<p>In general, the results are pretty strongly negative --- fairly strong assumptions are needed for something like this to work. As an extreme case, suppose that training and testing distributions have disjoint supports, so that the training sample can be nearly uninformative regarding the test performance.</p>

<p>That having been said, there is a body of research on learning (with) changing target concepts/distributions. Here are four fairly representative samples; once you do a follow-up search of who cites them and who they cite, you'll pretty much span the space:</p>

<p><a href="https://link.springer.com/chapter/10.1007/978-3-642-34106-9_13" rel="nofollow noreferrer">https://link.springer.com/chapter/10.1007/978-3-642-34106-9_13</a></p>

<p><a href="https://link.springer.com/article/10.1023/A:1007604202679" rel="nofollow noreferrer">https://link.springer.com/article/10.1023/A:1007604202679</a></p>

<p><a href="https://dl.acm.org/citation.cfm?id=269812" rel="nofollow noreferrer">https://dl.acm.org/citation.cfm?id=269812</a></p>

<p><a href="https://link.springer.com/article/10.1023/A:1007666507971" rel="nofollow noreferrer">https://link.springer.com/article/10.1023/A:1007666507971</a></p>

<p>Also potentially relevant: Transfer learning
<a href="https://en.wikipedia.org/wiki/Transfer_learning" rel="nofollow noreferrer">https://en.wikipedia.org/wiki/Transfer_learning</a></p>

CC BY-SA 4.0
2018-07-04T20:32:56.773Z
2018-07-04T20:32:56.773Z
Aryeh
<p>We know that the theory of <a href="https://en.wikipedia.org/wiki/Probably_approximately_correct_learning" rel="nofollow noreferrer">PAC-learning</a> is distribution-free, i.e. assuming that the test and train distributions are the same, we have guarantees on learning the hypothesis. </p>

<p>Question: what if the train/test(evaluation) distributions don't match; is there any result that tells us we can still learn something (say when the training distribution is log-concave and the test distribution is uniform). </p>

<machine-learning><lg.learning><dc.distributed-comp>
"Learning" when test and train distributions don't match
Daniel
# "Learning" when test and train distributions don't match

(Asked by: username_0 on 2018-07-04)

We know that the theory of [PAC-learning](https://en.wikipedia.org/wiki/Probably_approximately_correct_learning) is distribution-free, i.e. assuming that the test and train distributions are the same, we have guarantees on learning the hypothesis.

Question: what if the train/test(evaluation) distributions don't match; is there any result that tells us we can still learn something (say when the training distribution is log-concave and the test distribution is uniform).

**Tags:** machine-learning, lg.learning, dc.distributed-comp

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## 1 answers

### Answer by username_1 on 2018-07-04. Score: 3 | Accepted answer

In general, the results are pretty strongly negative --- fairly strong assumptions are needed for something like this to work. As an extreme case, suppose that training and testing distributions have disjoint supports, so that the training sample can be nearly uninformative regarding the test performance.

That having been said, there is a body of research on learning (with) changing target concepts/distributions. Here are four fairly representative samples; once you do a follow-up search of who cites them and who they cite, you'll pretty much span the space:

<https://link.springer.com/chapter/10.1007/978-3-642-34106-9_13>

<https://link.springer.com/article/10.1023/A:1007604202679>

<https://dl.acm.org/citation.cfm?id=269812>

<https://link.springer.com/article/10.1023/A:1007666507971>

Also potentially relevant: Transfer learning
<https://en.wikipedia.org/wiki/Transfer_learning>


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