Yes, the concepts introduced in this paper regarding NSdim and bounded approximation capacity can be extended to analyze the approximation capacity of other machine learning models beyond neural networks.
Generalization to Other Models: The framework of NSdim can be applied to various machine learning models, such as support vector machines (SVMs), decision trees, and ensemble methods. Each of these models has its own parameter space and complexity, which can be analyzed through the lens of NSdim to understand their approximation capabilities and limitations.
Model Complexity Analysis: The insights regarding bounded NPspace can inform the analysis of model complexity in other machine learning paradigms. For instance, in SVMs, the choice of kernel functions and their parameters can be evaluated in terms of their ability to span the function space effectively, similar to how NSdim is used for neural networks.
Regularization and Overfitting: The principles of regularization that are derived from the NSdim framework can be applied to other models to prevent overfitting. Understanding how the dimensionality of the parameter space affects the model's ability to generalize can lead to better regularization techniques across different machine learning algorithms.
Cross-Model Comparisons: The concepts can facilitate comparisons between different machine learning models. By quantifying their approximation capacities using NSdim, researchers can evaluate which models are more suitable for specific tasks based on their ability to approximate complex functions within bounded parameter spaces.
Extension to Non-Parametric Models: Even non-parametric models, such as Gaussian processes, can benefit from the insights provided by NSdim. The relationship between the complexity of the model and its ability to approximate functions can be explored, leading to a deeper understanding of their performance characteristics.
In summary, the theoretical insights from this paper can be effectively extended to analyze and improve the approximation capacity of a wide range of machine learning models, enhancing their applicability and performance across various domains.