I recently wrote a tiny bit about the style of the original published proof of the Erdős-Ko-Rado theorem. In this note I’ll write a bit about the theorem and a bit more about the style of some later proofs. In particular I want to write about two different readings of Katona’s proof. Continue reading Proof style in the Erdős-Ko-Rado theorem

# Erdős writing like a programmer

Here is a neat example of famous mathematician Pál Erdős (often rendered in English as Paul Erdős) writing like a programmer in 1961. He goes to some trouble to introduce notation that allows him to index everything from zero. Continue reading Erdős writing like a programmer

# I still think you can manufacture an unfair coin

In Gelman and Nolan’s paper “You Can Load a Die, But You Can’t Bias a Coin” The American Statistician, November 2002, Vol. 56, No. 4 it is argued you can’t easily produce a coin that is biased when flipped (and caught). A number of variations that can be easily biased (such as spinning) are also discussed.

Obviously Gelman and Nolan are smart and careful people. And we are discussing a well-regarded peer-reviewed article. So we don’t expect there is a major error. What we say is the abstraction they are using doesn’t match the physical abstraction I would pick. I pick a different one and I get different results. This is what I would like to discuss. Continue reading I still think you can manufacture an unfair coin

# What can be in an R data.frame column?

As an R programmer have you every wondered what can be in a `data.frame`

column? Continue reading What can be in an R data.frame column?

# New video course: Campaign Response Testing

I am proud to announce a new Win-Vector LLC statistics video course:

Campaign Response Testing

John Mount, Win-Vector LLC

Continue reading New video course: Campaign Response Testing

# How and why to return functions in R

One of the advantages of functional languages (such as R) is the ability to create and return functions “on the fly.” We will discuss one good use of this capability and what to look out for when creating functions in R. Continue reading How and why to return functions in R

# Using closures as objects in R

For more and more clients we have been using a nice coding pattern taught to us by Garrett Grolemund in his book *Hands-On Programming with R*: make a function that returns a list of functions. This turns out to be a classic functional programming techique: use closures to implement objects (terminology we will explain).

It is a pattern we strongly recommend, but with one caveat: it can leak references similar to the manner described in here. Once you work out how to stomp out the reference leaks the “function that returns a list of functions” pattern is really strong.

We will discuss this programming pattern and how to use it effectively. Continue reading Using closures as objects in R

# One place not to use the Sharpe ratio

Having worked in finance I am a public fan of the Sharpe ratio. I have written about this here and here.

One thing I have often forgotten (driving some bad analyses) is: the Sharpe ratio isn’t appropriate for models of repeated events that already have linked mean and variance (such as Poisson or Binomial models) or situations where the variance is very small (with respect to the mean or expectation). These are common situations in a number of large scale online advertising problems (such as modeling the response rate to online advertisements or email campaigns).

Photo “eggs in a basket” copyright MicoAssist appropriate CC license

In this note we will quickly explain the problem. Continue reading One place not to use the Sharpe ratio

# The Win-Vector R data science value pack

Win-Vector LLC is proud to announce the R data science value pack. 50% off our video course *Introduction to Data Science* (available at Udemy) and 30% off *Practical Data Science with R* (from Manning). Pick any combination of video, e-book, and/or print-book you want. Instructions below.

Please share and Tweet! Continue reading The Win-Vector R data science value pack

# Does Balancing Classes Improve Classifier Performance?

It’s a folk theorem I sometimes hear from colleagues and clients: that you must balance the class prevalence before training a classifier. Certainly, I believe that classification tends to be *easier* when the classes are nearly balanced, especially when the class you are actually interested in is the rarer one. But I have always been skeptical of the claim that artificially balancing the classes (through resampling, for instance) always helps, when the model is to be run on a population with the native class prevalences.

On the other hand, there are situations where balancing the classes, or at least enriching the prevalence of the rarer class, might be necessary, if not desirable. Fraud detection, anomaly detection, or other situations where positive examples are hard to get, can fall into this case. In this situation, I’ve suspected (without proof) that SVM would perform well, since the formulation of hard-margin SVM is pretty much distribution-free. Intuitively speaking, if both classes are far away from the margin, then it shouldn’t matter whether the rare class is 10% or 49% of the population. In the soft-margin case, of course, distribution starts to matter again, but perhaps not as strongly as with other classifiers like logistic regression, which explicitly encodes the distribution of the training data.

So let’s run a small experiment to investigate this question.

Continue reading Does Balancing Classes Improve Classifier Performance?