Time series domain adaptation aims to transfer the complex temporal dependence from the labeled source domain to the unlabeled target domain. Recent advances leverage the stable causal mechanism over observed variables to model the domain-invariant temporal dependence. However, modeling precise causal structures in high-dimensional data, such as videos, remains challenging. Additionally, direct causal edges may not exist among observed variables (e.g., pixels). These limitations hinder the applicability of existing approaches to real-world scenarios. To address these challenges, we find that the high-dimension time series data are generated from the low-dimension latent variables, which motivates us to model the causal mechanisms of the temporal latent process. Based on this intuition, we propose a latent causal mechanism identification framework that guarantees the uniqueness of the reconstructed latent causal structures. Specifically, we first identify latent variables by utilizing sufficient changes in historical information. Moreover, by enforcing the sparsity of the relationships of latent variables, we can achieve identifiable latent causal structures. Built on the theoretical results, we develop the Latent Causality Alignment (LCA) model that leverages variational inference, which incorporates an intra-domain latent sparsity constraint for latent structure reconstruction and an inter-domain latent sparsity constraint for domain-invariant structure reconstruction. Experiment results on eight benchmarks show a general improvement in the domain-adaptive time series classification and forecasting tasks, highlighting the effectiveness of our method in real-world scenarios.

The conventional mean square error for time series forecasting is a point-wise loss function, which ignores the temporal dependency of forecasting data points and results in unstable predictions. Although other methods involve shape information loss functions, such as dynamic time warping, they assign the same weights to each matching pair and result in suboptimal results when a wrong matching pair is chosen. Besides, although the optimal transport can assign different weights for each matching pair, they easily suffer from false alignment due to the time lag. To solve these challenges, we propose a Model-Agnostic loss function via Temporally Sensitive Optimal Transport (MA-TOT) as a differentiable loss function for time series forecasting, which combines temporally sensitive Wasserstein distance for adaptive matching pair chosen and Gromov-Wasserstein distance for multi-level-similarity-measurement. Extensive experiments of several of the latest time series forecasting models with our loss function on seven real-world benchmark datasets reflect the effectiveness of our method.

Domain adaptation for time-series forecasting, which spans several real-world applications, aims to transfer temporal patterns from labeled sources to unlabeled target distributions. Due to the complexity of temporal dependencies, it is difficult for the time domain alignment-based methods to capture the invariant information, hence several methods consider the frequency domain alignment and extract the domain-invariant frequencies. However, these methods usually sacrifice the domain-specific frequencies, which can lead to critical changes in the time domain and further result in suboptimal performance in time-series forecasting tasks. Going beyond frequency alignment, we develop the SDFDA as a solution to preserve the domain-specific frequency with an explicit frequency transformation. Technologically, the proposed method captures frequency information via a transformer-based architecture with minimal change constraints. Moreover, it bridges the relationship of frequency between the source and the target domains with a contrastive Whittle Likelihood restriction. Extensive experiments on benchmark datasets demonstrate that the SDFDA outperforms existing domain adaptation methods for time-series data, showcasing its effectiveness in real-world applications.

Although graph neural networks have achieved great success in the task of molecular property prediction in recent years, their generalization ability under out-of-distribution (OOD) settings is still under-explored. Most of the existing methods rely on learning discriminative representations for prediction, often assuming that the underlying semantic components are correctly identified. However, this assumption does not always hold, leading to potential misidentifications that affect model robustness. Different from these discriminative-based methods, we propose a generative model to ensure the Semantic-Components Identifiability, named SCI. We demonstrate that the latent variables in this generative model can be explicitly identified into semantic-relevant (SR) and semantic-irrelevant (SI) components, which contributes to better OOD generalization by involving minimal change properties of causal mechanisms. Specifically, we first formulate the data generation process from the atom level to the molecular level, where the latent space is split into SI substructures, SR substructures, and SR atom variables. Sequentially, to reduce misidentification, we restrict the minimal changes of the SR atom variables and add a semantic latent substructure regularization to mitigate the variance of the SR substructure under augmented domain changes. Under mild assumptions, we prove the block-wise identifiability of the SR substructure and the comment-wise identifiability of SR atom variables. Experimental studies achieve state-of-the-art performance and show general improvement on 21 datasets in 3 mainstream benchmarks. Moreover, the visualization results of the proposed SCI method provide insightful case studies and explanations for the prediction results.