Privacy concerns in machine learning are heightened by regulations such as the GDPR, which enforces the "right to be forgotten" (RTBF), driving the emergence of machine unlearning as a critical research field. Vertical Federated Learning (VFL) enables collaborative model training by aggregating a sample's features across distributed parties while preserving data privacy at each source. This paradigm has seen widespread adoption in healthcare, finance, and other privacy-sensitive domains. However, existing VFL systems lack robust mechanisms to comply with RTBF requirements, as unlearning methodologies for VFL remain underexplored. In this work, we introduce the first VFL framework with theoretically guaranteed unlearning capabilities, enabling the removal of any data at any time. Unlike prior approaches -- which impose restrictive assumptions on model architectures or data types for removal -- our solution is model- and data-agnostic, offering universal compatibility. Moreover, our framework supports asynchronous unlearning, eliminating the need for all parties to be simultaneously online during the forgetting process. These advancements address critical gaps in current VFL systems, ensuring compliance with RTBF while maintaining operational flexibility.We make all our implementations publicly available at https://github.com/wangln19/vertical-federated-unlearning.

In day-ahead electricity market, it is crucial for all market participants to have access to reliable and accurate price forecasts for their decision-making processes. Forecasting methods currently utilized in industrial applications frequently neglect the underlying mechanisms of price formation, while economic research from the perspective of supply and demand have stringent data collection requirements, making it difficult to apply in actual markets. Observing the characteristics of the day-ahead electricity market, we introduce two invariance assumptions to simplify the modeling of supply and demand curves. Upon incorporating the time invariance assumption, we can forecast the supply curve using the market equilibrium points from multiple time slots in the recent period. By introducing the price insensitivity assumption, we can approximate the demand curve using a straight line. The point where these two curves intersect provides us with the forecast price. The proposed model, forecasting suppl\textbf{Y} and demand cUrve simplified by Invariance, termed as YUI, is more efficient than state-of-the-art methods. Our experiment results in Shanxi day-ahead electricity market show that compared with existing methods, YUI can reduce forecast error by 13.8\% in MAE and 28.7\% in sMAPE. Code is publicly available at https://github.com/wangln19/YUI.

Most state-of-the-art deep domain adaptation techniques align source and target samples in a global fashion. That is, after alignment, each source sample is expected to become similar to any target sample. However, global alignment may not always be optimal or necessary in practice. For example, consider cross-domain fraud detection, where there are two types of transactions: credit and non-credit. Aligning credit and non-credit transactions separately may yield better performance than global alignment, as credit transactions are unlikely to exhibit patterns similar to non-credit transactions. To enable such fine-grained domain adaption, we propose a novel Knowledge-Inspired Subdomain Adaptation (KISA) framework. In particular, (1) We provide the theoretical insight that KISA minimizes the shared expected loss which is the premise for the success of domain adaptation methods. (2) We propose the knowledge-inspired subdomain division problem that plays a crucial role in fine-grained domain adaption. (3) We design a knowledge fusion network to exploit diverse domain knowledge. Extensive experiments demonstrate that KISA achieves remarkable results on fraud detection and traffic demand prediction tasks.