I want a subset of all simple paths in a relatively large network (~1k nodes and 5k-50k edges). Currently, I generate all simple paths (igraph::all_simple_paths) followed by subsetting. However, all_simple_paths is memory- and time-intensive for larger networks, and since I don't need all paths, running it seems like a waste.
My current strategy is randomly downsample network to a reasonable number of edges --> all_simple_paths --> subset. Repeating this a few times and combining seems to give reasonable results. However this still spends time generating paths I don't use. What are better ways to do this?
For clarity, any algorithm that generates a representative subset of all simple paths is sufficient. I assume that "representative" means an unbiased random sample.
Edit: I see this answer addressing a similar problem, but it's many times slower than all_simple_paths-->subset for my networks.
What I currently have:
I have a data frame with one column of factors called "Class" which contains 160 different classes. I have 1200 variables, each one being an integer and no individual cell exceeding the value of 1000 (if that helps). About 1/4 of the cells are the number zero. The total dataset contains 60,000 rows. I have already used the nearZeroVar function, and the findCorrelation function to get it down to this number of variables. In my particular dataset some individual variables may appear unimportant by themselves, but are likely to be predictive when combined with two other variables.
What I have tried:
First I tried just creating a random forest model then planned on using the varimp property to filter out the useless stuff, gave up after letting it run for days. Then I tried using fscaret, but that ran overnight on a 8-core machine with 64GB of RAM (same as the previous attempt) and didn't finish. Then I tried:
Feature Selection using Genetic Algorithms That ran overnight and didn't finish either. I was trying to make principal component analysis work, but for some reason couldn't. I have never been able to successfully do PCA within Caret which could be my problem and solution here. I can follow all the "toy" demo examples on the web, but I still think I am missing something in my case.
What I need:
I need some way to quickly reduce the dimensionality of my dataset so I can make it usable for creating a model. Maybe a good place to start would be an example of using PCA with a dataset like mine using Caret. Of course, I'm happy to hear any other ideas that might get me out of the quicksand I am in right now.
I have done only some toy examples too.
Still, here are some ideas that do not fit into a comment.
All your attributes seem to be numeric. Maybe running the Naive Bayes algorithm on your dataset will gives some reasonable classifications? Then, all attributes are assumed to be independent from each other, but experience shows / many scholars say that NaiveBayes results are often still useful, despite strong assumptions?
If you absolutely MUST do attribute selection .e.g as part of an assignment:
Did you try to process your dataset with the free GUI-based data-mining tool Weka? There is an "attribute selection" tab where you have several algorithms (or algorithm-combinations) for removing irrelevant attributes at your disposal. That is an art, and the results are not so easy to interpret, though.
Read this pdf as an introduction and see this video for a walk-through and an introduction to the theoretical approach.
The videos assume familiarity with Weka, but maybe it still helps.
There is an RWeka interface but it's a bit laborious to install, so working with the Weka GUI might be easier.
Is there any possible explanation for multiple optim instances with set starting values to return different results if run in parallel or one after another on a single core?
Basically, I do a rolling forecast with refitting of the model each time, so I can easily parallelize over the rolling windows, but the results are different if I do not parallelize...
Sadly, I don't have a simple reproducible example. I know that if I link to different BLAS then the results differ, so is there anything like different numerical precision / set of libraries used, that might cause this?
I am working on a problem that needs a numerical integration of a bivariate function, where each evaluation of the function takes about 1 minute. Since numerical integration on a single core would evaluate the function thousands to tens of thousand times, I would like to parallelize the calculation. Right now I am using the bruteforce approach that calculates a naive grid of points and add them up with appropriate area multipliers. This is definitely not efficient and I suspect any modern multidimensional numerical integration algorithm would be able to achieve the same precision with a lot fewer function evaluations. There are many packages in R that would calculate 2-d integration much more efficiently and accurately (e.g. R2Cuba), but I haven't found anything that can be easily parallelized on a cluster with SGE managed job queues. Since this is only a small part of a bigger research problem, I would like to see if this can be done with reasonable effort , before I try to parallelize one of the cubature-rule based methods in R by myself.
