Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Gaussian Mixture Models for Affordance Learning using Bayesian Networks

Pedro Osório, Alexandre Bernardino, Ruben Martinez-Cantin, José Santos-Victor

TL;DR

This work tackles autonomous affordance learning for embodied agents under noisy sensory observations by replacing fully observed discrete BN nodes with Gaussian Mixture Model (GMM) sensor representations. The core method extends prior BN-based affordance learning by coupling discrete object-action-effect nodes with continuous sensor nodes and applying an EM algorithm to learn parameters in the presence of hidden variables, including MAP-based structure initialization to avoid full Structural-EM. Empirical results on simple and complex BN benchmarks show that EM over the full GMM distribution yields substantial RMS-error reductions and improved log-likelihoods, especially as data volume grows or sensor noise increases. The findings demonstrate that probabilistic clustering of sensory inputs improves robustness and inference in affordance learning, albeit with computational costs and opportunities for online or scalable extensions.

Abstract

Affordances are fundamental descriptors of relationships between actions, objects and effects. They provide the means whereby a robot can predict effects, recognize actions, select objects and plan its behavior according to desired goals. This paper approaches the problem of an embodied agent exploring the world and learning these affordances autonomously from its sensory experiences. Models exist for learning the structure and the parameters of a Bayesian Network encoding this knowledge. Although Bayesian Networks are capable of dealing with uncertainty and redundancy, previous work considered complete observability of the discrete sensory data, which may lead to hard errors in the presence of noise. In this paper we consider a probabilistic representation of the sensors by Gaussian Mixture Models (GMMs) and explicitly taking into account the probability distribution contained in each discrete affordance concept, which can lead to a more correct learning.

Gaussian Mixture Models for Affordance Learning using Bayesian Networks

TL;DR

This work tackles autonomous affordance learning for embodied agents under noisy sensory observations by replacing fully observed discrete BN nodes with Gaussian Mixture Model (GMM) sensor representations. The core method extends prior BN-based affordance learning by coupling discrete object-action-effect nodes with continuous sensor nodes and applying an EM algorithm to learn parameters in the presence of hidden variables, including MAP-based structure initialization to avoid full Structural-EM. Empirical results on simple and complex BN benchmarks show that EM over the full GMM distribution yields substantial RMS-error reductions and improved log-likelihoods, especially as data volume grows or sensor noise increases. The findings demonstrate that probabilistic clustering of sensory inputs improves robustness and inference in affordance learning, albeit with computational costs and opportunities for online or scalable extensions.

Abstract

Affordances are fundamental descriptors of relationships between actions, objects and effects. They provide the means whereby a robot can predict effects, recognize actions, select objects and plan its behavior according to desired goals. This paper approaches the problem of an embodied agent exploring the world and learning these affordances autonomously from its sensory experiences. Models exist for learning the structure and the parameters of a Bayesian Network encoding this knowledge. Although Bayesian Networks are capable of dealing with uncertainty and redundancy, previous work considered complete observability of the discrete sensory data, which may lead to hard errors in the presence of noise. In this paper we consider a probabilistic representation of the sensors by Gaussian Mixture Models (GMMs) and explicitly taking into account the probability distribution contained in each discrete affordance concept, which can lead to a more correct learning.
Paper Structure (18 sections, 20 equations, 5 figures)

This paper contains 18 sections, 20 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Learning Object Affordances
  3. Developing Basic Skills
  4. Affordance Modeling and Learning
  5. Inference and Interaction Games
  6. Probabilistic clustering for Affordances
  7. Learning the Structure
  8. Learning the Parameters
  9. E step
  10. M step
  11. Results
  12. Procedure
  13. Simple Bayesian Network Results
  14. Complex Bayesian Network Results
  15. Conclusions and Future Work
  16. ...and 3 more sections

Figures (5)

  • Figure 1: BN with discrete,observed nodes
  • Figure 2: Bayesian Network of the new clustering approach. The affordances are still represented as interactions between discrete variables (squares). The GMM is represented by the new continuous variables (circles). Shaded shapes represents observed variables during training $\mathcal{X} = (Actions, Objects, Effects)$. However, during execution, we can estimate any variable of $\mathcal{X}$, given the other two observations. The thick arrows represent the new dependence of the sensors and their associated features
  • Figure 3: RMS error of the difference between learned parameters and the real ones given a database with 300 or 3000 cases. a) Sensor noise distributed according to $\mathcal{N}(0,1)$, b) Sensor noise distributed according to $\mathcal{N}(0,9)$ c) The simple Bayesian network.
  • Figure 4: a) RMS error of the difference between learned parameters and the real ones given a database with 300, 3000 or 10000 cases. b) Discrete variables of the realistic Bayesian network. The continuous variables (sensors) have been removed for clarification.
  • Figure 5: Evolution of the log-likelihood of the parameters for the realistic network with a database of 300 cases