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In machine learning or scientific computing, model performance is measuredwith an objective function. But why choose one objective over another?Information theory gives one answer: To maximize the information in the model,select the objective function that represents the error in the fewest bits. Toevaluate different objectives, transform them into likelihood functions. Aslikelihoods, their relative magnitude represents how strongly we should preferone objective versus another, and the log of that relation represents thedifference in their bit-length, as well as the difference in their uncertainty.In other words, prefer whichever objective minimizes the uncertainty. Under theinformation-theoretic paradigm, the ultimate objective is to maximizeinformation (and minimize uncertainty), as opposed to any specific utility. Weargue that this paradigm is well-suited to models that have many uses and nodefinite utility, like the large Earth system models used to understand theeffects of climate change.

How to select an objective function using information theory