Pareto Distribution

I didn't realize that the standard heavy-tailed distribution is the Pareto Distribution. It's a Heavy-tailed distribution which follows the Power Law. It is commonly used to describe wealth distributions.

Update (10/25/10): Another distribution I didn't know about is the negative multinomial distribution. Seems like I would have come across this with all of my work in text classification. Then again, length never seemed to be that useful in determining classification (esp. compared to words). And, I bet even the single failure negative multinomial had too-light of a tail to model actual document lengths accurately.

Open Source Machine Learning Software

I've just learned about mlpy which is open source python machine learning software. It includes a good variety of machine learning algorithms including SVM, k-NN, LASSO, ridge regression, k-mean clustering, k-median clustering, wavlet transforms, and resampling methods. It uses numpy as one would expect. But, I see no mention of the use of sparse matrices, so I suspect that the library would not scale well to large feature matrices, which is typically essential in my work.

It looks like a good resource for open source ML software is MLoss, which organized a NIPS workshop.

A Better Lady Tasting Tea?

I recently learned of the famous Lady Tasting Tea hypothesis test experiment. When I read of Rod Sturdivant's account of the experiment, it struck me that the experiment was not designed to maximize the amount of learned information for a fixed number of cups.

The designer of the experiment, R. A. Fisher, was trying to determine whether a lady could tell whether milk was poured before or after tea was poured into a cup. To test, he presented her with four cups poured milk-first and four cups poured tea-first in random order. This results in 70 possibilities and a 1.4%-chance of correctly determining the order given no ability. A single mistake on the part of the lady would make it impossible to reject the no-ability hypothesis with reasonable (p=0.05) confidence.

If Fisher had instead flipped 8 coins, filling milk first if head and tea first if tails, then there would have been 256 possibilities with a 0.4%-chance (1/256) of guessing all 8 correct given no ability and a 3.9%-chance (9/256) of guessing 7-or-8 correct with no ability. So, with this method, a single mistake would have still allowed one to reject the no-ability hypothesis.

Of course, the coin-flip test is technically more difficult because of the need to make absolute determinations, rather than merely determining an ordering of the cups, as is the case in the permutation test.