## Learning Probabilistic Models: An Expected Utility Maximization Approach

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***Craig Friedman, Sven Sandow*; 4(Jul):257-291, 2003.

### Abstract

We consider the problem of learning a probabilistic model from the viewpoint of an expected utility maximizing decision maker/investor who would use the model to make decisions (bets), which result in well defined payoffs.
In our new approach, we seek good out-of-sample model performance by
considering a one-parameter family of Pareto optimal models,
which we define in terms of consistency with the training data
and consistency with a prior (benchmark) model. We measure the
former by means of the large-sample distribution of a vector of
sample-averaged features, and the latter by means of a
generalized relative entropy.
We express each Pareto optimal model as the solution of a strictly convex optimization problem and its strictly concave (and tractable) dual. Each dual problem is a regularized maximization of expected utility over a well-defined family of functions.
Each Pareto optimal model is robust: maximizing worst-case outperformance relative to the benchmark model.
Finally, we select the Pareto optimal model with maximum (out-of-sample) expected utility.
We show that our method reduces to the minimum relative entropy method if and only if the utility function is a member of a three-parameter logarithmic family.

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