Hierarchical probabilistic models are able to use a large number of parameters to create a model with a high representation power. However, it is well known that increasing the number of parameters also increases the complexity of the model which leads to a bias-variance trade-off. Although it is a classical problem, the bias-variance trade-off between hidden layers and higher-order interactions have not been well studied. In our study, we propose an efficient inference algorithm for the log-linear formulation of the higher-order Boltzmann machine using a combination of Gibbs sampling and annealed importance sampling. We then perform a bias-variance decomposition to study the differences in hidden layers and higher-order interactions. Our results have shown that using hidden layers and higher-order interactions have a comparable error with a similar order of magnitude and using higher-order interactions produce less variance for smaller sample size.

本研究提出了一种有效的算法来研究使用隐藏层和高阶交互的Boltzmann机的偏差-方差分解。研究结果表明，使用高阶交互可以产生更少的方差，具有相当的误差大小和使用隐藏层相似的数量级。

使用高阶特征交互在分层概率模型中的偏差-方差折衷