IMHO Neither you nor Noah correctly explains the parametric vs non-parametric model.
Nonparametric models are not “parameterless” models, as you and Noah suggest.
The opposite is that all models with parameters are parametric, which inevitably claim that all models are stored in the computer, but that's not true.
Nonparametric models do not have a *fixed number* of parameters. There are still parameters. example:
Non-parametric: Supports decision trees, vector machines. Neither has a fixed number of parameters. In a decision tree, additional subtrees can be grown at all times, increasing the number of parameters. In the Support Vector Machine, you can add support vectors to increase the number of parameters. Importantly, both cases gradually improve both the number of parameters and their value during training/learning.
Parametric: Neural networks, linear models. Number of modifications for the parameters. The value of the parameter evolves during training/learning, but the number of parameters remains the same.
From Wikipedia: (https://en.wikipedia.org/wiki/nonparametric_statistics#non-parametric_models)
“A nonparametric model differs from a parametric model in that the model structure is not a priori specified, but instead determined from the data. The term nonparametric does not mean that such a model is completely lacking parameters, and does not mean that the number and nature of the parameters is flexible and has not been modified in advance.”