I have found that using sparse grid achieves the best compromise between speed and accuracy in multi-dimensional integration, and it's easily parallized on the cluster because it doesn't involve any sequential steps. It won't be as accurate as other sequentially adpative integration algorithms but it is much better than the naive method because it provides a much sparser grid of points to calculate on each core.
The following R code deals with 2-dimensional integration, but can be easily modified for higher dimensions. The apply function towards the end can be easily parallelized on a cluster.
sg.int<-function(g,...,lower,upper)
{ require("SparseGrid")
lower<-floor(lower)
upper<-ceiling(upper)
if (any(lower>upper)) stop("lower must be smaller than upper")
gridss<-as.matrix(expand.grid(seq(lower[1],upper[1]-1,by=1),seq(lower[2],upper[2]-1,by=1)))
sp.grid <- createIntegrationGrid( 'KPU', dimension=2, k=5 )
nodes<-gridss[1,]+sp.grid$nodes
weights<-sp.grid$weights
for (i in 2:nrow(gridss))
{
nodes<-rbind(nodes,gridss[i,]+sp.grid$nodes)
weights<-c(weights,sp.grid$weights)
}
gx.sp <- apply(nodes, 1, g,...)
val.sp <- gx.sp %*%weights
val.sp
}
Crossposted with STATS.se since this problem could straddle both STATs.se/SO
https://stats.stackexchange.com/questions/17712/parallelize-solve-for-ax-b
I have some extremely large sparse matrices created using spMatrix function from the matrix package.
Using the solve() function works for my Ax=b issue, but it takes a very long time. Several days.
I noticed that http://cran.r-project.org/web/packages/RScaLAPACK/RScaLAPACK.pdf
appears to have a function that can parallelize the solve function, however, it can take several weeks to get new packages installed on this particular server.
The server already has the snow package installed it.
So
Is there a way of using snow to parallelize this operation?
If not, are there other ways to speed up this type of operation?
Are there other packages like RScaLAPACK? My search on RScaLAPACK seemed to suggest people had a lot of issues with it.
Thanks.
[EDIT] -- Additional details
The matrices are about 370,000 x 370,000.
I'm using it to solve for alpha centrality, http://en.wikipedia.org/wiki/Alpha_centrality. I was originally using the alpha centrality function in the igraph package, but it would crash R.
More details
This is on a single machine with 12 cores and 96 gigs of memory (I believe)
It's a directed graph along the lines of paper citation relationships.
Calculating condition number and density will take awhile. Will post as it comes available.
Will crosspost on stat.SE and will add a link back to here
[Update 1: For those just tuning in: The original question involved parallelizing computations to solving a regression problem; given that the underlying problem is related to alpha centrality, some of the issues, such as bagging and regularized regression may not be as immediately applicable, though that leads down the path of further statistical discussions.]
There are a bundle of issues to address here, from the infrastructural to the statistical.
Infrastructure
[Updated - also see Update #2 below.]
Regarding parallelized linear solvers, you can replace R's BLAS / LAPACK library with one that supports multithreaded computations, such as ATLAS, Goto BLAS, Intel's MKL, or AMD's ACML. Personally, I use AMD's version. ATLAS is irritating, because one fixes the number of cores at compilation, not at run-time. MKL is commercial. Goto is not well supported anymore, but is often the fastest, but only by a slight margin. It's under the BSD license. You can also look at Revolution Analytics's R, which includes, I think, the Intel libraries.
So, you can start using all of the cores right away, with a simple back-end change. This could give you a 12X speedup (b/c of the number of cores) or potentially much more (b/c of better implementation). If that brings down the time to an acceptable range, then you're done. :) But, changing the statistical methods could be even better.
