Languages of Learning

A language is a set of primitives which can be combined to succesfully create complex objects. Languages arise in all sorts of situations: mechanical construction, martial arts, communication, etc… Languages appear to be the key to succesfully creating complex objects—it is difficult to come up with any convincing example of a complex object which is not built using some language. Since languages are so crucial to success, it is interesting to organize various machine learning research programs by language.

The most common language in machine learning are languages for representing the solution to machine learning. This includes:

  1. Bayes Nets and Graphical Models A language for representing probability distributions. The key concept supporting modularity is conditional independence. Michael Kearns has been working on extending this to game theory.
  2. Kernelized Linear Classifiers A language for representing linear separators, possibly in a large space. The key form of modularity here is kernelization.
  3. Neural Networks A language for representing and learning functions. The key concept supporting modularity is backpropagation. (Yann LeCun gave some very impressive demos at the Chicago MLSS.)
  4. Decision Trees Another language for representing and learning functions. The key concept supporting modularity is partitioning the input space.

Many other learning algorithms can be seen as falling into one of the above families.

In addition there are languages related to various aspects of learning.

  1. Reductions A language for translating between varying real-world losses and core learning algorithm optimizations.
  2. Feature Languages Exactly how features are specified varies from on learning algorithm to another. Several people have been working on languages for features that cope with sparsity or the cross-product nature of databases.
  3. Data interaction languages The statistical query model of learning algorithms provides a standardized interface between data and learning algorithm.

These lists surely miss some languages—feel free to point them out below.

With respect to research “interesting” language-related questions include:

  1. For what aspects of learning is a language missing? Anytime adhocery is encountered, this suggests that there is room for a language. Finding what is not there is both hard and valuable.
  2. Are any of these languages fundamentally flawed or fundamentally advantageous with respect to another language?
  3. What are the most easy to use and effective primitives for these languages?

Wikis for Summer Schools and Workshops

Chicago ’05 ended a couple of weeks ago. This was the sixth Machine Learning Summer School, and the second one that used a wiki. (The first was Berder ’04, thanks to Gunnar Raetsch.) Wikis are relatively easy to set up, greatly aid social interaction, and should be used a lot more at summer schools and workshops. They can even be used as the meeting’s webpage, as a permanent record of its participants’ collaborations — see for example the wiki/website for last year’s NVO Summer School.

A basic wiki is a collection of editable webpages, maintained by software called a wiki engine. The engine used at both Berder and Chicago was TikiWiki — it is well documented and gets you something running fast. It uses PHP and MySQL, but doesn’t require you to know either. Tikiwiki has far more features than most wikis, as it is really a full Content Management System. (My thanks to Sebastian Stark for pointing this out.) Here are the features we found most useful:

  • Bulletin boards, or forums. The most-used one was the one for social events, which allowed participants to find company for doing stuff without requiring organizer assistance. While conferences, by their inherently less interactive nature, don’t usually benefit from all aspects of wikis, this is one feature worth adding to every one. [Example]

    Other useful forums to set up are “Lost and Found”, and discussion lists for lectures — although the latter only work if the lecturer is willing to actively answer questions arising on the forum. You can set forums up so that all posts to them are immediately emailed to someone.

  • Editable pages. For example, we set up pages for each lecture that we were able to edit easily later as more information (e.g. slides) became available. Lecturers who wanted to modify their pages could do so without requiring organizer help or permission. (Not that most of them actually took advantage of this in practice… but this will happen in time, as the wiki meme infects academia.) [Example]
  • Sign-up sheets. Some tutorials or events were only open to a limited number of people. Having editable pages means that people can sign up themselves. [Example]
  • FAQs. You can set up general categories, and add questions, and place the same question in different categories. We set most of this up before the summer school, with directions of how to get there from the airport, what to bring, etc. We also had volunteers post answers to anticipated FAQs like the location of local restaurants and blues clubs. [Example]
  • Menus. You can set up the overall layout of the webpage, by specifying the locations and contents menus on the left and right of a central `front page’. This is done via the use of `modules’, and makes it possible for your wiki pages to completely replace the webpages — if you are willing to make some aesthetic sacrifices.
  • Different levels of users: The utopian wiki model of having ‘all pages editable by everyone’ is … well, utopian. You can set up different groups of users with different permissions.

