Machine and statistical learning mainly consists of first deciding on a parametric model and then fitting its corresponding parameters. For this model fitting, it is usual to consider a loss function. There are in the literature several types of models based on non-additive measures. The most common examples include models based on fuzzy integrals (as e.g., Choquet and Sugeno integrals). In this case, given some data, a measure is identified and the model is built. That is, we build a data-driven model based on a non-additive measure (or on several non-additive measures). Then, once the measure is identified, we are often interested in their analysis and visualization to understand its properties. In this paper we give an overview of measure identification and measure analysis.

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Data-Driven Identification of Non-additive Measures

  • Vicenç Torra,
  • Zuzana Ontkovičová

摘要

Machine and statistical learning mainly consists of first deciding on a parametric model and then fitting its corresponding parameters. For this model fitting, it is usual to consider a loss function. There are in the literature several types of models based on non-additive measures. The most common examples include models based on fuzzy integrals (as e.g., Choquet and Sugeno integrals). In this case, given some data, a measure is identified and the model is built. That is, we build a data-driven model based on a non-additive measure (or on several non-additive measures). Then, once the measure is identified, we are often interested in their analysis and visualization to understand its properties. In this paper we give an overview of measure identification and measure analysis.