ATFNet: Adaptive Time-Frequency Ensembled Network for Long-term Time Series Forecasting

The intricate nature of time series data analysis benefits greatly from the distinct advantages offered by time and frequency domain representations. While the time domain is superior in representing local dependencies, particularly in non-periodic series, the frequency domain excels in capturing global dependencies, making it ideal for series with evident periodic patterns. To capitalize on both of these strengths, we propose ATFNet, an innovative framework that combines a time domain module and a frequency domain module to concurrently capture local and global dependencies in time series data. Specifically, we introduce Dominant Harmonic Series Energy Weighting, a novel mechanism for dynamically adjusting the weights between the two modules based on the periodicity of the input time series. In the frequency domain module, we enhance the traditional Discrete Fourier Transform (DFT) with our Extended DFT, designed to address the challenge of discrete frequency misalignment. Additionally, our Complex-valued Spectrum Attention mechanism offers a novel approach to discern the intricate relationships between different frequency combinations. Extensive experiments across multiple real-world datasets demonstrate that our ATFNet framework outperforms current state-of-the-art methods in long-term time series forecasting.

Towards Optimal Neural Networks: the Role of Sample Splitting in Hyperparameter Selection

When artificial neural networks have demonstrated exceptional practical success in a variety of domains, investigations into their theoretical characteristics, such as their approximation power, statistical properties, and generalization performance, have made significant strides. In this paper, we construct a novel theory for understanding the effectiveness of neural networks by discovering the mystery underlying a common practice during neural network model construction: sample splitting. Our theory demonstrates that, the optimal hyperparameters derived from sample splitting can enable a neural network model that asymptotically minimizes the prediction risk. We conduct extensive experiments across different application scenarios and network architectures, and the results manifest our theory's effectiveness.