  • Calendars. Useful for scheduling, and for changes to schedules. (With the number of changes we had, we really needed this.) You can have multiple calendars e.g. one for lectures, another for practical sessions, and another for social events — and users can overlay them on each other. [Example]

A couple of other TikiWiki features that we didn’t get working at Chicago, but would have been nice to have, are these:

  • Image Galleries. Gunnar got this working at Berder, where it was a huge success. Photographs are great icebreakers, even the ones that don’t involve dancing on tables.
  • Surveys. These are easy to set up, and have option for participants to see, or not to see, the results of surveys — useful when asking people to rate lectures.

TikiWiki also has several features that we didn’t use, such as blogs and RSS feeds. It also has a couple of bugs (and features that are bad enough to be called bugs), such as permission issues and the inability to print calendars neatly. These will doubtless get cleaned up in due course.

Finally, owing to much prodding from John and some other MLSS participants, I’ve written up my experiences in using TikiWiki @ Chicago ’05 on my website, including installation instructions and a list of “Good Things to Do”. This documentation is meant to be a survival guide complementary to the existing TikiWiki documentation, which can sometimes be overwhelming.

Families of Learning Theory Statements

The diagram above shows a very broad viewpoint of learning theory.

arrow Typical statement Examples
Past->Past Some prediction algorithm A does almost as well as any of a set of algorithms. Weighted Majority
Past->Future Assuming independent samples, past performance predicts future performance. PAC analysis, ERM analysis
Future->Future Future prediction performance on subproblems implies future prediction performance using algorithm A. ECOC, Probing

A basic question is: Are there other varieties of statements of this type? Avrim noted that there are also “arrows between arrows”: generic methods for transforming between Past->Past statements and Past->Future statements. Are there others?

Is the Goal Understanding or Prediction?

Steve Smale and I have a debate about goals of learning theory.

Steve likes theorems with a dependence on unobservable quantities. For example, if D is a distribution over a space X x [0,1], you can state a theorem about the error rate dependent on the variance, E(x,y)~D (y-Ey’~D|x[y’])2.

I dislike this, because I want to use the theorems to produce code solving learning problems. Since I don’t know (and can’t measure) the variance, a theorem depending on the variance does not help me—I would not know what variance to plug into the learning algorithm.

Recast more broadly, this is a debate between “declarative” and “operative” mathematics. A strong example of “declarative” mathematics is “a new kind of science”. Roughly speaking, the goal of this kind of approach seems to be finding a way to explain the observations we make. Examples include “some things are unpredictable”, “a phase transition exists”, etc…

“Operative” mathematics helps you make predictions about the world. A strong example of operative mathematics is Newtonian mechanics in physics: it’s a great tool to help you predict what is going to happen in the world.

In addition to the “I want to do things” motivation for operative mathematics, I find it less arbitrary. In particular, two reasonable people can each be convinced they understand a topic in ways so different that they do not understand the viewpoint. If these understandings are operative, the rest of us on the sidelines can better appreciate which understanding is “best”.

Research Styles in Machine Learning

Machine Learning is a field with an impressively diverse set of reseearch styles. Understanding this may be important in appreciating what you see at a conference.

  1. Engineering. How can I solve this problem? People in the engineering research style try to solve hard problems directly by any means available and then describe how they did it. This is typical of problem-specific conferences and communities.
  2. Scientific. What are the principles for solving learning problems? People in this research style test techniques on many different problems. This is fairly common at ICML and NIPS.
  3. Mathematical. How can the learning problem be mathematically understood? People in this research style prove theorems with implications for learning but often do not implement (or test algorithms). COLT is a typical conference for this style.

Many people manage to cross these styles, and that is often beneficial.

Whenver we list a set of alternative, it becomes natural to think “which is best?” In this case of learning it seems that each of these styles is useful, and can lead to new useful discoveries. I sometimes see failures to appreciate the other approaches, which is a shame.