N-ary Gaussian Model Modeling Pointing Uncertainty Across Task Scenarios Using an Automated Multi-Gaussian Modeling Pipeline

Paper Title

N-ary Gaussian Model Modeling Pointing Uncertainty Across Task Scenarios Using an Automated Multi-Gaussian Modeling Pipeline

Publication Info

• Topic area: Modeling pointing uncertainty in human-computer interaction (HCI) tasks.
• Keywords: N-ary Gaussian Model, pointing uncertainty, endpoint distribution, Bayesian Information Criterion, Shapley values, multi-Gaussian framework, spatial-temporal modeling, input modality, display devices, automated modeling.

Background and Problem

• Problem / challenge: Existing models for endpoint distribution in pointing tasks are either black-box models that lack interpretability or white-box models that require extensive manual effort and domain expertise to construct. These models often fail to generalize across diverse task scenarios or incorporate multiple influencing factors such as input modality, display device, and temporal constraints.
• Significance: Understanding and predicting endpoint distributions in pointing tasks is critical for optimizing user interfaces, reducing error rates, and improving interaction performance across a variety of HCI applications.
• Motivation and related work: Prior models, such as Fitts’ Law and multi-Gaussian frameworks (e.g., Dual and Ternary Gaussian models), have been used to predict movement time and error rates but are limited in their ability to generalize across complex scenarios. Automated modeling attempts, like those using Bayesian Information Criterion (BIC) or black-box methods, have shown promise but often lack interpretability or scalability.

Solution

• Proposed approach: The N-ary Gaussian Model, an automated pipeline for modeling endpoint distributions in pointing tasks, built upon the multi-Gaussian framework. It systematically incorporates task attributes into Gaussian components and optimizes model selection using BIC and Shapley values.
• Novelty:
  1. Automated generation and optimization of Gaussian components without predefined equations.
  2. Integration of cross-device, input modality, and temporal constraints into spatial pointing uncertainty modeling.
  3. Use of BIC for model selection and Shapley values for filtering low-contribution terms, balancing simplicity and accuracy.
  4. Demonstration of generalizability across 7 datasets, covering diverse task scenarios (1D, 2D, 3D, static, dynamic, and temporal).
• Procedure and key techniques:
  1. Map task attributes to Gaussian components and instantiate them using predefined functional forms.
  2. Use BIC to select the optimal model by balancing fit and complexity.
  3. Apply Shapley values to quantify term contributions and filter low-impact terms.
  4. Validate the model on diverse datasets and compare performance against white-box and black-box baselines.

Results

• Concrete findings:
  • Achieved an average reduction of 28.759% in Mean Wasserstein Distance (MWD) compared to white-box baselines across 7 datasets.
  • Reduced Mean Absolute Error (MAE) in error rate prediction by 19.07% on average.
  • Maintained competitive accuracy with black-box models while using significantly fewer parameters (mean: 12.429 vs. 2467.429 for Feedforward Neural Networks).
• Advantage over baselines:
  • Outperformed white-box models in all datasets, with an average MWD reduction of 6.074.
  • Achieved comparable performance to black-box models despite using far fewer parameters, demonstrating better interpretability and efficiency.
• Experiments / evaluation:
  • Evaluated on 7 datasets spanning 1D, 2D, and 3D tasks, with varying attributes such as input modality, display device, and temporal constraints.
  • Benchmarked against white-box models (e.g., Ternary Gaussian) and black-box models (SVM, FNN).
  • Conducted cross-validation to assess robustness and generalization.
• Limitations and future work:
  • Assumes endpoint distributions follow a normal distribution and focuses on regular geometric target shapes.
  • Relies on data quality and may include terms with limited interpretability.
  • Limited to explicitly logged attributes; future work could explore richer logging schemes and parallelized computations for scalability.

Summary

The N-ary Gaussian Model provides an automated and extensible solution for modeling endpoint distributions in pointing tasks, addressing limitations of prior white-box and black-box models. By leveraging BIC for model selection and Shapley values for term filtering, it balances simplicity, interpretability, and predictive accuracy. The model demonstrated robust performance across diverse datasets, reducing error rates and outperforming baselines in MWD. Its ability to incorporate novel task attributes, such as input modality and temporal constraints, makes it a valuable tool for HCI research and UI optimization. Future work will focus on extending the model to handle more complex scenarios and improving computational efficiency.