Mixability of Integral Losses: a Key to Efficient Online Aggregation of Functional and Probabilistic Forecasts

• URL: http://arxiv.org/abs/1912.07048v4
• Date: Mon, 06 Jan 2025 14:52:07 GMT
• Title: Mixability of Integral Losses: a Key to Efficient Online Aggregation of Functional and Probabilistic Forecasts
• Authors: Alexander Korotin, Vladimir V'yugin, Evgeny Burnaev,
• Abstract summary: We adapt basic mixable (and exponentially concave) loss functions to compare functional predictions and prove that these adaptations are also mixable (exp-concave) As an application of our main result, we prove that various loss functions used for probabilistic forecasting are mixable (exp-concave)
• Score: 72.32459441619388
• License:
• Abstract: In this paper we extend the setting of the online prediction with expert advice to function-valued forecasts. At each step of the online game several experts predict a function, and the learner has to efficiently aggregate these functional forecasts into a single forecast. We adapt basic mixable (and exponentially concave) loss functions to compare functional predictions and prove that these adaptations are also mixable (exp-concave). We call this phenomenon mixability (exp-concavity) of integral loss functions. As an application of our main result, we prove that various loss functions used for probabilistic forecasting are mixable (exp-concave). The considered losses include Sliced Continuous Ranked Probability Score, Energy-Based Distance, Optimal Transport Costs and Sliced Wasserstein-2 distance, Beta-2 and Kullback-Leibler divergences, Characteristic function and Maximum Mean Discrepancies.

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