Vertical federated learning (VFL) is a promising area for time series forecasting in industrial applications, such as predictive maintenance and machine control. Critical challenges to address in manufacturing include data privacy and over-fitting on small and noisy datasets during both training and inference. Additionally, to increase industry adaptability, such forecasting models must scale well with the number of parties while ensuring strong convergence and low-tuning complexity. We address those challenges and propose 'Secret-shared Time Series Forecasting with VFL' (STV), a novel framework that exhibits the following key features: i) a privacy-preserving algorithm for forecasting with SARIMAX and autoregressive trees on vertically partitioned data; ii) serverless forecasting using secret sharing and multi-party computation; iii) novel N-party algorithms for matrix multiplication and inverse operations for direct parameter optimization, giving strong convergence with minimal hyperparameter tuning complexity. We conduct evaluations on six representative datasets from public and industry-specific contexts. Our results demonstrate that STV's forecasting accuracy is comparable to those of centralized approaches. They also show that our direct optimization can outperform centralized methods, which include state-of-the-art diffusion models and long-short-term memory, by 23.81% on forecasting accuracy. We also conduct a scalability analysis by examining the communication costs of direct and iterative optimization to navigate the choice between the two. Code and appendix are available: https://github.com/adis98/STV

翻译：垂直联邦学习（VFL）是工业应用中时间序列预测（如预测性维护和机器控制）的一个前景广阔的领域。制造业中需要解决的关键挑战包括数据隐私问题，以及在训练和推断过程中对小型噪声数据集的过拟合问题。此外，为提高工业适应性，此类预测模型必须在确保强收敛性和低调优复杂度的同时，能够良好地随参与方数量扩展。我们针对这些挑战，提出了“基于VFL的秘密共享时间序列预测”（STV）这一新颖框架，该框架展现出以下关键特性：i) 一种在垂直分区数据上使用SARIMAX和自回归树进行预测的隐私保护算法；ii) 利用秘密共享和多方计算实现无服务器预测；iii) 用于直接参数优化的新颖N方矩阵乘法和逆运算算法，能以最小的超参数调优复杂度实现强收敛。我们在来自公开和特定行业背景的六个代表性数据集上进行了评估。我们的结果表明，STV的预测精度与集中式方法相当。结果还表明，我们的直接优化方法在预测精度上可以比集中式方法（包括最先进的扩散模型和长短期记忆网络）高出23.81%。我们还通过考察直接优化与迭代优化的通信成本进行了可扩展性分析，以指导二者之间的选择。代码和附录可见：https://github.com/adis98/STV