标题： 大规模选择集和样本量下的多项式概率模型的可扩展变分推断 显示英文标题

标题： Scalable Variational Inference for Multinomial Probit Models under Large Choice Sets and Sample Sizes

摘要： 多元概率模型（MNP）由于能够捕捉不同选择之间的灵活替代模式，被广泛用于分析分类结果。在高维选择设置中，传统的基于似然和马尔可夫链蒙特卡洛（MCMC）估计器变得计算上不可行。本研究引入了一种快速且准确的条件变分推断（CVI）方法来校准MNP模型参数，该方法可扩展到大样本和大选择集。使用神经嵌入定义了相关潜在效用上的灵活变分分布，并使用重参数化技巧确保生成协方差矩阵的正定性。所得的CVI估计器类似于变分自编码器，其中变分模型是编码器，MNP的数据生成过程是解码器。采用直接估计和Gumbel SoftMax近似来进行argmax操作以选择具有最高潜在效用的选项。这消除了从高维截断正态分布中抽样的需求，随着选项数量的增长显著降低了计算成本。所提出的方法在参数恢复方面与MCMC相当。它可以在大约28分钟内校准包含20个选项和一百万条观测值的MNP参数，比现有基准快约36倍且更准确。 显示英文摘要

摘要： The multinomial probit (MNP) model is widely used to analyze categorical outcomes due to its ability to capture flexible substitution patterns among alternatives. Conventional likelihood based and Markov chain Monte Carlo (MCMC) estimators become computationally prohibitive in high dimensional choice settings. This study introduces a fast and accurate conditional variational inference (CVI) approach to calibrate MNP model parameters, which is scalable to large samples and large choice sets. A flexible variational distribution on correlated latent utilities is defined using neural embeddings, and a reparameterization trick is used to ensure the positive definiteness of the resulting covariance matrix. The resulting CVI estimator is similar to a variational autoencoder, with the variational model being the encoder and the MNP's data generating process being the decoder. Straight through estimation and Gumbel SoftMax approximation are adopted for the argmax operation to select an alternative with the highest latent utility. This eliminates the need to sample from high dimensional truncated Gaussian distributions, significantly reducing computational costs as the number of alternatives grows. The proposed method achieves parameter recovery comparable to MCMC. It can calibrate MNP parameters with 20 alternatives and one million observations in approximately 28 minutes roughly 36 times faster and more accurate than the existing benchmarks in recovering model parameters.