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Say we have a known model $M$ with unknown parameters and more specifically, $M$ is a parametric model.

Parameter estimation on $M$ is applying an appropriate method for estimating the parameters.

My question is: If we know the form/shape of the model $M$ up to unknown parameters, and applying a machine learning algorithm such as gradient descent, does this fall under machine/statistical learning?

Or is it still only parameter estimation using a borrowed method since the model form is known?

It seems the former question is yes since we are "learning" the parameters rather than just doing some algebraic/calculus manipulation to get suitable estimators directly.

My confusion comes from that what reading I have done on machine learning/statistical learning is that the goal is to estimate the model itself or rather the function $f$ which gives the model. Of course, parameter estimation is something utilized in machine/statistical learning but seems the situation I described is a instance of machine/statistical learning, perhaps this instance would be more specifically referred to as parametric machine/statistical learning

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  • $\begingroup$ You can use and often do use statistics/machine learning to estimate parameters of a model. $\endgroup$
    – Henry
    Dec 13, 2022 at 19:25
  • $\begingroup$ @Henry do you know if there is a term to distinguish between machine learning in which the form of model is known but the parameters are not and the model is itself unknown? Perhaps this is trivial but the term 'machine learning' seems to be often used in quite vague terms. $\endgroup$
    – oliverjones
    Dec 13, 2022 at 20:27
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    $\begingroup$ "Machine learning" is vague: some people say it is the use of computers to make predictions , others that it is statistics rediscovered by computer programmers who did not do a statistics course so used different terminology for the same thing. The terminology includes "model selection", "model tuning" and "model training" as different steps so if you impose the model before seeing the data rather than have the machine decide it, you simply skip the first step. $\endgroup$
    – Henry
    Dec 13, 2022 at 23:54
  • $\begingroup$ Thank you that makes it more clear, sometimes you just need someone else to explain a concept in their words for it to make sense. $\endgroup$
    – oliverjones
    Dec 14, 2022 at 1:12

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Yes. It is both. You can use either language.

"Machine learning" is not a term with a formal, precise mathematical definition. What you describe can be considered a form of machine learning.

In practice, when doing model parameter estimation, it's common that what we really care about is the model and the parameters themselves, e.g., because they will help us make inferences about the causal structure of the real world, or because we care about the model itself. In contrast, much use of machine learning focuses more on prediction rather than inference: we care more about predicting future outputs from the model and the parameters are only a means to an end.

Ultimately, to misquote Shakespeare, a rose by any other name is still a rose.

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