Poisson GLM

[Koen Van den Berge]

Hi,

Suppose that I'd like to fit a constrained Poisson GLM using CVXR, much like the logistic regression example in the documentation.
The program does not seem to optimize the function using either maximum likelihood formulation

    ## MWE
    library(CVXR)
    y <- rpois(n=100, lambda=50)
    X <- matrix(rnorm(100), ncol=1)
    betaHat <- Variable(1)
    obj <- sum(y* log(exp(X %*% betaHat)) - exp(X %*% betaHat))
    prob <- Problem(Maximize(obj))
    result <- CVXR::solve(prob)

or a Poisson loss formulation

    obj <- mean(exp(X %*% betaHat) - y * log(exp(X %*% betaHat)))
    prob <- Problem(Minimize(obj))
    result <- CVXR::solve(prob)

returning the error Error in construct_intermediate_chain(object, candidate_solvers, gp = gp) : Problem does not follow DCP rules. However, the problem does follow DGP rules. Consider calling this function with gp = TRUE. Setting gp=TRUE gives an opposite error.

Am I overlooking something?

[Balasubramanian Narasimhan]

Not sure what you are trying to do with the logs/exp in the objective. See below. Both ways will yield the same result.

> y <- rpois(n=100, lambda=50)
> X <- matrix(rnorm(100), ncol=1)
> betaHat <- Variable(1)
> obj <- sum(y* X %*% betaHat - exp(X %*% betaHat))
> prob <- Problem(Maximize(obj))
> result <- CVXR::solve(prob)
> result$getValue(betaHat)
[1] 1.496695
> obj <- mean(exp(X %*% betaHat) - y * X %*% betaHat)
> prob <- Problem(Minimize(obj))
> result <- CVXR::solve(prob)
> result$getValue(betaHat)
[1] 1.496695

[Koen Van den Berge]

I see, that's useful. Many thanks!