Training/test divergence in chess leads to "blunder of the century"

In class, I noted that catastrophic things can happen when the training data do not sufficiently represent situations that can occur in real life -- this is often referred to as the divergence between training data and test data. An interesting instance of this happening in the real world: a high stakes human-vs-machine chess match where the position on the board was simply outside the "repertoire" of the human grandmaster.

It turns out that this has been referred to as "the blunder of the century". In blog comments immediately afterwards, one person wrote, in all seriousness:

I have a bad feeling. No, I can't believe that Kramnik really just overlooked a mate in one. It is almost a must: he may have come down with some health problem, what was able to "disconnect" his thinking (like a mini-stroke or temporary cerebral ischemia or something along that line). At this point I am concerned about his health.I wouldn't be surprised if the next news would be that he is in a hospital.

Chess enthusiasts may be interested in this detailed analysis of what happened, including, as a mentioned, analysis looking at the grandmaster's visual attention as an indicator of what he was thinking at the time.

Monothetic Class

Thanks to Bill for pointing out the concept of monotheticity. (Did I just create a word?)

In a quick googling, most notions of this term seem to be fairly intuitive and easy to grasp:

monothetic

A Dictionary of Zoology | Date: 1999

monothetic In numerical classification schemes, the use of a single criterion or attribute as the basis for each subdivision of a sample population, as for example in association analysis. Compare POLYTHETIC.

(http://www.encyclopedia.com/doc/1O8-monothetic.html)

Monothetic / polythetic classification

A monothetic class is defined in terms of characteristics that are both necessary and sufficient in order to identify members of that class. This way of defining a class is also termed the Aristotelian definition of a class.

A polythetic class is defined in terms of a broad set of criteria that are neither necessary nor sufficient. Each member of the category must possess a certain minimal number of defining characteristics, but none of the features has to be found in each member of the category. This way of defining classes is associated with Wittgenstein's concept of "family resemblances." Monothetic type is a type in which all members are identical on all characteristics. Polythetic type is a type in which all members are similar, but not identical.
...

(http://www.db.dk/bh/lifeboat_ko/CONCEPTS/monothetic.htm)


But it can get worse... :

We call an algebraic group monothetic if it possesses a dense cyclic subgroup. For an arbitrary field k we describe the structure of all, not necessarily affine, monothetic k-groups G and determine in which cases G has a k-rational generator.
...

(http://www.austms.org.au/Publ/Jamsa/V82P3/r104.html)


Polytheticity (YAY! Another new word!) seems to me closely related with fuzzy sets and fuzzy membership, in that they both share the concept of prototypicality; however, in order to be, say, ".7 bird" you don't have to possess 70% of the bird properties (even if they could be monothetically listed ;-)). So these concepts are not the same.


If you want to read more about the relations of these concepts to other probably relevanty concepts to many of us, such as taxonomies, there's also this book:

Typologies and Taxonomies

By Kenneth D. Bailey

(http://books.google.com/books?id=1TaYulGjhLYC&pg=PA7&lpg=PA7&dq=monothetic+class&source=web&ots=LP0J1C8hgW&sig=Vn05C3UEjpxSc2Qksdb9KKrVU_Q&hl=en&sa=X&oi=book_result&resnum=10&ct=result)


-Yuval

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This is the class blog for Linguistics 848, Seminar on Computational Learning (an advanced seminar in computational linguistics) at the University of Maryland, Fall 2008. See the course page for more information.