基于平稳Fokker-Planck抽样的贝叶斯推断
Bayesian Inference Based on Stationary Fokker-Planck Sampling
摘要：
提出了一种新的形式主义贝叶斯学习的背景下，复杂的推理模型。该方法是基于使用的固定福克-普朗克（SFP）的方法来采样后验密度。固定Fokker-Planck采样推广了Gibbs采样算法，适用于任意和未知的条件密度。通过SFP过程，可以构造后验的条件和边缘的近似解析表达式。在SFP的每个阶段，近似条件被用来定义一个吉布斯采样过程，这是收敛到完整的联合后验。通过分析边缘，概述了人工神经网络背景下的有效学习方法。在分类和回归的例子中，进行了离线和增量式的贝叶斯推断和后验的极大似然估计。SFP与其他Monte Carlo策略在一般问题中的任意密度的采样的比较。结果表明，SFP是能够跳跃大的低概率区域，而不需要仔细调整任何步长参数。事实上，SFP方法只需要一小部分有意义的参数，这些参数可以根据明确的、与问题无关的指导方针来选择。SFP的计算成本，衡量损失函数评估，线性增长与给定的模型的尺寸。
英文摘要：
A novel formalism for Bayesian learning in the context of complex inference models is proposed. The method is based on the use of the Stationary Fokker--Planck (SFP) approach to sample from the posterior density. Stationary Fokker--Planck sampling generalizes the Gibbs sampler algorithm for arbitrary and unknown conditional densities. By the SFP procedure approximate analytical expressions for the conditionals and marginals of the posterior can be constructed. At each stage of SFP, the approximate conditionals are used to define a Gibbs sampling process, which is convergent to the full joint posterior. By the analytical marginals efficient learning methods in the context of Artificial Neural Networks are outlined. Off--line and incremental Bayesian inference and Maximum Likelihood Estimation from the posterior is performed in classification and regression examples. A comparison of SFP with other Monte Carlo strategies in the general problem of sampling from arbitrary densities is also presented. It is shown that SFP is able to jump large low--probabilty regions without the need of a careful tuning of any step size parameter. In fact, the SFP method requires only a small set of meaningful parameters which can be selected following clear, problem--independent guidelines. The computation cost of SFP, measured in terms of loss function evaluations, grows linearly with the given model's dimension.
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