Get only hessian diagonal instead of the whole hessian matrix?

[Tomas T.]

Hello,

Is there a possibility to calculate just the second derivatives of each vector element, i.e. just the diagonal of the hessian matrix instead of the whole matrix?

I am calling diag(F$jacfun()$jacobian()) on a Tape object F to get the second derivatives, but since the hessian dimensions are 9000x9000, it takes way too long, and all the elements except of the diagonal are zero anyways.

I tried to call $jacfun(sparse = TRUE), but it doesn't help, result is the same.

Below is a simplified reproducible code. 

Thanks in advance!

Tomas

library(RTMB)

N <- 9000
d <- data.frame(present = rbinom(N, 1, 0.3))

inv.logit <- plogis

# log likelihood but I need the vector for each data point rather than just a sum
ll_pa <- function (data, par)
{
y <- data
p <- inv.logit(par)

y0 <- y$present == 0
y1 <- y$present == 1
ll_ <- numeric(nrow(y))
ll_[y1] <- log(p[y1])
ll_[y0] <- log(1 - p[y0])
sum(ll_)
}

cmb <- function(f, data) function(par) f(data, par)
# closure trick somewhere from the RTMB docs, to tie this to particular data and prevent unnecessary headaches!


F <- MakeTape(cmb(ll_pa, data = d), numeric(N))


p1 <- rnorm(N)

F$jacobian(p1) # first derivatives are alright

# second derivatives
der2 <- F$jacfun()$jacobian(p1)
# takes too long, calculating the whole hessian matrix, when I need just the diagonal

der2b <- F$jacfun(sparse = TRUE)$jacobian(p1) # surprisingly, this yields exactly the same result

identical(der2, der2b)

[Kasper Kristensen]

You can construct a function representing the sparse Hessian like this:

H <- F$jacfun()$jacfun(sparse=TRUE)

And then evaluate it by diag(H(p1)).

[Tomas T.]

Thanks Kasper! This works perfectly, and it is fast!

I was also able to get the 3rd derivative by F$jacfun()$jacfun(sparse = TRUE)$jacfun(sparse = TRUE).

Thanks!

Tomas

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