# R Performance (Part II)

In R performance (Part I), we looked into how to write R code in an efficient way.

In the second part, we will look into more explicit ways of improving R performance.

# Parallel Loops

Doing some sort of loop is almost unavoidable in R. A simple optimisation is to run the loop in parallel.

A obvious machine learning application is when running cross-validation. If you want to run 10-fold cross-validation, if you have 10 cores available, you can run them all in parallel.

The parallel library has a multicore version of lapply, let’s look at the example below:

If you already make use of lapply etc. in your code, modifying to use the multi-core version requires very little code changes.

Sadly this code will not work on Windows as it relies on Unix’s fork command. Instead use the following on a Windows machine:

Update: Nathan VanHoudnos has re-implemented the mclapply function to support Windows, see his comment for more details on how to use this.

Update: One issue I have observed when using mclapply on Linux, if the machine runs out of memory, R will arbitrarily and silently kill processes on some of the cores. This will mean you will not get as many results as you expect. A good error check is to ensure your results has the correct size e.g. same size as your inputs

If instead you prefer for loop syntax,  you can use the foreach package:

The important command here is %dopar%, this says to perform the loop in parallel. If you were to use  %do% it would run on a single process.

#### Memory Usage

In a Unix system (I have no idea how this will work on Windows), when you fork a process (what mclapply does), you get a copy of the current processes memory (think R environment).

However this is called “copy-on-write”, which means unless you modifying the data it will never physically be copied.

This is important, as much as possible you should try to avoid modifying the data inside your mclapply function. However, often this is unavoidable e.g. in your cross validation loop you will need to split data into test and train. In this case, you just need to be aware you will be increasing your memory usage. You may have to trade off how many cores you can use with how much memory you have available.

# Optimised Linear Algebra Library

The default BLAS library used by R is not particular well tuned and has no support for multiple cores. Switching to an alternative BLAS implementation can give a significant speed boost.

Nathan VanHoudnos has an excellent guide on installing alternative BLAS libraries. Here I will summarise the different options:

###### OpenBLAS

OpenBLAS is generally the easiest to install (on Ubuntu you can use apt-get) and has out of the box support for multicore matrix operations.

On major issue (described here) is that currently OpenBLAS multicore matrix operations do not play well with R’s other multicore functionality (parallel, foreach). Trying to use them together will result in segfaults. However, as long as you are aware of this you can design your code around this e.g. only using parallel loops when nothing inside of the loop utilises matrix algebra.

###### ATLAS

ATLAS has the potential to be the most tuned to your particular machine setup. However using out-of-the-box installations (e.g. via apt-get) will generally only support a single core.

In order to get the most out of ATLAS (multicore, optimised to your machine) you will need to compile it from source and this can be a painful experience and probably only worthwhile if you are familiar with compiling from source on Unix machines.

###### MKL

Intel provide their Math Kernel Library (MKL) optimised version of BLAS. It works on Intel and Intel compatible processors. Revolution R comes with MKL pre-packaged with it.

R-Bloggers has a guide to installing MKL. Note, MKL is free for non-commercial usage, but commercial usage will require a license.

###### vecLib

If you are using Mac OS X, Apple kindly provide you with a optimised BLAS library. Details of how to link with R can be found here. It is very easy to link and provides excellent performance.

However, this only works with Mac OS X, so not really relevant if you are planning to work in a server environment,

###### Which to use?

Obviously what to use is completely up to you, all have some disadvantages. Personally, I use vecLib on my Mac and we use OpenBLAS on our servers. This means we have to write our R code to not to use parallel loops and mutlicore matrix operations at the same time. However this is not a massive overhead (if you are trying to do both at the same time you will generally end up thrashing your CPUs anyway). The advantage is, spinning up new R servers does not involve any compilation from source.

# Pay

At this point, linking to optimised BLAS version may look quite painful. Instead an alternative option is to pay for Revolution R. They pre-build their version of R with an optimised multicore BLAS version. They have various benchmarks on the performance improvements.

