Frequency Adaptive Normalization For Non-stationary Time Series Forecasting

Time series forecasting typically needs to address non-stationary data with evolving trend and seasonal patterns. To address the non-stationarity, reversible instance normalization has been recently proposed to alleviate impacts from the trend with certain statistical measures, e.g., mean and variance. Although they demonstrate improved predictive accuracy, they are limited to expressing basic trends and are incapable of handling seasonal patterns. To address this limitation, this paper proposes a new instance normalization solution, called frequency adaptive normalization (FAN), which extends instance normalization in handling both dynamic trend and seasonal patterns. Specifically, we employ the Fourier transform to identify instance-wise predominant frequent components that cover most non-stationary factors. Furthermore, the discrepancy of those frequency components between inputs and outputs is explicitly modeled as a prediction task with a simple MLP model. FAN is a model-agnostic method that can be applied to arbitrary predictive backbones. We instantiate FAN on four widely used forecasting models as the backbone and evaluate their prediction performance improvements on eight benchmark datasets. FAN demonstrates significant performance advancement, achieving 7.76% ~ 37.90% average improvements in MSE.

Data Imputation with Iterative Graph Reconstruction

Effective data imputation demands rich latent ``structure" discovery capabilities from ``plain" tabular data. Recent advances in graph neural networks-based data imputation solutions show their strong structure learning potential by directly translating tabular data as bipartite graphs. However, due to a lack of relations between samples, those solutions treat all samples equally which is against one important observation: ``similar sample should give more information about missing values." This paper presents a novel Iterative graph Generation and Reconstruction framework for Missing data imputation(IGRM). Instead of treating all samples equally, we introduce the concept: ``friend networks" to represent different relations among samples. To generate an accurate friend network with missing data, an end-to-end friend network reconstruction solution is designed to allow for continuous friend network optimization during imputation learning. The representation of the optimized friend network, in turn, is used to further optimize the data imputation process with differentiated message passing. Experiment results on eight benchmark datasets show that IGRM yields 39.13% lower mean absolute error compared with nine baselines and 9.04% lower than the second-best.