# Boosted Enhanced Quantile Regression Neural Networks with Spatiotemporal Permutation Entropy for Complex System Prognostics

arXiv: https://arxiv.org/abs/2507.14194 · HTML: https://mlsanity.com/paper/2507.14194/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 37 references that are in the map.
- First posted on arXiv 14 Jul 2025.

## Builds on (most cited first, 8 of 8)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [Deep Huber quantile regression networks](https://mlsanity.com/paper/2306.10306/) (2023)
- [Enhanced Quantile Regression with Spiking Neural Networks for Long-Term System Health Prognostics](https://mlsanity.com/paper/2501.05087/) (2025)

## Built on by (most cited first, 1 of 1)

- [Long Horizon Transformer Quantile Fault Prediction for Multi Site Industrial Predictive Maintenance](https://mlsanity.com/paper/2609.04840/) (2026)

## Abstract (arXiv)

This paper presents an integrative prognostic framework that combines Spatiotemporal Permutation Entropy (STPE), Boosted Enhanced Quantile Regression Neural Networks (B-EQRNNs), Gated Temporal Attention, a Spiking Neural Network (SNN) refinement stage, and a Temporal Fusion Transformer (TFT) classifier. The motivation is long-horizon fault prediction in distributed industrial electronic systems, where single-sensor or point-estimate models can miss weak spatially propagating degradation signatures and provide limited uncertainty information. The proposed pipeline first converts 70-channel sensor streams into multiscale STPE descriptors, then learns conditional quantile representations and attention-weighted temporal context before final Normal/Abnormal classification. Evaluation is reported on a nine-system industrial electronic-sensor dataset with 48-, 90-, and 168-hour prediction horizons. The comparison includes a tree-based LightGBM baseline and modern sequence baselines available under the same preprocessing protocol, including LSTM, Autoformer, and TCN models. The full pipeline reaches 81.17% accuracy at the 168-hour horizon and is evaluated with component ablations, computational-cost analysis, and an explicit reproducibility protocol. The contribution is therefore framed as a validated hybrid architecture for uncertainty-aware spatiotemporal prognostics rather than as a new standalone learning theory.