Revolution R also has various libraries for handling large datasets, parallelised statistical modelling algorithms, etc. Although it all comes with a fairly hefty price tag.

Update: Revolution R have just announced Revolution R Open a free version of Revolution R. In particular it comes linked against MKL and has the Reproducible R Toolkit to manage package upgrades. Currently this looks like the best option for using R in a production environment.

# Byte Code Compiler

The compiler package allows you to compile R functions to a lower-level byte code. This can provide performance improvements of between 2-5X.

Let’s look at a very simple example below:

The cmpfun is used to compile the function to byte code. You call your function in the exact same way you would before. To compare performance:

In this case, we see around a 2.9X speedup. You will see the best speed-up on functions that involve mostly numerical calculations. If your functions mainly call pre-built R functions or manipulate data types, you probably won’t see any drastic speed-up.

You can also enable Just-In-Time (JIT) compilation, removing the need to call cmpfun directly:

The value passed to enableJIT controls the level of compilation, it should be between 0 and 3, 0 being no compilation; 3 being max compilation. This may initially slow down R as all the functions need to be compiled, but may later speed it up. You can also enable it via the R_ENABLE_JIT environment variable.

For more information, R-statistics has a great tutorial on compiler library and JIT.

# Summary

R is constantly evolving, so along with these tips you should always try to keep your R version up to date to get the latest performance improvements.

Radford Neal has done a bunch of optimisations, some of which were adopted into R Core, and many others which were forked off into pqR. At the time of writing, I don’t think pqR is ready for production work, but definitely worth watching.

With well optimised code, the right libraries, R is capable of handling pretty large data problems. At some point, your data may be too large for R to handle. At this point I look to Hadoop and Spark to scale even further. My rough guide, if your data is greater than 50GB (after pre-processing) R is probably not the right choice.

# R Performance (Part I)

R as a programming language is often considered slow. However, more often than not it is how the R code is written that makes it slow. I’ve see people wait hours for an R script to finish, while with a few modifications it will take minutes.

In this post I will explore various ways of speeding up your R code by writing better code. In part II, I will focus on tools ands libraries you can use to optimise R.

# Vectorisation

The single most important advice when writing R code is to vectorise it as much as possible. If you have ever used MATLAB, you will be aware of the difference vectorised vs. un-vectorised code in terms of speed.

Let us look at an example:

Here we have used a loop to increment the contents of a. Now using a vectorised approach:

Notice the massive performance increase in elapsed time.

Another consideration is to look at using  inherently vectorised commands like ifelse and diff. Let’s look at the example below:

Again we see elapsed time has been massively reduced, a 93X reduction.

When you have a for loop in your code, think about how you can rewrite it in a vectorised way.

# Looping

Sometimes it is impossible to avoid a loop, for example:

• When the result depends on the previous iteration of the loop

If this is the case some things to consider:

• Ensure you are doing the absolute minimum inside the loop. Take any non-loop dependent calculations outside of the loop.
• Make the number of iterations as small as possible. For instance if your choice is to iterate over the levels of a factor or iterate over all the elements, usually iterating over the levels will be much faster

If you have to loop, do as little as possible in it

# Growing Objects

A common pitfall is growing an object inside of a loop.  Below I give an example of this:

Here we are constantly growing the vector inside of the loop. As the vector grows, we need more space to hold it, so we end up copy data to a new location. This constant allocation and copying causes the code to be very slow and memory fragmentation.

In the next example, we have pre-allocated the space we needed. This time the code is 266X faster.

We can of course do this allocation directly without the loop, making the code even faster:

If you don’t know how much space you will need, it may be useful to allocate an upper-bound of space, then remove anything unused once your loop is complete.

A more common scenario is to see something along the lines of:

At the bottom of your loop, you are rbinding or cbinding the result you calculated in your loop to an existing data frame.

Instead, build a list of pieces and put them all together in one go:

Avoid growing data structures inside a loop.

