Are All Unseen Data Out-of-Distribution?

Distributions of unseen data have been all treated as out-of-distribution (OOD), making their generalization a significant challenge. Much evidence suggests that the size increase of training data can monotonically decrease generalization errors in test data. However, this is not true from other observations and analysis. In particular, when the training data have multiple source domains and the test data contain distribution drifts, then not all generalization errors on the test data decrease monotonically with the increasing size of training data. Such a non-decreasing phenomenon is formally investigated under a linear setting with empirical verification across varying visual benchmarks. Motivated by these results, we redefine the OOD data as a type of data outside the convex hull of the training domains and prove a new generalization bound based on this new definition. It implies that the effectiveness of a well-trained model can be guaranteed for the unseen data that is within the convex hull of the training domains. But, for some data beyond the convex hull, a non-decreasing error trend can happen. Therefore, we investigate the performance of popular strategies such as data augmentation and pre-training to overcome this issue. Moreover, we propose a novel reinforcement learning selection algorithm in the source domains only that can deliver superior performance over the baseline methods.

TFDNet: Time-Frequency Enhanced Decomposed Network for Long-term Time Series Forecasting

Long-term time series forecasting is a vital task and has a wide range of real applications. Recent methods focus on capturing the underlying patterns from one single domain (e.g. the time domain or the frequency domain), and have not taken a holistic view to process long-term time series from the time-frequency domains. In this paper, we propose a Time-Frequency Enhanced Decomposed Network (TFDNet) to capture both the long-term underlying patterns and temporal periodicity from the time-frequency domain. In TFDNet, we devise a multi-scale time-frequency enhanced encoder backbone and develop two separate trend and seasonal time-frequency blocks to capture the distinct patterns within the decomposed trend and seasonal components in multi-resolutions. Diverse kernel learning strategies of the kernel operations in time-frequency blocks have been explored, by investigating and incorporating the potential different channel-wise correlation patterns of multivariate time series. Experimental evaluation of eight datasets from five benchmark domains demonstrated that TFDNet is superior to state-of-the-art approaches in both effectiveness and efficiency.