You've not mentioned the amount of RAM available (or the distribution of it per core or machine), but A sparse solver should be pretty smart about managing RAM accesses and not try to chew on too much data at once. Nonetheless, if it is on one machine and if things are being done naively, then you may encounter a lot of swapping. In that case, take a look at packages like biglm, bigmemory, ff, and others. The former addresses solving linear equations (or GLMs, rather) in limited memory, the latter two address shared memory (i.e. memory mapping and file-based storage), which is handy for very large objects. More packages (e.g. speedglm and others) can be found at the CRAN Task View for HPC.
A semi-statistical, semi-computational issue is to address visualization of your matrix. Try sorting by the support per row & column (identical if graph is undirected, else do one then the other, or try a reordering method like reverse Cuthill-McKee), and then use image() to plot the matrix. It would be interesting to see how this is shaped, and that affects which computational and statistical methods one could try.
Another suggestion: Can you migrate to Amazon's EC2? It is inexpensive, and you can manage your own installation. If nothing else, you can prototype what you need and migrate it in-house once you have tested the speedups. JD Long has a package called segue that apparently makes life easier for distributing jobs on Amazon's Elastic MapReduce infrastructure. No need to migrate to EC2 if you have 96GB of RAM and 12 cores - distributing it could speed things up, but that's not the issue here. Just getting 100% utilization on this machine would be a good improvement.
Statistical
Next up are multiple simple statistical issues:
BAGGING You could consider sampling subsets of your data in order to fit the models and then bag your models. This can give you a speedup. This can allow you to distribute your computations on as many machines & cores as you have available. You can use SNOW, along with foreach.
REGULARIZATION The glmnet supports sparse matrices and is very fast. You would be wise to test it out. Be careful about ill-conditioned matrices and very small values of lambda.
RANK Your matrices are sparse: are they full rank? If they are not, that could be part of the issue you're facing. When matrices are either singular or very nearly so (check your estimated condition number, or at least look at how your 1st and Nth eigenvalues compare - if there's a steep drop off, you're in trouble - you might check eval1 versus ev2,...,ev10,...). Again, if you have nearly singular matrices, then you need to go back to something like glmnet to shrink out the variables are either collinear or have very low support.
BOUNDING Can you reduce the bandwidth of your matrix? If you can block diagonalize it, that's great, but you'll likely have cliques and members of multiple cliques. If you can trim the most poorly connected members, then you may be able to estimate their alpha centrality as being upper bounded by the lowest value in the same clique. There are some packages in R that are good for this sort of thing (check out Reverse Cuthill-McKee; or simply look to see how you'd convert it into rectangles, often relating to cliques or much smaller groups). If you have multiple disconnected components, then, by all means, separate the data into separate matrices.
ALTERNATIVES Are you wedded to the Alpha Centrality? There may be other measures that are monotonically correlated (i.e. have high rank correlation) with the same value that could be calculated more cheaply or at least implemented quite efficiently. If those will work, then your analyses could proceed with a lot less effort. I have a few ideas, but SO isn't really the place to go about that discussion.
For more statistical perspectives, appropriate Q&A should occur on the stats.stackexchange.com, Cross-Validated.
Update 2: I was a bit too quick in answering and didn't address this from the long-term perspective. If you are planning to do research on such systems for the long-term, you should look at other solvers that may be more applicable to your type of data and computing infrastructure. Here is a very nice directory of the options for both solvers and pre-conditioners. It seems this doesn't include IBM's "Watson" solver suite. Although it may take weeks to get software installed, it's quite possible that one of the packages is already installed if you have a good HPC administrator.
Also, keep in mind that R packages can be installed to the user directory - you need not have a package installed in the general directory. If you need to execute something as a user other than yourself, you could also download a package to the scratch or temporary space (if you're running within just 1 R instance, but using multiple cores, check out tempdir).