<p>In the paper <a href="http://aboumoustafa.org/KAM_ECML2015.pdf" rel="nofollow noreferrer">Generalization in Unsupervised Learning</a> (2015), <a href="http://aboumoustafa.org/" rel="nofollow noreferrer">Abou-Moustafa</a> and Schuurmans develop an approach to assess the generalization of an unsupervised learning algorithm <span class="math-container">$A$</span> on a given dataset <span class="math-container">$S$</span> and how to compare the generalization ability of two unsupervised learning algorithms <span class="math-container">$A_1$</span> and <span class="math-container">$A_2$</span>, for the same learning task.</p>

<p>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 <span class="math-container">$A$</span>'s expected loss.</p>

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

CC BY-SA 4.0
2020-04-19T23:14:11.527Z
2020-04-19T23:31:09.580Z
2020-04-19T23:31:09.580Z
nbro
<p>I've been learning a little bit about generalization theory, and in particular, the PAC (and PAC-Bayes) approach to thinking about this problem.</p>

<p>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?</p>

<p>Any ideas?</p>

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2020-04-19T23:08:03.143Z
Cross-posted: https://ai.stackexchange.com/q/20382/1794, https://cstheory.stackexchange.com/q/46660/5038.  Please [do not post the same question on multiple sites](https://meta.stackexchange.com/q/64068).
D.W.
<machine-learning><unsupervised-learning><generalization><pac-learning>
Is there a notion of generalization in unsupervised learning?
Marcel
# Is there a notion of generalization in unsupervised learning?

(Asked by: username_0 on 2020-04-19)

I've been learning a little bit about generalization theory, and in particular, the PAC (and PAC-Bayes) approach to thinking about this problem.

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?

**Tags:** machine-learning, unsupervised-learning, generalization, pac-learning

> **Comments:**
> **username_1**: Cross-posted: https://ai.stackexchange.com/q/20382/1794, https://cstheory.stackexchange.com/q/46660/5038.  Please [do not post the same question on multiple sites](https://meta.stackexchange.com/q/64068).  

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## 1 answers

### Answer by username_2 on 2020-04-19. Score: 1 | Accepted answer

In the paper [Generalization in Unsupervised Learning](http://aboumoustafa.org/KAM_ECML2015.pdf) (2015), [Abou-Moustafa](http://aboumoustafa.org/) 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.


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