by Joseph Rickert

In last week’s post, I sketched out the history of Generalized Linear Models and their implementations. In this post I’ll attempt to outline how GLM functions evolved in R to handle large data sets.

The first function to make it possible to build GLM models with datasets that are too big to fit into memory was the bigglm()from Thomas Lumley’s biglm package which was released to CRAN in May 2006. bigglm()is an example of a external memory or “chunking” algorithm. This means that data is read from some source on disk and processed one chunk at a time. Conceptually, chunking algorithms work as follows: a program reads a chunk of data into memory, performs intermediate calculations to compute the required sufficient statistics, saves the results and reads the next chunk. The process continues until the entire dataset is processed. Then, if necessary, the intermediate results are assembled into a final result.

According to the documentation trail, bigglm()is based on Alan Miller’s 1991 refinement (algorithm AS 274 implemented in Fortran 77) to W. Morevin Genetlemen’s 1975 Algol algorithm ( AS 75). Both of these algorithms work by updating the Cholesky decomposition of the design matrix with new observations. For a model with p variables, only the p x p triangular Cholesky factor and a new row of data need to be in memory at any given time.

bigglm()does not do the chunking for you. Working with the algorithm requires figuring out how to feed it chunks of data from a file or a database that are small enough to fit into memory with enough room left for processing. ( Have a look at the make.data() function defined on page 4 of the biglm pdf for the prototype example of chunking by passing a function to bigglm()’s data argument.) bigglm() and the biglm package offer few features for working with data. For example, bigglm() can handle factors but it assumes that the factor levels are consistent across all chunks. This is very reasonable under the assumption that the appropriate place to clean and prepare the data for analysis is the underlying database.

The next steps in the evolution of building GLM models with R was the development of memory-mapped data structures along with the appropriate machinery to feed bigglm() data stored on disk. In late 2007, Dan Alder et al. released the ff package which provides data structures that, from R's point of view, make data residing on disk appear is if it were in RAM. The basic idea is that only a chunk (pagesize) of the underlying data file is mapped into memory and this data can be fed to bigglm(). This strategy really became useful in 2011 when Edwin de Jonge, Jan Wijffels and Jan van der Laan released ffbase, a package of statistical functions designed to exploit ff’s data structures. ffbase contains quite a few functions including some for basic data manipulation such as ffappend() and ffmatch(). For an excellent example of building a bigglm() model with a fairly large data set have a look at the post from the folks at BNOSAC. This is one of the most useful, hands-on posts with working code for building models with R and large data sets to be found. (It may be a testimony to the power of provocation.)

Not longer after ff debuted (June 2008), Michael Kane, John Emerson and Peter Haverty released bigmemory, a package for working with large matrices backed by memory-mapped files. Thereafter followed a sequence of packages in the Big Memory Project, including biganalytics, for exploiting the computational possibilities opened by by bigmemory. bigmemory packages are built on the Boost Interprocess C++ library and were designed to facilitate parallel programming with foreach, snow, Rmpi and multicore and enable distributed computing from within R. The biganalytics package contains a wrapper function for bigglm() that enables building GLM models from very large files mapped to big.matrix objects with just a few lines of code.

The initial release in early August 2010 of the RevoScaleR package for Revolution R Enterprise included rxLogit(), a function for building logistic regression models on very masive data sets. rxLogit() was one of the first of RevoScaleR’s Parallel External Memory Algorithms (PEMA). These algorithms are designed specifically for high performance computing with large data sets on a variety of distributed platforms. In June 2012, Revolution Analytics followed up with rxGlm(), a PEMA that implements all of the all of the standard GLM link/family pairs as well as Tweedie models and user-defined link functions. As with all of the PEMAS, scripts including rxGlm() may be run on different platforms just by changing a few lines of code that specifies the user’s compute context. For example, a statistician could test out a model on a local PC or cluster and then change the compute context to run it directly on a Hadoop cluster.

The only other Big Data GLM implementation accessible through an R package of which I am aware is h20.glm() function that is part of the 0xdata’s JVM implementation of machine learning algorithms which was announced in October 2013. As opposed the the external memory R implementations described above, H20 functions run in the distributed memory created by the H20 process. Look here for h20.glm() demo code.

And that's it, I think this brings us up to date with R based (or accessible) functions for running GLMs on large data sets.

Aside from the inability of glm() to cope with very large datasets, another problem I've had with training GLMs is dealing with cases where the underlying optimization algorithm fails, possibly due to an inappropriate choice of initial parameters.

I've had some success with a technique that I saw on a blog somewhere -- selecting a small subset of the data, training an initial model on the subset, and using that model's fitted parameters as the initial parameters to the full GLM. However, I've also noticed that bigglm has much more success in fitting these "difficult" models, possibly due to its underlying algorithm being different.

So, that's another reason to choose bigglm over glm.

Posted by: Jeff Stuckman | May 25, 2014 at 09:18