# Small Variance Asymptotics for Non-Parametric Online Robot Learning

arXiv: https://arxiv.org/abs/1610.02468 · HTML: https://mlsanity.com/paper/1610.02468/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Oct 2016.

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

- [Learning from demonstration with model-based Gaussian process](https://mlsanity.com/paper/1910.05005/) (2019)
- [Mixture Models for the Analysis, Edition, and Synthesis of Continuous Time Series](https://mlsanity.com/paper/2104.10731/) (2021)
- [Generalizing Robot Imitation Learning with Invariant Hidden Semi-Markov Models](https://mlsanity.com/paper/1811.07489/) (2018)

## Abstract (arXiv)

Small variance asymptotics is emerging as a useful technique for inference in large scale Bayesian non-parametric mixture models. This paper analyses the online learning of robot manipulation tasks with Bayesian non-parametric mixture models under small variance asymptotics. The analysis yields a scalable online sequence clustering (SOSC) algorithm that is non-parametric in the number of clusters and the subspace dimension of each cluster. SOSC groups the new datapoint in its low dimensional subspace by online inference in a non-parametric mixture of probabilistic principal component analyzers (MPPCA) based on Dirichlet process, and captures the state transition and state duration information online in a hidden semi-Markov model (HSMM) based on hierarchical Dirichlet process. A task-parameterized formulation of our approach autonomously adapts the model to changing environmental situations during manipulation. We apply the algorithm in a teleoperation setting to recognize the intention of the operator and remotely adjust the movement of the robot using the learned model. The generative model is used to synthesize both time-independent and time-dependent behaviours by relying on the principles of shared and autonomous control. Experiments with the Baxter robot yield parsimonious clusters that adapt online with new demonstrations and assist the operator in performing remote manipulation tasks.