Robust Ordinal Regression for Subsets Comparisons with Interactions
This work addresses preference learning for decision makers in scenarios involving subset comparisons, but it appears incremental as it builds on existing robust ordinal regression methodologies.
The paper tackles the problem of learning decision maker preferences between subsets using a robust ordinal regression method that accounts for interactions between elements, and it evaluates the approach on synthetic and real-world data to assess prediction richness and reliability.
This paper is dedicated to a robust ordinal method for learning the preferences of a decision maker between subsets. The decision model, derived from Fishburn and LaValle (1996) and whose parameters we learn, is general enough to be compatible with any strict weak order on subsets, thanks to the consideration of possible interactions between elements. Moreover, we accept not to predict some preferences if the available preference data are not compatible with a reliable prediction. A predicted preference is considered reliable if all the simplest models (Occam's razor) explaining the preference data agree on it. Following the robust ordinal regression methodology, our predictions are based on an uncertainty set encompassing the possible values of the model parameters. We define a robust ordinal dominance relation between subsets and we design a procedure to determine whether this dominance relation holds. Numerical tests are provided on synthetic and real-world data to evaluate the richness and reliability of the preference predictions made.