# Apply Functions

The R library has a whole host of apply functions:

It is worth becoming familiar with them all. Neil Saunders has created a great introduction to all the apply functions.

In most situations using apply may not be any faster than using a loop (for instance the apply function is just doing a loop under the hood). The main advantage is that it avoids growing objects in the loop as the apply functions handle stitching the data together.

In Part II we will introduced the parallel versions of apply that can increase performance further.

Know your apply functions and use them where it makes sense

# Mutable Functions

One important point to remember about R, is that parameters to functions are passed by value. This, in theory, means that each time you pass something to a function it creates a copy. However, in practice, R will under the hood not create a copy as long as you don’t mutate the value of the variable inside the function.

If you can make your functions immutable (e.g. don’t change the values of the parameters passed in), you will save significant amounts of memory and CPU time by not copying.

Let’s looks at a really simple case:

Here f1 mutates x, while f2 does not. Running with a fairly large vector,  several times and looking at the average:

We see that on average, f2 is slightly quicker as we have avoided the additional temporary copy that is done under the hood in f1.

Try to make functions immutable.

## Summary

To reiterate the main points:

1. When you have a for loop in your code, think about how you can rewrite it in a vectorised way.
2. If you have to loop, do as little as possible in it
3. Avoid growing data structures inside a loop
4. Know your apply functions and use them where it makes sense
5. Try to make functions immutable

Following these tips when writing your R code should greatly improve the efficiency. For some more general tips to help your R code I also recommend:

# Calibrating Classifier Probabilties

You’ve built your classifier, run cross-validation and have a super high AUC. So you are done right? Maybe not.

Most classifiers output a score of how likely an observation is to be in the positive class. Usually these scores are between 0 and 1 and get called probabilities. However these probabilities often do not reflect reality, e.g. a probability of 20% may not mean it has a 20% chance of happening, it could have a 10%, 50%, 70%, etc. chance of happening. Our aim should be that our model outputs accurately reflect posterior probabilities $$P(Y=1|x)$$.

In the post we will mainly focus on binary classifiers. Later in the post will will talk about how to extend these ideas to mutliclass problems.

# Why it happens

Our models can output inaccurate probabilities for a variety of reasons:

• Flawed model assumptions (e.g. independence in a Naive Bayes Model)
• Hidden features not available at training time
• Deficiencies in the learning algorithm.

In terms of learning algorithms, as noted in Niculescu-Mizil et al and through my own research:

• Naive Bayes tends to push probabilities toward the extremes of 0 and 1.
• SVMs and boosted trees tend to push probabilities away from 0 and 1 (toward the centre)
• Neural networks and random forests tend to have well calibrated probabilities.
• Regularisation also tends to push probabilities toward the centre.

# Do we care?

Whether or not we want well calibrated probabilities depends entirely on the problem we are trying to solve.

If we only need to rank observations from most likely to least likely, then calibration is unnecessary.

Examples of problems I have worked on where calibrated probabilities are extremely important:

• Loan default prediction – Banks will generally be setting thresholds on the probabilities, auto-reject if probability of default is above 30%, etc.
• Ad Click Prediction – Decided what ad to show, how much to bid. You might use a baseline Click Through Rate (CTR), and compare your prediction to this to see how much more you are willing to pay for this ad impression. 1
• Demographics Estimation of Websites – Imagine you have predictions of gender/ages, as probabilities, for a number of web users. Estimating the gender distribution on a website, can be done by just averaging the probabilities of the users seen on the site. Any bias in the probabilities, will generate a bias in your estimate.

# Visualisation

A reliability diagram is a relatively simple technique for visualising how well calibrated our classifier is.  As described in Niculescu-Mizil et al:

On real problems where the true conditional probabilities are not known, model calibration can be visualized with reliability diagrams (DeGroot & Fienberg, 1982). First, the prediction space is discretized into ten bins. Cases with predicted value between 0 and 0.1 fall in the first bin, between 0.1 and 0.2 in the second bin, etc.
For each bin, the mean predicted value is plotted against the true fraction of positive cases. If the model is well calibrated the points will fall near the diagonal line.

