正则化Ising推理的变分伪随机方法
Variational Pseudolikelihood for Regularized Ising Inference
摘要：
本文提出了一种变分方法来求解伊辛模型的最大伪随机推论。变分算法计算效率更高，并且比$L_2$正则化的最大伪像推理以及具有伪计数正则化的平均场和孤立自旋对近似更好地预测样本外相关性。该方法的关键是变分能量，它通过将耦合缩小到零来规范推理问题，同时仍然允许一些大的耦合来解释强相关性。通过训练伊辛模型来表示字母A-J，使用来自不同计算机字体的字母样本来说明变分伪像方法的效用。
英文摘要：
I propose a variational approach to maximum pseudolikelihood inference of the Ising model. The variational algorithm is more computationally efficient, and does a better job predicting out-of-sample correlations than $L_2$ regularized maximum pseudolikelihood inference as well as mean field and isolated spin pair approximations with pseudocount regularization. The key to the approach is a variational energy that regularizes the inference problem by shrinking the couplings towards zero, while still allowing some large couplings to explain strong correlations. The utility of the variational pseudolikelihood approach is illustrated by training an Ising model to represent the letters A-J using samples of letters from different computer fonts.
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