@article{Luo_Sugiyama_2019, title={Bias-Variance Trade-Off in Hierarchical Probabilistic Models Using Higher-Order Feature Interactions}, volume={33}, url={https://ojs.aaai.org/index.php/AAAI/article/view/4362}, DOI={10.1609/aaai.v33i01.33014488}, abstractNote={<p>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 <em>hiddenlayers</em> and <em>higher-order interactions</em> 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 <em>hidden layers</em> and <em>higher-order interactions</em>. Our results have shown that using <em>hidden layers</em> and <em>higher-order interactions</em> have a comparable error with a similar order of magnitude and using <em>higherorder interactions</em> produce less variance for smaller sample size.</p>}, number={01}, journal={Proceedings of the AAAI Conference on Artificial Intelligence}, author={Luo, Simon and Sugiyama, Mahito}, year={2019}, month={Jul.}, pages={4488-4495} }