Wavelet-based Disentangled Adaptive Normalization for Non-stationary Times Series Forecasting

Forecasting non-stationary time series is a challenging task because their statistical properties often change over time, making it hard for deep models to generalize well. Instance-level normalization techniques can help address shifts in temporal distribution. However, most existing methods overlook the multi-component nature of time series, where different components exhibit distinct non-stationary behaviors. In this paper, we propose Wavelet-based Disentangled Adaptive Normalization (WDAN), a model-agnostic framework designed to address non-stationarity in time series forecasting. WDAN uses discrete wavelet transforms to break down the input into low-frequency trends and high-frequency fluctuations. It then applies tailored normalization strategies to each part. For trend components that exhibit strong non-stationarity, we apply first-order differencing to extract stable features used for predicting normalization parameters. Extensive experiments on multiple benchmarks demonstrate that WDAN consistently improves forecasting accuracy across various backbone model. Code is available at this repository: https://github.com/MonBG/WDAN.

An Optimization Framework For Anomaly Detection Scores Refinement With Side Information

This paper considers an anomaly detection problem in which a detection algorithm assigns anomaly scores to multi-dimensional data points, such as cellular networks' Key Performance Indicators (KPIs). We propose an optimization framework to refine these anomaly scores by leveraging side information in the form of a causality graph between the various features of the data points. The refinement block builds on causality theory and a proposed notion of confidence scores. After motivating our framework, smoothness properties are proved for the ensuing mathematical expressions. Next, equipped with these results, a gradient descent algorithm is proposed, and a proof of its convergence to a stationary point is provided. Our results hold (i) for any causal anomaly detection algorithm and (ii) for any side information in the form of a directed acyclic graph. Numerical results are provided to illustrate the advantage of our proposed framework in dealing with False Positives (FPs) and False Negatives (FNs). Additionally, the effect of the graph's structure on the expected performance advantage and the various trade-offs that take place are analyzed.