# Identifying Explicit Parsimonious Piece-wise Polynomial Relationships in Industrial time-series: Application to manipulator robots

arXiv: https://arxiv.org/abs/2605.28320 · HTML: https://mlsanity.com/paper/2605.28320/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 13 references that are in the map.
- First posted on arXiv 27 May 2026.

## Builds on (most cited first, 4 of 4)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Do Deep Neural Networks Contribute to Multivariate Time Series Anomaly Detection?](https://mlsanity.com/paper/2204.01637/) (2022)
- [Is it worth it? Comparing six deep and classical methods for unsupervised anomaly detection in time series](https://mlsanity.com/paper/2212.11080/) (2022)

## Abstract (arXiv)

This paper addresses the problem of identifying parsimonious explicit piece-wise polynomial relationships that might involve a relatively large number of raw features. The algorithm leverages a recently proposed identification algorithm that yields parsimonious implicit relationships enabling to derive normality characterization in the context of anomaly detection and localization. The algorithm proposed in this paper goes a step further by deriving explicit piece-wise representations that are built using the set of polynomials involved in the implicit representations. The framework is illustrated on the problem of identifying parsimonious explicit representations of the inverse model of a 6-axis manipulator robot. Moreover, further experiments on a 4-axis robot are also shown which are designed to investigate the generalization capability of parsimonious models compared to state-of-the-art DNNs structures, when models face unseen contexts of use.