Re: [R] Use apply only on non-missing values

From: Doran, Harold <HDoran_at_air.org>
Date: Thu, 03 Jun 2010 13:21:11 -0400

Actually, this is clever. I modified your advice and vectorized this as:

1/ (1 + exp(b_vector - t(matrix(theta, nrow= nrow(dat) , ncol= ncol(dat)))))

Instead of using the apply() function as I did before. In terms of speed, this new solution is immensely faster, as you also noted. Now, whether it works on my real world problem is TBD. It is running now, slowly.

From: Joris Meys [mailto:jorismeys_at_gmail.com] Sent: Wednesday, June 02, 2010 7:35 PM
To: Doran, Harold
Cc: r-help_at_r-project.org
Subject: Re: [R] Use apply only on non-missing values

Not really a direct answer on your question, but:
> system.time(replicate(10000,apply(as.matrix(theta), 1, rasch, b_vector)))

   user system elapsed
   4.51 0.03 4.55

> system.time(replicate(10000,theta%*%t(b_vector)))

   user system elapsed
   0.25 0.00 0.25

It does make a difference on large datasets... Cheers
Joris
On Wed, Jun 2, 2010 at 4:44 PM, Doran, Harold <HDoran_at_air.org<mailto:HDoran_at_air.org>> wrote: I have a function that I am currently using very inefficiently. The following are needed to illustrate the problem:

set.seed(12345)
dat <- matrix(sample(c(0,1), 110, replace = TRUE), nrow = 11, ncol=10) mis <- sample(1:110, 5)
dat[mis] <- NA
theta <- rnorm(11)
b_vector <- runif(10, -4,4)
empty <- which(is.na<http://is.na>(t(dat)))

So, I have a matrix (dat) with some values within the matrix missing. In my real world problem, the matrix is huge, and most values are missing. The function in question is called derivs() and is below. But, let me step through the inefficient portions.

First, I create a matrix of some predicted probabilities as:

rasch <- function(theta,b) 1/ (1 + exp(b-theta)) mat <- apply(as.matrix(theta), 1, rasch, b_vector)

However, I only need those predicted probabilities in places where the data are not missing. So, the next step in the function is

mat[empty] <- NA

which manually places NAs in places where the data are missing (notice the matrix 'mat' is the transpose of the data matrix and so I get the empty positions from the transpose of dat).

Afterwards, the function computes the gradient and hessians needed to complete the MLE estimation.

All of this works in the sense that it yields the correct answers for my problem. But, the glaring problem is that I create predicted probabilities for every cell in 'mat' when in many cases they are not needed. I end up replacing those values with NAs. In my real world problem, this is horribly inefficient and slow.

My question is then is there a way to use apply such that is computes the necessary predicted probabilities only when the data are not missing to yield the matrix 'mat'. My desired end result is the matrix 'mat' created after the manually placing the NAs in the appropriate cells.

Thanks
Harold

derivs <- function(dat, b_vector, theta){

                               mat <- apply(as.matrix(theta), 1, rasch, b_vector)
                               mat[empty] <- NA
                               gradient <- -(colSums(dat, na.rm = TRUE) - rowSums(mat, na.rm = TRUE))
                               hessian <-  -(rowSums(mat * (1-mat), na.rm = TRUE))
                               list('gradient' = gradient, 'hessian' = hessian)
               }



> sessionInfo()

R version 2.10.1 (2009-12-14)
i386-pc-mingw32

locale:
[1] LC_COLLATE=English_United States.1252 LC_CTYPE=English_United States.1252 LC_MONETARY=English_United States.1252

[4] LC_NUMERIC=C                           LC_TIME=English_United States.1252

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base

loaded via a namespace (and not attached): [1] tools_2.10.1
>

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--
Joris Meys
Statistical Consultant

Ghent University
Faculty of Bioscience Engineering
Department of Applied mathematics, biometrics and process control

Coupure Links 653
B-9000 Gent

tel : +32 9 264 59 87
Joris.Meys_at_Ugent.be
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