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Is the relationship indeed deterministic as in your example? If so there shouldn't be any reason to have two models, just apply the proper feature transformation and stick it into a single one. Are the features living in the same domain? If they do a multi-task model would make sense. If not I would start with independent models. If you wanted to get fancy you could also try to a couple of feature extractors on each input that map to some shared latent space on which you define a MTGP model. But I'd start simple. |
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I am trying to apply multi-objective Bayesian optimization, I have 2 objective functions that I am trying to approximate using GP. Each objective function can be approximated using different but somehow related data. For instance, if the first objective function is fitted using data x, then the second objective function is fitted using data x multiplied by constant array (c), such as x*c. I am wondering if there is a way to fit both objectives using multi-tasks multivariate GP, or its better to fit each objective separately using multi-dimensional GP? please note that I have 200 observations and each observation consists of 14 variables . Thanks
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