# Directionality-Aware Mixture Model Parallel Sampling for Efficient Linear Parameter Varying Dynamical System Learning

arXiv: https://arxiv.org/abs/2309.02609 · HTML: https://mlsanity.com/paper/2309.02609/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Sep 2023.

## Built on by (most cited first, 3 of 3)

- [Elastic Motion Policy: An Adaptive Dynamical System for Robust and Efficient One-Shot Imitation Learning](https://mlsanity.com/paper/2503.08029/) (2025)
- [The Unreasonable Effectiveness of Discrete-Time Gaussian Process Mixtures for Robot Policy Learning](https://mlsanity.com/paper/2505.03296/) (2025)
- [VIDP: Variable Impedance Diffusion Policy for Compliant Robot Manipulation from Diverse Demonstrations](https://mlsanity.com/paper/2608.06210/) (2026)

## Abstract (arXiv)

The Linear Parameter Varying Dynamical System (LPV-DS) is an effective approach that learns stable, time-invariant motion policies using statistical modeling and semi-definite optimization to encode complex motions for reactive robot control. Despite its strengths, the LPV-DS learning approach faces challenges in achieving a high model accuracy without compromising the computational efficiency. To address this, we introduce the Directionality-Aware Mixture Model (DAMM), a novel statistical model that applies the Riemannian metric on the n-sphere mathbbSn to efficiently blend non-Euclidean directional data with ℝm Euclidean states. Additionally, we develop a hybrid Markov chain Monte Carlo technique that combines Gibbs Sampling with Split/Merge Proposal, allowing for parallel computation to drastically speed up inference. Our extensive empirical tests demonstrate that LPV-DS integrated with DAMM achieves higher reproduction accuracy, better model efficiency, and near real-time/online learning compared to standard estimation methods on various datasets. Lastly, we demonstrate its suitability for incrementally learning multi-behavior policies in real-world robot experiments.