用共轭结构提升多模态神经网络的预测精度与不确定性量化
Multi-modal Bayesian Neural Network Surrogates with Conjugate Last-Layer Estimation
- 在最后一层引入共轭分布，支持高效贝叶斯推断
- 在部分数据缺失时仍保持高精度预测与可靠不确定性估计
- 适合需要高可信度建模的优化、反问题等场景
随着数据采集与仿真能力的提升，从多模态和多源数据中学习的多模态学习正成为重要研究方向。利用多个辅助模态数据训练代理模型，可有效支持高成本目标量的建模，在优化、反问题或敏感性分析等外层应用中具有潜力。本文提出两种多模态贝叶斯神经网络代理模型，通过在最后一层采用条件共轭分布，实现基于随机变分推断（SVI）的参数估计，并提出一种在部分观测缺失情况下进行共轭SVI估计的方法。实验表明，该方法在标量与时间序列数据上均显著优于单模态代理模型，在预测精度和不确定性量化方面表现更优。
原文摘要 · Abstract (English)
As data collection and simulation capabilities advance, multi-modal learning, the task of learning from multiple modalities and sources of data, is becoming an increasingly important area of research. Surrogate models that learn from data of multiple auxiliary modalities to support the modeling of a highly expensive quantity of interest have the potential to aid outer loop applications such as optimization, inverse problems, or sensitivity analyses when multi-modal data are available. We develop two multi-modal Bayesian neural network surrogate models and leverage conditionally conjugate distributions in the last layer to estimate model parameters using stochastic variational inference (SVI). We provide a method to perform this conjugate SVI estimation in the presence of partially missing observations. We demonstrate improved prediction accuracy and uncertainty quantification compared to uni-modal surrogate models for both scalar and time series data.
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