# Vertical Federated Learning with Missing Features During Training and Inference

arXiv: https://arxiv.org/abs/2410.22564 · HTML: https://mlsanity.com/paper/2410.22564/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 34 references that are in the map.
- First posted on arXiv 29 Oct 2024.

## Builds on (most cited first, 19 of 19)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Vertical Federated Learning: Concepts, Advances and Challenges](https://mlsanity.com/paper/2211.12814/) (2022)
- [In Defense of the Unitary Scalarization for Deep Multi-Task Learning](https://mlsanity.com/paper/2201.04122/) (2022)
- [Multi-Participant Multi-Class Vertical Federated Learning](https://mlsanity.com/paper/2001.11154/) (2020)
- [SplitNN-driven Vertical Partitioning](https://mlsanity.com/paper/2008.04137/) (2020)
- [An Extensive Data Processing Pipeline for MIMIC-IV](https://mlsanity.com/paper/2204.13841/) (2022)
- [FedCVT: Semi-supervised Vertical Federated Learning with Cross-view Training](https://mlsanity.com/paper/2008.10838/) (2020)
- [Privacy-preserving Federated Adversarial Domain Adaption over Feature Groups for Interpretability](https://mlsanity.com/paper/2111.10934/) (2021)
- [Vertical Federated Knowledge Transfer via Representation Distillation for Healthcare Collaboration Networks](https://mlsanity.com/paper/2302.05675/) (2023)
- [Practical Lossless Federated Singular Vector Decomposition over Billion-Scale Data](https://mlsanity.com/paper/2105.08925/) (2021)
- [A Hybrid Self-Supervised Learning Framework for Vertical Federated Learning](https://mlsanity.com/paper/2208.08934/) (2022)
- [Communication-Efficient Vertical Federated Learning with Limited Overlapping Samples](https://mlsanity.com/paper/2303.16270/) (2023)
- [Vertical Semi-Federated Learning for Efficient Online Advertising](https://mlsanity.com/paper/2209.15635/) (2022)
- [Robust and IP-Protecting Vertical Federated Learning against Unexpected Quitting of Parties](https://mlsanity.com/paper/2303.18178/) (2023)
- [A Survey of Privacy Threats and Defense in Vertical Federated Learning: From Model Life Cycle Perspective](https://mlsanity.com/paper/2402.03688/) (2024)
- [VFed-SSD: Towards Practical Vertical Federated Advertising](https://mlsanity.com/paper/2205.15987/) (2022)
- [Communication-efficient Vertical Federated Learning via Compressed Error Feedback](https://mlsanity.com/paper/2406.14420/) (2024)
- [Robust Collaborative Inference with Vertically Split Data Over Dynamic Device Environments](https://mlsanity.com/paper/2312.16638/) (2023)

## Built on by (most cited first, 6 of 6)

- [FLOSS: Federated Learning with Opt-Out and Straggler Support](https://mlsanity.com/paper/2507.23115/) (2025)
- [Heterogeneity-Aware Knowledge Sharing for Graph Federated Learning](https://mlsanity.com/paper/2601.21589/) (2026)
- [Deep Latent Variable Model based Vertical Federated Learning with Flexible Alignment and Labeling Scenarios](https://mlsanity.com/paper/2505.11035/) (2025)
- [X-VFL: A New Vertical Federated Learning Framework with Cross Completion and Decision Subspace Alignment](https://mlsanity.com/paper/2508.05568/) (2025)
- [Hierarchical Dual-Strategy Unlearning for Biomedical and Healthcare Intelligence Using Imperfect and Privacy-Sensitive Medical Data](https://mlsanity.com/paper/2511.19498/) (2025)
- [Mixture of Predefined Experts: Maximizing Data Usage on Vertical Federated Learning](https://mlsanity.com/paper/2602.12708/) (2026)

## Abstract (arXiv)

Vertical federated learning trains models from feature-partitioned datasets across multiple clients, who collaborate without sharing their local data. Standard approaches assume that all feature partitions are available during both training and inference. Yet, in practice, this assumption rarely holds, as for many samples only a subset of the clients observe their partition. However, not utilizing incomplete samples during training harms generalization, and not supporting them during inference limits the utility of the model. Moreover, if any client leaves the federation after training, its partition becomes unavailable, rendering the learned model unusable. Missing feature blocks are therefore a key challenge limiting the applicability of vertical federated learning in real-world scenarios. To address this, we propose LASER-VFL, a vertical federated learning method for efficient training and inference of split neural network-based models that is capable of handling arbitrary sets of partitions. Our approach is simple yet effective, relying on the sharing of model parameters and on task-sampling to train a family of predictors. We show that LASER-VFL achieves a O(1/√T) convergence rate for nonconvex objectives and, under the Polyak-Lojasiewicz inequality, it achieves linear convergence to a neighborhood of the optimum. Numerical experiments show improved performance of LASER-VFL over the baselines. Remarkably, this is the case even in the absence of missing features. For example, for CIFAR-100, we see an improvement in accuracy of 19.3% when each of four feature blocks is observed with a probability of 0.5 and of 9.5% when all features are observed. The code for this work is available at https://github.com/Valdeira/LASER-VFL.