Is there a notion of generalization in unsupervised learning?

So, I started to wonder if there is an analogous version of "generalization" in Unsupervised Learning? I.e., is there a general framework that encapsulates how "good" an unsupervised learning method is? There's reconstruction error for learning lower dimensional representations, but what about unsupervised clustering?

Any ideas?

• – D.W.
Apr 19 '20 at 23:08

In the paper Generalization in Unsupervised Learning (2015), Abou-Moustafa and Schuurmans develop an approach to assess the generalization of an unsupervised learning algorithm $$A$$ on a given dataset $$S$$ and how to compare the generalization ability of two unsupervised learning algorithms $$A_1$$ and $$A_2$$, for the same learning task.

They first provide a more abstract and general definition of an unsupervised learning algorithm and loss function. Then they define the expected risk, empirical risk and generalization gap in a similar way to the case of supervised learning. Finally, they derive an upper bound on $$A$$'s expected loss.

Of course, you should read the paper for more details. Specifically, section 2 (page 3) describes their setting in detail.