficiently solves the problem of evaluating the quality of a given trained model and generating new samples in a reasonable amount of time. Moreover, we show that this sampling technique can also be used to improve the computation of the log-likelihood gradient during training, leading to dramatic improvements in training RBMs with artificial clustered datasets. On real low-dimensional datasets, this new training method fits RBM models with significantly faster relaxation dynamics than those obtained with standard PCD recipes. We also show that TMC sampling can be used to recover the free-energy profile of the RBM. This proves to be extremely useful to compute the probability distribution of a given model and to improve the generation of new decorrelated samples in slow PCD-trained models.

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