Lots of open education resources for your gadgetry

While not related exclusively to statistics, this resource does relate to open education. This page at OpenCulture.com gives a large list of resources of books, courses, and media you can use to fill your new (or old) gadget. They have a list of free online courses as well, with statistics falling under computer science, engineering, and mathematics.

Sounds like Christmas and New Year’s resolution wrapped up into one nice gift!

A statistician’s view of Stanford’s open Introduction to Databases class

In addition to the Introduction to Machine Learning class (which I have reviewed), I took a class on introduction to databases, taught by Prof. Jennifer Widom. This class consisted of video lectures, review questions, and exercises. Topics covered included XML (markup, DTDs, schema, XPath, XQuery, and XSLT) and relational databases (relational algebra, database normalization, SQL, constraints, triggers, views, authentication, online analytical processing, and recursion). At the end we had a quick lesson on NoSQL systems just to introduce the topic and discuss where they are appropriate.

This class was different in structure from the Machine Learning class in two ways: there were two exams and the potential for a statement of accomplishment.

I think any practicing statistician should learn at least the material on relational databases, because data storage and retrieval is such an important part of statistics today. Many different statistical packages now connect to relational databases through technologies like ODBC, and knowledge of SQL can enhance the use of these systems. For example, for subset analyses it is usually better to do subsetting with the database than pull all the data into the statistical analysis package and then perform the subset. In biostatistics, the data are usually collected in a database using an electronic data capture or paper-based system, which store the data in an Oracle database.

I found that I already use the material in this course, even though I typically don’t write SQL queries more complicated than a simple subset. Some of the examples for the exercises involved representing a social network, which may help when I do my own analyses of networks. Other examples were of relationships that you might find in biostatistics and other fields.

I found that by spending up to 5 hours a week on the class I was able to get a lot out of it. Unfortunately, Stanford is not offering this in the winter quarter, but they have promised to offer this again in the future. I heartily recommend it for anyone practicing statistics, and the price is right.

MIT launches online learning initiative

This may not relate directly to statistics, but it relate to my experiences in an online introductory machine learning class.

MIT has decided to launch online public classes of its own. It looks like they are making the platform open-source as well and encouraging other institutions to go online as well.

This may well be the most exciting development in education in years. Hopefully it won’t be too long before we see efforts to get hardware into disadvantaged neighborhoods or other countries (such as the one laptop per child project from a few years ago) combined with this online education.

For Stanford’s winter 2012 classes, check out Class Central.

A statistician’s view on Stanford’s public machine learning course

This past fall, I took Stanford’s class on machine learning. Overall, it was a terrific experience, and I’d like to share a few thoughts on it:

• A lot of participants were concerned that it was a watered down version of Stanford’s CS229. And, in fact, the course was more limited in scope and more applied than the official Stanford class. However, I found this to be a strength. Because I was already familiar with most of the methods in the beginning (linear and multiple regression, logistic regression), I could focus more on the machine learning perspective that the class brought to these methods. This helped in later sections where I wasn’t so familiar with the methods.
• The embedded review questions and the end of section review questions were very well done, with some randomization algorithm making it impossible to guess until everything was right.
• Programming exercises were done in Octave, an open source Matlab-like programming environment. I really enjoyed doing this programming, because it meant I essentially programmed regression and logistic regression algorithms by hand with the exception of a numerical optimization algorithm. I got a huge confidence boost when I managed to get the backpropagation algorithm for neural networks correct. Emphasis on these exercises was on the loops, which you could code using “slow” loops (for loops, for instance), but then really needed to vectorize using the principles of linear algebra. For instance, there was an algorithm for a recommender system that would take hours if coded using for loops, but ran in minutes using a vectorized implementation. (This is because the implicit loops of vectorization were run using optimized linear algebra routines.) In statistics, we don’t always worry about implementation details so much, but in machine learning situations, implementation is important because these algorithms often need to run in real time.
• The class encouraged me to look at the Kaggle competitions. I’m not doing terribly well in them, but now at least I’m hacking on some data myself and learning a lot in the process.
• The structure of the public class helps a lot over, for example, the iTunes U version of the class. But now I’m looking at the CS 229 lectures on iTunes U and am understanding them a lot more now.
• Kudos to Stanford for taking the lead on this effort. This is the next logical progression of distance education, and takes a lot of effort and time.

