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Straight to the point, I'm a math student and I have a course this year called Statistical Learning. From the description, the course contains:

Large datasets analysis, regression, principal components analysis, clustering, decision making using trees, neural networks, bayesian networks, support vector machines and applications of the above using R.

The suggested coursebook is "Statistical Learning with applications in R" by Springer.

My understanding is that Machine Learning is a field of Artificial Intelligence on learning by making predictions and analysis on data.

Since most of the topics mentioned above are covered in machine learning, is Statistical Learning related to Machine Learning or is it just a synonym? My guess is that Statistical Learning

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These are pretty much the same thing. But if you want to make a distinction, for me machine learning, as a subfield of artificial intelligence, is more about a pratictal (or computer science) point of view. Statistical learning is a general (abstract) theory that can be applied with the different methods and algorithms that your course contains.

See https://en.wikipedia.org/wiki/Statistical_learning_theory

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