Below we provide a piece of R code for producing relibability diagrams. Here we generalise the number of bins to be a user defined parameter.

In the figure below we show an example reliability plot. Ideally the reliability plot (red line) should be as close to the diagonal line as possible. As there is significant deviation from the diagonal, calibrating the probabilities will possible help.

It is also worth mentioning that if you take the mean of the score distribution, it should ideally be close to the prior.

# Techniques for calibration

## Overfitting

The most important step is to create a separate dataset to perform calibration with. Our steps for calibration are:

• Split dataset into test and train
• Split the train set into model training and calibration.
• Train the model on train set
• Score test and calibration set
• Train the calibration model on calibration set
• Score the test set using calibration

How much data to use for calibration will depend on the amount of data you have available. The calibration model will generally only be fitting a small number of parameters (so you do not need a huge volume of data). I would aim for around 10% of your training data, but at a minimum of at least 50 examples.

## Platt Scaling

Platt Scaling essentially involves fitting a logistic regression on the classifier output. Originally developed to fit probabilities to the outputs of SVM 2, it is also well suited to the output of most other classifiers.

The reliability diagram below shows the original reliability plot (green) and after Platt Scaling (red).

The Platt Scalding should not change the rank of the observations, so measures such as AUC will be unaffected. However, measures like Log Loss 3 will be improved. In this example, Log Loss was originally 0.422 and improved to 0.418.

In Platt’s original paper suggests , instead of using the original {0,1} targets in the calibration sample, it suggests to mapping to:

$$t_+=\frac{N_+ + 1}{N_+ + 2}$$

$$t_-=\frac{1}{N_-+2}$$

where $$N_+$$  and $$N_-$$ are the number of positive and negative examples in the calibration sample.

To some extent this introduces a level of regularisation. Imagine if you only gave probabilities of either 0 or 1 and you correctly predicted all examples. Your Log Loss would be zero. With Platt’s transformation, you Log Loss would be non-zero. As the Log Loss is what you are optimising when fitting the logistic regression, a level of regularisation is introduced.

In my experiments, this transformation had little to no effect on the reliability diagram and Log Loss, so seems an unnecessary step. It may be useful if you have very few examples and overfitting is more of a concern (therefore regularisation would help). You could also use a ridge or lasso regression.

## Isotonic Regression

With Isotonic Regression you make the assumption:

$$y_i = m(f_i) + \epsilon_{i}$$

where $$m$$ is an isotonic (monotonically increasing or decreasing) function. This is the exact same assumptions we would use for least squares, except $$m$$ is now a isotonic function instead of linear.

Below is an R example of how to perform isotonic regression using the isoreg function.

In the figure below we show an example of the sort of function fitted by the isotonic regression model:Notice how it goes up in steps instead of a smooth curve. To smooth the fit, we perform a linear interpolation between each step.

In the reliability plot above, the original uncalibarated scores are shown in green and the isotonic regression scores are shown in red. In this example we find isotonic regression actually made it worse. The Log Loss for instance went from 0.422 to 0.426. The AUC was also reduced.

# Multiclass Classification

What happens if you have more than two classes? Firstly I would recommend visualising the problem as a series of reliability diagrams. For k classes, you can create k reliability diagrams.

Secondly, you can take the score for each of your k classes and plug them into a multinomial logistic regression. The superb glmnet package implements a multinomial logistic regression. You can set the regularisation parameter to something quite small. One word of caution, if you have many classes, overfitting can become an issue. At this point it is worth optimising the regularisation parameter.

If your favourite machine learning model (e.g. SVM) doesn’t directly support multi-class classification, you can fit a 1 vs. all set of classifiers and then plug each of those scores into the  multinomial logistic regression.

# Summary

Classifier probability calibration can be an important step in your machine learning pipeline. The first step is to always visualise and see how much of an issue you have. In general I have found Platt Scaling to be the simplest and most effective approach to most calibration of classification problems.