I need to compute a hat matrix (as from linear regression). Standard R code would be:
H <- tcrossprod(tcrossprod(X, solve(crossprod(X))), X)
with X being a relatively large matrix (i.e 1e5*100), and this line has to run thousands of times. I understand the most limiting part is the inverse computation, but the crossproducts may be time-consuming too. Is there any faster alternative to perform these matrix operations? I tried Rcpp and reviewed several posts but any alternative I tested was slower. Maybe I did not code properly my C++ code, as I am not an advanced C++ programmer.
Thanks!
Chasing the code for this line by line is a little difficult because the setup of R code is a little on the complicated side. But read on, pointers below.
The important part is that the topic has been discussed many times: what happens is that R dispatches this to the BLAS (Basic Linear Algebra Subprogram) and LAPACK (Linear Algebra PACKage) libraries. Which contain the most efficient code known to man for this. In general, you cannot gain on it by rewriting.
One can gain performance differences by switching one BLAS/LAPACK implementation for another---there are many, many posts on this online too. R itself comes with the so-called 'reference BLAS' known to be correct, but slowest. You can switch to Atlas, OpenBLAS, MKL, ... depending on your operating system; instructions on how to do so are in some of the R manuals that come with your installation.
For completeness, per file src/main/names.c the commands %*%, crossprod and tcrossprod all refer to do_matprod. This is in file src/main/array.c and does much argument checking and arranging and branching on types of arguments but e.g. one path then calls
F77_CALL(dsyrk)(uplo, trans, &nc, &nr, &one, x, &nr, &zero, z, &nc
FCONE FCONE);
which is this LAPACK function. It is essentially the same for all others making this an unlikely venue for your optimisation.
I am working on a small project in survival analysis and making use of the paper:
Lagakos, De Gruttolla - Analysis of Doubly Censored Data, with applications to AIDS.
Before implementing their code in R, I wanted to know if there were already packages that implement the method they describe. I am aware of the package dblcens however, it's functions use an EM algorithm rather than the algorithm described by Lagakos and De Gruttolla.
Has this algorithm already been implemented in some R package?
Thank you.
Does there exist a simple, cheatsheet-like document which compiles the best practices for mathematical computing in R? Does anyone have a short list of their best-practices? E.g., it would include items like:
For large numerical vectors x, instead of computing x^2, one should compute x*x. This speeds up calculations.
To solve a system $Ax = b$, never solve $A^{-1}$ and left-multiply $b$. Lower order algorithms exist (e.g., Gaussian elimination)
I did find a nice numerical analysis cheatsheet here. But I'm looking for something quicker, dirtier, and more specific to R.
#Dirk Eddelbeuttel has posted a bunch of stuff on "high performance computing with R". He's also a regular so will probably come along and grab some well-deserved reputation points. While you are waiting you can read some of his stuff here:
http://dirk.eddelbuettel.com/papers/ismNov2009introHPCwithR.pdf
There is an archive of the r-devel mailing list where discussions about numerical analysis issues relating to R performance occur. I will often put its URL in the Google advanced search page domain slot when I want to see what might have been said in the past: https://stat.ethz.ch/pipermail/r-devel/
Instead of starting to code in Matlab, I recently started learning R, mainly because it is open-source. I am currently working in data mining and machine learning field. I found many machine learning algorithms implemented in R, and I am still exploring different packages implemented in R.
I have quick question: how do you compare R to Matlab for data mining application, its popularity, pros and cons, industry and academic acceptance etc.? Which one would you choose and why?
I went through various comparisons for Matlab vs R against various metrics but I am specifically interested to get answer for its applicability in Data Mining and ML.
Since both language are pretty new for me I was just wondering if R would be a good choice or not.
I appreciate any kind of suggestions.
For the past three years or so, i have used R daily, and the largest portion of that daily use is spent on Machine Learning/Data Mining problems.
I was an exclusive Matlab user while in University; at the time i thought it was
an excellent set of tools/platform. I am sure it is today as well.
