Even relatively trivial modeling procedures can consume a lot of time, which is critical both for optimization and update of models. Multiple blog-posts showed that they are able to improve the performance of linear algebra operations in R, especially those of the infamous R-benchmark And so we want to find out if nvblas can speed up computations just as easily! The particular pick of functions simply reflects which models and packages we currently use at INWT Statistics. So those are the most interesting ones for us to look at.

When you have a thorough understanding of how these methods are implemented, you may, in part, anticipate some of the results.

## Linear algebra handwritten notes

With this setup, it is relatively easy to change the BLAS library by configuring it via an environment variable:. The xgboost-package plays a special role in our tests: additionally to change the BLAS-package to nvblas the optimization done by xgboost does not improve much by using different blas-versions , one can change the optimization-algorithm to gpu-hist , if the package is installed correctly.

This approach to the histogram tree growth method is optimized for GPUs and should outperform the cpu-version. This was done for our tests. The experiments were done for different sample sizes and numbers of categorical and numerical features. We show the results for a sample of , and categorical as well as numerical features. If you think this is small: we do not analyse images, videos or gene expression data; this is a somewhat realistic scenario in which performance becomes interesting and relevant for us.

The R-benchmark needs 5. The plots show the speed of the methods using different BLAS-versions.

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When we started out we were hoping for a clear winner and somehow we also found one. However depending on your pick of models and applications there are some unexpected results. We hoped to see that nvblas would easily outperform all other libraries. Of course it is not that simple. For statistical modeling, the libraries which have been tuned, optimized and debugged for decades are hard to beat. R news and tutorials contributed by R bloggers. Home About RSS add your blog! Here you will find daily news and tutorials about R , contributed by over bloggers.

There are many ways to follow us - By e-mail: On Facebook: If you are an R blogger yourself you are invited to add your own R content feed to this site Non-English R bloggers should add themselves- here. Madrid, Spain. Recent Posts R Companion to Linear Algebra Step by Step, part 1 How to interactively examine any R code — 4 ways to not just read the code, but delve into it step-by-step How do we combine errors, in biology?

August 6, We know to multiply the first input by the first value, the second input by the second value, etc. We could try this:. As an input passes an operation, it creates an output item. We usually write a matrix with a capital letter F , and a single input column with lowercase x. Why does RC ordering make sense? Writing them together:. They should match! If our inputs have 3 components, our operations should expect 3 items. Assuming 3 inputs, we can whip up a few 1-operation matrices:.

How about this guy? And yes, when we decide to treat inputs as vector coordinates, the operations matrix will transform our vectors. These are geometric interpretations of multiplication, and how to warp a vector space. Just remember that vectors are examples of data to modify.

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These dollar values could come from another matrix that multiplied the number of shares by their price. Fancy that!

We want to adjust each stock value, using something similar to the identity matrix:. Making sense? Three inputs enter, four outputs leave. We can crunch the numbers by hand, or use a Wolfram Alpha calculation :. The Transpose operation, indicated by t tau , converts rows to columns. Linear algebra emerged in the s yet spreadsheets were invented in the s.

I blame the gap on poor linear algebra education. As the matrix evolves into the identity matrix, the values of x, y and z are revealed on the output side. This process, called Gauss-Jordan elimination, saves time. Words have technical categories to describe their use nouns, verbs, adjectives. Matrices can be similarly subdivided. If the input was a unit vector representing area or volume of 1 , the determinant is the size of the transformed area or volume. The eigenvalue is the amount the eigenvector is scaled up or down when going through the matrix.

What if we want the metric version? Take the instructions, treat them like text, and convert the units. An operations matrix is similar: commands to modify.

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Applying one operations matrix to another gives a new operations matrix that applies both transformations, in order. The beauty of linear algebra is representing an entire spreadsheet calculation with a single letter. Want to apply the same transformation a few times? Yes, because you asked nicely. Time to expand our brains. Now our operations matrix has an extra, known value to play with! Want the geeky explanation? We skew that higher dimension, which looks like a slide in the current one.

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For example: take input x, y, z, 1 and run it through:. We keep the dummy entry, and can do more slides later. BetterExplained helps k monthly readers with friendly, insightful math lessons more. An Intuitive Guide to Linear Algebra. We missed the key insight: Linear algebra gives you mini-spreadsheets for your math equations.