# Share Secrets for Privacy: Confidential Forecasting with Vertical Federated Learning

arXiv: https://arxiv.org/abs/2405.20761 · HTML: https://mlsanity.com/paper/2405.20761/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 45 references that are in the map.
- First posted on arXiv 31 May 2024.

## Builds on (most cited first, 10 of 10)

- [A Survey on Deep Learning in Medical Image Analysis](https://mlsanity.com/paper/1702.05747/) (2017)
- [Split learning for health: Distributed deep learning without sharing raw patient data](https://mlsanity.com/paper/1812.00564/) (2018)
- [Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models](https://mlsanity.com/paper/2208.09399/) (2022)
- [Federated Optimization:Distributed Optimization Beyond the Datacenter](https://mlsanity.com/paper/1511.03575/) (2015)
- [Private federated learning on vertically partitioned data via entity resolution and additively homomorphic encryption](https://mlsanity.com/paper/1711.10677/) (2017)
- [VAFL: a Method of Vertical Asynchronous Federated Learning](https://mlsanity.com/paper/2007.06081/) (2020)
- [Evaluating time series forecasting models: An empirical study on performance estimation methods](https://mlsanity.com/paper/1905.11744/) (2019)
- [Large-Scale Secure XGB for Vertical Federated Learning](https://mlsanity.com/paper/2005.08479/) (2020)
- [An Efficient Learning Framework For Federated XGBoost Using Secret Sharing And Distributed Optimization](https://mlsanity.com/paper/2105.05717/) (2021)
- [Providing Accurate Models across Private Partitioned Data: Secure Maximum Likelihood Estimation](https://mlsanity.com/paper/1710.06933/) (2017)

## Built on by (most cited first, 2 of 2)

- [Asynchronous Multi-Server Federated Learning for Geo-Distributed Clients](https://mlsanity.com/paper/2406.01439/) (2024)
- [Private Vertical Federated Inference for Time-Series](https://mlsanity.com/paper/2605.08343/) (2026)

## Abstract (arXiv)

Vertical federated learning (VFL) is a promising area for time series forecasting in many applications, such as healthcare and manufacturing. Critical challenges to address include data privacy and over-fitting on small and noisy datasets during both training and inference. Additionally, such forecasting models must scale well with the number of parties while ensuring strong convergence and low-tuning complexity. We address these challenges and propose ``Secret-shared Time Series Forecasting with VFL'' (STV), a novel framework with the following key features: i) a privacy-preserving algorithm for forecasting with SARIMAX and autoregressive trees on vertically-partitioned data; ii) decentralised forecasting using secret sharing and multi-party computation; and iii) novel N-party algorithms for matrix multiplication and inverse operations for exact parameter optimization, giving strong convergence with minimal tuning complexity. We evaluate on six representative datasets from public and industry-specific contexts. Results demonstrate that STV's forecasting accuracy is comparable to those of centralized approaches. Our exact optimization outperforms centralized methods, including state-of-the-art diffusion models and long-short-term memory, by 23.81% on forecasting accuracy. We also evaluate scalability by examining the communication costs of exact and iterative optimization to navigate the choice between the two. STV's code and supplementary material is available online: https://github.com/adis98/STV.