标题： 一种用于压缩贝叶斯模型参数的方法及其在逻辑序列预测模型中的应用 显示英文标题

标题： A Method for Compressing Parameters in Bayesian Models with Application to Logistic Sequence Prediction Models

摘要： 贝叶斯分类和回归中高阶交互作用的处理在很大程度上是不可行的，因为需要应用马尔可夫链蒙特卡洛（MCMC）方法，且参数数量会随着阶数的增加而迅速增长。 在本文中，我们展示了如何通过有效减少参数数量来使其可行，利用了对于所有训练案例来说许多交互作用具有相同值的事实。 我们的方法使用一个“压缩”参数来表示与所有训练案例具有相同值的一组模式相关的所有参数之和。 使用对称稳定分布作为原始参数的先验，我们可以轻松找到这些压缩参数的先验。 因此，在使用MCMC训练模型时，我们只需处理更少的压缩参数。 压缩参数的数量可能在考虑最高可能阶数之前就已经收敛。 在模型训练之后，我们可以根据需要将这些压缩参数拆分为原始参数，以对测试案例进行预测。 我们详细展示了如何对逻辑序列预测模型进行参数压缩。 在模拟数据和真实数据上的实验表明，我们的压缩方法确实可以大幅减少参数数量。 显示英文摘要

摘要： Bayesian classification and regression with high order interactions is largely infeasible because Markov chain Monte Carlo (MCMC) would need to be applied with a great many parameters, whose number increases rapidly with the order. In this paper we show how to make it feasible by effectively reducing the number of parameters, exploiting the fact that many interactions have the same values for all training cases. Our method uses a single ``compressed'' parameter to represent the sum of all parameters associated with a set of patterns that have the same value for all training cases. Using symmetric stable distributions as the priors of the original parameters, we can easily find the priors of these compressed parameters. We therefore need to deal only with a much smaller number of compressed parameters when training the model with MCMC. The number of compressed parameters may have converged before considering the highest possible order. After training the model, we can split these compressed parameters into the original ones as needed to make predictions for test cases. We show in detail how to compress parameters for logistic sequence prediction models. Experiments on both simulated and real data demonstrate that a huge number of parameters can indeed be reduced by our compression method.