Maximum Likelihood Optimization
Answered
Hello,
I just found out about Gurobi optimization today, and I'm wondering about its general capabilities with maximum likelihood inference. Are there ways to perform maximum likelihood optimizations, like one would do using R's optim() function? So the objective function would be one that calculates a likelihood value, given vectors for univariate data, an expected mean vector, and a covariance matrix. Just to emphasize, I work primarily in R, and I'm a complete beginner to Gurobi optimizations.
Best,
Ricardo Aranda
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Gurobi Staff
Hi Ricardo,
My knowledge about R and Maximum Likelihood Optimization is very limited, thus I hope that someone in the community might provide a more precise answer.
Are there ways to perform maximum likelihood optimizations, like one would do using R's optim() function? So the objective function would be one that calculates a likelihood value, given vectors for univariate data, an expected mean vector, and a covariance matrix.
You can solve your model with Gurobi As long as you are able to formulate the model you used in the \(\texttt{optim()}\) function as a (mixed-integer) linear or (mixed-integer) quadratic program. I found a presentation from the EPFL where the authors describe a possible MIP representation of a Maximum Likelihood Estimation model (first ~12 slides of this presentation), which might apply to your problem.
I would recommend having a look at our MILP tutorials to first get a better understanding what kind of problems Gurobi can solve. As a next step, I would recommend having a look at our R examples. In particular the mip.R, diet.R, and workforce1.R examples together with the documentation of our R API overview and details should provide a good starting point. I hope that this helps in tackling your issue and getting started with Gurobi.
Best regards,
Jaromił0 -
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