The Neural Network Toolbox, the Optimization Toolbox, Statistics Toolbox,
and Curve Fitting Toolbox are each highly desirable (if not essential)
for someone using MATLAB for ML/Data Mining work, yet they are all separate from
the base MATLAB environment--in other words, they have to be purchased separately.
My Top 5 list for Learning ML/Data Mining in R:
Mining Association Rules in R
This refers to a couple things: First, a group of R Package that all begin arules (available from CRAN); you can find the complete list (arules, aruluesViz, etc.) on the Project Homepage. Second, all of these packages are based on a data-mining technique known as Market-Basked Analysis and alternatively as Association Rules. In many respects, this family of algorithms is the essence of data-mining--exhaustively traverse large transaction databases and find above-average associations or correlations among the fields (variables or features) in those databases. In practice, you connect them to a data source and let them run overnight. The central R Package in the set mentioned above is called arules; On the CRAN Package page for arules, you will find links to a couple of excellent secondary sources (vignettes in R's lexicon) on the arules package and on Association Rules technique in general.
The standard reference, The Elements of Statistical
Learning by Hastie et al.
The most current edition of this book is available in digital form for free. Likewise, at the book's website (linked to just above) are all data sets used in ESL, available for free download. (As an aside, i have the free digital version; i also purchased the hardback version from BN.com; all of the color plots in the digital version are reproduced in the hardbound version.) ESL contains thorough introductions to at least one exemplar from most of the major
ML rubrics--e.g., neural metworks, SVM, KNN; unsupervised
techniques (LDA, PCA, MDS, SOM, clustering), numerous flavors of regression, CART,
Bayesian techniques, as well as model aggregation techniques (Boosting, Bagging)
and model tuning (regularization). Finally, get the R Package that accompanies the book from CRAN (which will save the trouble of having to download the enter the datasets).
CRAN Task View: Machine Learning
The +3,500 Packages available
for R are divided up by domain into about 30 package families or 'Task Views'. Machine Learning
is one of these families. The Machine Learning Task View contains about 50 or so
Packages. Some of these Packages are part of the core distribution, including e1071
(a sprawling ML package that includes working code for quite a few of
the usual ML categories.)
Revolution Analytics Blog
With particular focus on the posts tagged with Predictive Analytics
ML in R tutorial comprised of slide deck and R code by Josh Reich
A thorough study of the code would, by itself, be an excellent introduction to ML in R.
And one final resource that i think is excellent, but didn't make in the top 5:
A Guide to Getting Stared in Machine Learning [in R]
posted at the blog A Beautiful WWW
Please look at the CRAN Task Views and in particular at the CRAN Task View on Machine Learning and Statistical Learning which summarises this nicely.
Both Matlab and R are good if you are doing matrix-heavy operations. Because they can use highly optimized low-level code (BLAS libraries and such) for this.
However, there is more to data-mining than just crunching matrixes. A lot of people totally neglect the whole data organization aspect of data mining (as opposed to say, plain machine learning).
And once you get to data organization, R and Matlab are a pain. Try implementing an R*-tree in R or matlab to take an O(n^2) algorithm down to O(n log n) runtime. First of all, it totally goes against the way R and Matlab are designed (use bulk math operations wherever possible), secondly it will kill your performance. Interpreted R code for example seems to run at around 50% of the speed of the C code (try R built-in k-means vs. flexclus k-means); and the BLAS libraries are optimized to an insane level, exploiting cache sizes, data alignment, advanced CPU features. If you are adventurous, try implementing a manual matrix multiplication in R or Matlab, and benchmark it against the native one.
Don't get me wrong. There is a lot of stuff where R and matlab are just elegant and excellent for prototyping. You can solve a lot of things in just 10 lines of code, and get a decent performance out of it. Writing the same thing by hand would be hundreds of lines, and probably 10x slower. But sometimes you can optimize by a level of complexity, which for large data sets does beat the optimized matrix operations of R and matlab.
If you want to scale up to "Hadoop size" on the long run, you will have to think about data layout and organization, too, unless all you need is a linear scan over the data. But then, you could just be sampling, too!
