# Anomaly Detection for Non-stationary Time Series using Recurrent Wavelet Probabilistic Neural Network

arXiv: https://arxiv.org/abs/2505.11321 · HTML: https://mlsanity.com/paper/2505.11321/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 45 references that are in the map.
- First posted on arXiv 16 May 2025.

## Builds on (most cited first, 12 of 12)

- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [Cyclical Learning Rates for Training Neural Networks](https://mlsanity.com/paper/1506.01186/) (2015)
- [Transformers in Time Series: A Survey](https://mlsanity.com/paper/2202.07125/) (2022)
- [Anomaly Transformer: Time Series Anomaly Detection with Association Discrepancy](https://mlsanity.com/paper/2110.02642/) (2021)
- [Deep Learning for Anomaly Detection: A Survey](https://mlsanity.com/paper/1901.03407/) (2019)
- [LSTM-based Encoder-Decoder for Multi-sensor Anomaly Detection](https://mlsanity.com/paper/1607.00148/) (2016)
- [TranAD: Deep Transformer Networks for Anomaly Detection in Multivariate Time Series Data](https://mlsanity.com/paper/2201.07284/) (2022)
- [Classification-Based Anomaly Detection for General Data](https://mlsanity.com/paper/2005.02359/) (2020)
- [Time-Series Anomaly Detection Service at Microsoft](https://mlsanity.com/paper/1906.03821/) (2019)
- [An Evaluation of Anomaly Detection and Diagnosis in Multivariate Time Series](https://mlsanity.com/paper/2109.11428/) (2021)
- [Anomaly Detection in Univariate Time-series: A Survey on the State-of-the-Art](https://mlsanity.com/paper/2004.00433/) (2020)
- [Deep Anomaly Detection for Time-series Data in Industrial IoT: A Communication-Efficient On-device Federated Learning Approach](https://mlsanity.com/paper/2007.09712/) (2020)

## Abstract (arXiv)

In this paper, an unsupervised Recurrent Wavelet Probabilistic Neural Network (RWPNN) is proposed, which aims at detecting anomalies in non-stationary environments by modelling the temporal features using a nonparametric density estimation network. The novel framework consists of two components, a Stacked Recurrent Encoder-Decoder (SREnc-Dec) module that captures temporal features in a latent space, and a Multi-Receptive-field Wavelet Probabilistic Network (MRWPN) that creates an ensemble probabilistic model to characterise the latent space. This formulation extends the standard wavelet probabilistic networks to wavelet deep probabilistic networks, which can handle higher data dimensionality. The MRWPN module can adapt to different rates of data variation in different datasets without imposing strong distribution assumptions, resulting in a more robust and accurate detection for Time Series Anomaly Detection (TSAD) tasks in the non-stationary environment. We carry out the assessment on 45 real-world time series datasets from various domains, verify the performance of RWPNN in TSAD tasks with several constraints, and show its ability to provide early warnings for anomalous events.