Do models without parameters exist? I am reading "A Course in Machine Learning" and, in chapter 2, the author says:

"For most models, there will be associated parameters. These are
the things that we use the data to decide on. Parameters in a decision
tree include: the specific questions we asked, the order in which we
asked them, and the classification decisions at the leaves."

My question is about the first sentence. Is there any model in machine learning that does not have parameters? I can't think of any. For sure there are models without hyperparameters (for instance, the linear model does not contain any hyperparameter, but it still contains 2 parameters, the slope and the y-intercept).

If such parameterless models exist, what are their purpose then? Isn't it the whole point of training to tune a model's parameters?
Is there any model in machine learning that does not have parameters?


Yes. k-nearest neighbors  is parameterless (there is only a single hyper-parameter $k$).


  If such parameterless models exist, what are their purpose then? Isn't it the whole point of training to tune a model's parameters?


Exactly: such models require no training at all. k-NN in particular relies on knowing the data set upon prediction. Anything close to "training" this model would be pushing data points to a set, but these do not count as parameters.