Yesterday I found two new books about Data mining. These series of books entitled by ‘Data Mining’ address the need by presenting in-depth description of novel mining algorithms and many useful applications. In addition to understanding each section deeply, the two books present useful hints and strategies to solving problems in the following chapters.The progress of data mining technology and large public popularity establish a need for a comprehensive text on the subject. Books are: “New Fundamental Technologies in Data Mining” here http://www.intechopen.com/books/show/title/new-fundamental-technologies-in-data-mining & “Knowledge-Oriented Applications in Data Mining” here http://www.intechopen.com/books/show/title/knowledge-oriented-applications-in-data-mining These are open access books so you can download it for free or just read on online reading platform like I do. Cheers!
We should not forget the origin sources for these two software: scientific computation and also signal processing leads to Matlab but statistics leads to R.
I used matlab a lot in University since we have one installed on Unix and open to all students. However, the price for Matlab is too high especially compared to free R. If your major focus is not on matrix computation and signal processing, R should work well for your needs.
I think it also depends in which field of study you are. I know of people in coastal research that use a lot of Matlab. Using R in this group would make your life more difficult. If a colleague has solved a problem, you can't use it because he fixed it using Matlab.
I would also look at the capabilities of each when you are dealing with large amounts of data. I know that R can have problems with this, and might be restrictive if you are used to an iterative data mining process. For example looking at multiple models concurrently. I don't know if MATLAB has a data limitation.
I admit to favoring MATLAB for data mining problems, and I give some of my reasoning here:
Why MATLAB for Data Mining?
I will admit to only a passing familiarity with R/S-Plus, but I'll make the following observations:
R definitely has more of a statistical focus than MATLAB. I prefer building my own tools in MATLAB, so that I know exactly what they're doing, and I can customize them, but this is more of a necessity in MATLAB than it would be in R.
Code for new statistical techniques (spatial statistics, robust statistics, etc.) often appears early in S-Plus (I assume that this carries over to R, at least some).
Some years ago, I found the commercial version of R, S-Plus to have an extremely limited capacity for data. I cannot say what the state of R/S-Plus is today, but you may want to check if your data will fit into such tools comfortably.
I'm checking a simple moving average crossing strategy in R. Instead of running a huge simulation over the 2 dimenional parameter space (length of short term moving average, length of long term moving average), I'd like to implement the Particle Swarm Optimization algorithm to find the optimal parameter values. I've been browsing through the web and was reading that this algorithm was very effective. Moreover, the way the algorithm works fascinates me...
Does anybody of you guys have experience with implementing this algorithm in R? Are there useful packages that can be used?
Thanks a lot for your comments.
Martin
Well, there is a package available on CRAN called pso, and indeed it is a particle swarm optimizer (PSO).
I recommend this package.
It is under actively development (last update 22 Sep 2010) and is consistent with the reference implementation for PSO. In addition, the package includes functions for diagnostics and plotting results.
It certainly appears to be a sophisticated package yet the main function interface (the function psoptim) is straightforward--just pass in a few parameters that describe your problem domain, and a cost function.
More precisely, the key arguments to pass in when you call psoptim:
dimensions of the problem, as a vector
(par);
lower and upper bounds for each
variable (lower, upper); and
a cost function (fn)
There are other parameters in the psoptim method signature; those are generally related to convergence criteria and the like).
Are there any other PSO implementations in R?
There is an R Package called ppso for (parallel PSO). It is available on R-Forge. I do not know anything about this package; i have downloaded it and skimmed the documentation, but that's it.
Beyond those two, none that i am aware of. About three months ago, I looked for R implementations of the more popular meta-heuristics. This is the only pso implementation i am aware of. The R bindings to the Gnu Scientific Library GSL) has a simulated annealing algorithm, but none of the biologically inspired meta-heuristics.
The other place to look is of course the CRAN Task View for Optimization. I did not find another PSO implementation other than what i've recited here, though there are quite a few packages listed there and most of them i did not check other than looking at the name and one-sentence summary.