I also took the databases class, which was even more structured with a mid-term and final exam. This was a bit of a stretch for me, but learning about data storage and retrieval is a good complement to statistics and machine learning. I’ve coded a few complex SQL queries in my life, but this class really took my understanding of both XML-based and relational database systems to the next level.

Stanford is offering machine learning again, along with a gaggle of other classes. I recommend you check them out. (Find a list, for example, at the bottom of the page of Probabilistic Graph Models site.) (Note: Stanford does not offer official credit for these classes.)

It’s not every day a new statistical method is published in Science

I’ll have to check this out – Maximal Information-based Nonparametric Exploration (MINE - har har). The link to the paper in Science.

I haven’t looked at this very much yet. It appears to be a way of weeding out potential variable relationships for further exploration. Because it’s nonparametric, relationships don’t have to be linear, and spurious relationships are controlled with a false discovery rate method. A jar file and R file are both provided.

From datasets to algorithms in R

Many statistical algorithms are taught and implemented in terms of linear algebra. Statistical packages often borrow heavily from optimized linear algebra libraries such as LINPACK, LAPACK, or BLAS. When implementing these algorithms in systems such as Octave or MATLAB, it is up to you to translate the data from the use case terms (factors, categories, numerical variables) into matrices.

In R, much of the heavy lifting is done for you through the formula interface. Formulas resemble y ~ x1 + x2 + …, and are defined in relation to a data.frame. There are a few features that make this very powerful:

• You can specify transformations automatically. For example, you can do y ~ log(x1) + x2 + … just as easily.
• You can specify interactions and nesting.
• You can automatically create a numerical matrix for a formula using model.matrix(formula).
• Formulas can be updated through the update() function.

Recently, I wanted to create predictions via Bayesian model averaging method (bma library on CRAN), but did not see where the authors implemented it. However, it was very easy to create a function that does this:

predict.bic.glm <- function(bma.fit,new.data,inv.link=plogis) {
    # predict.bic.glm
    #  Purpose: predict new values from a bma fit with values in a new dataframe
    #
    # Arguments:
    #  bma.fit - an object fit by bic.glm using the formula method
    #  new.data - a data frame, which must have variables with the same names as the independent
    #             variables as was specified in the formula of bma.fit
    #             (it does not need the dependent variable, and ignores it if present)
    #  inv.link - a vectorized function representing the inverse of the link function
    #
    # Returns:
    #  a vector of length nrow(new.data) with the conditional probabilities of the independent
    #  variable being 1 or TRUE
    # TODO: make inv.link not be specified, but rather extracted from glm.family of bma.fit$call
   
    form <- formula(bma.fit$call$f)[-2] # extract formula from the call of the fit.bma, drop dep var
    des.matrix <- model.matrix(form,new.data)
    pred <- des.matrix %*% matrix(bma.fit$postmean,nc=1)
    pred <- inv.link(pred)
    return(pred)
}

The first task of the function finds the formula that was used in the call of the bic.glm() call, and the [-2] subscripting removes the dependent variable. Then the model.matrix() function creates a matrix of predictors with the original function (minus dependent variable) and new data. The power here is that if I had interactions or transformations in the original call to bic.glm(), they are replicated automatically on the new data, without my having to parse it by hand. With a new design matrix and a vector of coefficients (in this case, the expectation of the coefficients over the posterior distributions of the models), it is easy to calculate the conditional probabilities.

In short, the formula interface makes it easy to translate from the use case terms (factors, variables, dependent variables, etc.) into linear algebra terms where algorithms are implemented. I’ve only scratched the surface here, but it is worth investing some time into formulas and their manipulation if you intend to implement any algorithms in R.

R-bloggers

For a long time, I have relied on R-bloggers for new, interesting, arcane, and all around useful information related to R and statistics. Now my R-related material is appearing there.

If you use the R package at all, R-bloggers should be in your feed aggregator.