Regression games

The solution of a TU cooperative game can be a distribution of the value of the grand coalition, i.e. it can be a distribution of the payo (utility) all the players together achieve. In a regression model, the evaluation of the explanatory variables can be a distribution of the overall t, i.e. the t of the model every regressor variable is involved. Furthermore, we can take regression models as TU cooperative games where the explanatory (regressor) variables are the players. In this paper we introduce the class of regression games, characterize it and apply the Shapley value to evaluating the explanatory variables in regression models. In order to support our approach we consider Young (1985)'s axiomatization of the Shapley value, and conclude that the Shapley value is a reasonable tool to evaluate the explanatory variables of regression models

Associative polynomial functions over bounded distributive lattices

The associativity property, usually defined for binary functions, can be generalized to functions of a given fixed arity n>=1 as well as to functions of multiple arities. In this paper, we investigate these two generalizations in the case of polynomial functions over bounded distributive lattices and present explicit descriptions of the corresponding associative functions. We also show that, in this case, both generalizations of associativity are essentially the same.Comment: Final versio

Automatic leukocyte nucleus segmentation by intuitionistic fuzzy divergence based thresholding

The paper proposes a robust approach to automatic segmentation of leukocyte‟s nucleus from microscopic blood smear images under normal as well as noisy environment by employing a new exponential intuitionistic fuzzy divergence based thresholding technique. The algorithm minimizes the divergence between the actual image and the ideally thresholded image to search for the final threshold. A new divergence formula based on exponential intuitionistic fuzzy entropy has been proposed. Further, to increase its noise handling capacity, a neighborhood-based membership function for the image pixels has been designed. The proposed scheme has been applied on 110 normal and 54 leukemia (chronic myelogenous leukemia) affected blood samples. The nucleus segmentation results have been validated by three expert haematologists. The algorithm achieves an average segmentation accuracy of 98.52% in noise-free environment. It beats the competitor algorithms in terms of several other metrics. The proposed scheme with neighborhood based membership function outperforms the competitor algorithms in terms of segmentation accuracy under noisy environment. It achieves 93.90% and 94.93% accuracies for Speckle and Gaussian noises respectively. The average area under the ROC curves comes out to be 0.9514 in noisy conditions, which proves the robustness of the proposed algorithm

Opinion dynamics and wisdom under conformity

Buechel B, Hellmann T, Klößner S. Opinion dynamics and wisdom under conformity. Working Papers. Center for Mathematical Economics. Vol 469. Bielefeld: Center for Mathematical Economics; 2013.We study a dynamic model of opinion formation in social networks. In our model, boundedly rational agents update opinions by averaging over their neighbors' expressed opinions, but may misrepresent their own opinion by conforming or counter-conforming with their neighbors. We show that an agent's social influencev on the long-run group opinion is increasing in network centrality and decreasing in conformity. For efficiency of information aggregation (\wisdom"), misrepresentation of opinions need not undermine wisdom. Given the network, we provide the optimal distribution of conformity levels in the society and show which agents should be more conforming in order to increase wisdom

Robust ordinal regression in preference learning and ranking

Multiple Criteria Decision Aiding (MCDA) offers a diversity of approaches designed for providing the decision maker (DM) with a recommendation concerning a set of alternatives (items, actions) evaluated from multiple points of view, called criteria. This paper aims at drawing attention of the Machine Learning (ML) community upon recent advances in a representative MCDA methodology, called Robust Ordinal Regression (ROR). ROR learns by examples in order to rank a set of alternatives, thus considering a similar problem as Preference Learning (ML-PL) does. However, ROR implements the interactive preference construction paradigm, which should be perceived as a mutual learning of the model and the DM. The paper clarifies the specific interpretation of the concept of preference learning adopted in ROR and MCDA, comparing it to the usual concept of preference learning considered within ML. This comparison concerns a structure of the considered problem, types of admitted preference information, a character of the employed preference models, ways of exploiting them, and techniques to arrive at a final ranking