Category: Machine Learning

…is discussed in this nytimes article. I generally expect such approaches to become more common since computers are getting faster, machine learning is getting better, and data is becoming more plentiful. This is another example where machine learning technology may have a huge economic impact. Some side notes:

1. We-in-research know almost nothing about how these things are done (because it is typically a corporate secret).
2. … but the limited discussion in the article seem naive from a machine learning viewpoint.
   1. The learning process used apparently often fails to take into account transaction costs.
   2. What little of the approaches is discussed appears modeling based. It seems plausible that more direct prediction methods can yield an edge.
3. One difficulty with stock picking as a research topic is that it is inherently a zero sum game (for every winner, there is a loser). Much of the rest of research is positive sum (basically, everyone wins).

A few weeks ago I read this. David Blei and I spent some time thinking hard about this a few years back (thanks to Kary Myers for pointing us to it):

In short I was thinking that “bayesian belief updating” and “maximum entropy” were two othogonal principles. But it appear that they are not, and that they can even be in conflict !
Example (from Kass 1996); consider a Die (6 sides), consider prior knowledge E[X]=3.5.
Maximum entropy leads to P(X)= (1/6, 1/6, 1/6, 1/6, 1/6, 1/6).
Now consider a new piece of evidence A=”X is an odd number”
Bayesian posterior P(X|A)= P(A|X) P(X) = (1/3, 0, 1/3, 0, 1/3, 0).
But MaxEnt with the constraints E[X]=3.5 and E[Indicator function of A]=1 leads to (.22, 0, .32, 0, .47, 0) !! (note that E[Indicator function of A]=P(A))
Indeed, for MaxEnt, because there is no more ‘6′, big numbers must be more probable to ensure an average of 3.5. For bayesian updating, P(X|A) doesn’t have to have a 3.5 expectation. P(X) and P(X|a) are different distributions.
Conclusion ? MaxEnt and bayesian updating are two different principle leading to different belief distributions. Am I right ?

I don’t believe there is any paradox at all between MaxEnt (perhaps more generally, MinRelEnt) and Bayesian updates. Here, straight MaxEnt make no sense. The implication of the problem is that the ensemble average 3.5 is no longer an active constraint. That is, we no longer believe the contraint E[X]=3.5 once we have the additional data that X is an odd number. The sequential update using minimum relative entropy is identical to Bayes rule and produces the correct answer. These two answers are simply (correct) answers to different questions.

It was a fine time for learning in Pittsburgh. John and Sam mentioned some of my favorites. Here’s a few more worth checking out:

Online Multitask Learning
Ofer Dekel, Phil Long, Yoram Singer
This is on my reading list. Definitely an area I’m interested in.

Maximum Entropy Distribution Estimation with Generalized Regularization
Miroslav Dudík, Robert E. Schapire

Learning near-optimal policies with Bellman-residual minimization based fitted policy iteration and a single sample path
András Antos, Csaba Szepesvári, Rémi Munos
Again, on the list to read. I saw Csaba and Remi talk about this and related work at an ICML Workshop on Kernel Reinforcement Learning. The big question in my head is how this compares/contrasts with existing work in reductions to reinforcement learning. Are there advantages/disadvantages?

Higher Order Learning On Graphs> by Sameer Agarwal, Kristin Branson, and Serge Belongie, looks to be interesteding. They seem to poo-poo “tensorization” of existing graph algorithms.

Cover Trees for Nearest Neighbor (Alina Beygelzimer, Sham Kakade, John Langford) finally seems to have gotten published. It’s an embarrassment to the community that it took this long– and a reminder of how diligent one has to be in ensuring good work gets published. This seems to happen on a regular basis. (See A New View of EM.)

Finally, I thought this one was very cool:
Constructing Informative Priors by Rajat Raina, Andrew Y. Ng, Daphne Koller.
Same interest as the first paper on the list.
Check them out!