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采用可逆 SGLD 提议的小批量 Metropolis–Hastings 方法AI 解读

Traditional Markov chain Monte Carlo (MCMC) algorithms are computationally intensive and do not scale well to large data. In particular, the Metropolis–Hastings (MH) algorithm requires passing over the entire dataset to evaluate the likelihood ratio in each iteration. We propose a general framework for performing MH-MCMC using mini-batches of the whole dataset and show that this gives rise to approximately a tempered stationary distribution. We prove that the algorithm…

指数族中对比散度算法的收敛性AI 解读

The Contrastive Divergence (CD) algorithm has achieved notable success in training energy-based models including Restricted Boltzmann Machines and played a key role in the emergence of deep learning. The idea of this algorithm is to approximate the intractable term in the exact gradient of the log-likelihood function by using short Markov chain Monte Carlo (MCMC) runs. The approximate gradient is computationally-cheap but biased. Whether and why the CD algorithm provides an…

贝叶斯序贯分割的多元密度估计AI 解读

Consider a class of densities that are piecewise constant functions over partitions of the sample space defined by sequential coordinate partitioning. We introduce a prior distribution for a density in this function class and derive in closed form the marginal posterior distribution of the corresponding partition. A computationally efficient method, based on sequential importance sampling, is presented for the inference of the partition from this posterior distribution.…

可选 Pólya 树与贝叶斯推断AI 解读

We introduce an extension of the Pólya tree approach for constructing distributions on the space of probability measures. By using optional stopping and optional choice of splitting variables, the construction gives rise to random measures that are absolutely continuous with piecewise smooth densities on partitions that can adapt to fit the data. The resulting “optional Pólya tree” distribution has large support in total variation topology and yields posterior distributions…

不同扫描方式下 Gibbs 采样器的协方差结构与收敛速率AI 解读

SUMMARY This paper presents results on covariance structure and convergence for the Gibbs sampler with both systematic and random scans. It is shown that, under conditions that guarantee the compactness of the Markov forward operator and irreducibility of the corresponding chain, the Gibbs sampling scheme converges geometrically in terms of Pearson χ 2-distance. In particular, for the random scan, the autocovariance can be expressed as variances of iterative conditional…