Error in optim(): searching for global minimum for a univariate function

问题

I am trying to optmize a function in R

The function is the Likelihood function of negative binominal when estimating only mu parameter. This should not be a problem since the function clearly has just one point of maximum. But, I am not being able to reach the desirable result.

The function to be optmized is:

EMV <- function(data, par) {

    Mi  <- par
    Phi <- 2
    N   <- NROW(data)

    Resultado <- log(Mi/(Mi + Phi))*sum(data) + N*Phi*log(Phi/(Mi + Phi))
    return(Resultado)
}

Data is a vector of negative binomial variables with parameters 2 and 2

data <- rnegbin(10000, mu = 2, theta = 2)

When I plot the function having mu as variable with the following code:

x <- seq(0.1, 100, 0.02)
z <- EMV(data,0.1)
for (aux in x) {z <- rbind(z, EMV(data,aux))}
z <- z[2:NROW(z)]
plot(x,z)

I get the following curve:

And the maximum value of z is close to parameter value --> 2

x[which.max(z)]

But the optimization is not working with BFGS

Error in optim(par = theta, fn = EMV, data = data, method = "BFGS") : 
non-finite finite-difference value [1]

And is not going to right value using SANN, for example:

$par
[1] 5.19767e-05

$value
[1] -211981.8

$counts
function gradient 
   10000       NA 

$convergence
[1] 0

$message
NULL

The questions are:

What am I doing wrong?
Is there a way to tell optim that the param should be bigger than 0?
Is there a way to tell optim that I want to maximize the function? (I am afraid the optim is trying to minimize and is going to a very small value where function returns smallest values)

回答1:

Minimization or Maximization?

Although ?optim says it can do maximization, but that is in a bracket, so minimization is default:

fn: A function to be minimized (or maximized) ...

Thus, if we want to maximize an objective function, we need to multiply an -1 to it, and then minimize it. This is quite a common situation. In statistics we often want to find maximum log likelihood, so to use optim(), we have no choice but to minimize the negative log likelihood.

Which method to use?

If we only do 1D minimization, we should use method "Brent". This method allows us to specify a lower bound and an upper bound of search region. Searching will start from one bound, and search toward the other, until it hit the minimum, or it reach the boundary. Such specification can help you to constrain your parameters. For example, you don't want mu to be smaller than 0, then just set lower = 0.

When we move to 2D or higher dimension, we should resort to "BFGS". In this case, if we want to constrain one of our parameters, say a, to be positive, we need to take log transform log_a = log(a), and reparameterize our objective function using log_a. Now, log_a is free of constraint. The same goes when we want constrain multiple parameters to be positive.

How to change your code?

EMV <- function(data, par) {

    Mi  <- par
    Phi <- 2
    N   <- NROW(data)

    Resultado <- log(Mi/(Mi + Phi))*sum(data) + N*Phi*log(Phi/(Mi + Phi))
    return(-1 * Resultado)
}

optim(par = theta, fn = EMV, data = data, method = "Brent", lower = 0, upper = 1E5)

回答2:

The help file for optim says: "By default optim performs minimization, but it will maximize if control$fnscale is negative." So if you either multiply your function output by -1 or change the control object input, you should get the right answer.

来源：https://stackoverflow.com/questions/37738423/error-in-optim-searching-for-global-minimum-for-a-univariate-function

标签

optimization