论文标题
将混合多项式logit模型的贝叶斯推断缩放到非常大的数据集
Scaling Bayesian inference of mixed multinomial logit models to very large datasets
论文作者
论文摘要
与标准的Markov-Markov-Chain Monte Carlo（MCMC）方法相比，在混合多项式Logit模型中，差异推理方法已导致近似贝叶斯推断的计算效率显着提高，而无需损害精度。但是，尽管它们证明了效率的提高，但现有的方法仍然受到重要的限制，这些局限性阻止了它们扩展到很大的数据集，同时提供了灵活性，以允许先前的分布并捕获复杂的后验分布。在本文中，我们提出了一种摊销的变异推理方法，该方法利用了随机反向传播，自动分化和GPU加速计算，以有效地将混合多项式Logit模型中的贝叶斯推断缩放到非常大的数据集中。此外，我们展示了如何使用归一化流程来增加后近似值的柔韧性。通过一项广泛的仿真研究，我们从经验上表明，所提出的方法能够在传统的MSLE和MCMC方法上实现多个数量级的计算加速，而无需损害估计准确性。
Variational inference methods have been shown to lead to significant improvements in the computational efficiency of approximate Bayesian inference in mixed multinomial logit models when compared to standard Markov-chain Monte Carlo (MCMC) methods without compromising accuracy. However, despite their demonstrated efficiency gains, existing methods still suffer from important limitations that prevent them to scale to very large datasets, while providing the flexibility to allow for rich prior distributions and to capture complex posterior distributions. In this paper, we propose an Amortized Variational Inference approach that leverages stochastic backpropagation, automatic differentiation and GPU-accelerated computation, for effectively scaling Bayesian inference in Mixed Multinomial Logit models to very large datasets. Moreover, we show how normalizing flows can be used to increase the flexibility of the variational posterior approximations. Through an extensive simulation study, we empirically show that the proposed approach is able to achieve computational speedups of multiple orders of magnitude over traditional MSLE and MCMC approaches for large datasets without compromising estimation accuracy.
