Similarity-based and Iterative Label Noise Filters for Monotonic Classification

Monotonic ordinal classification has received an increasing interest in the latest years. Building monotone models from these problems usually requires datasets that verify monotonic relationships among the samples. When the monotonic relationships are not met, changing the labels may be a viable option, but the risk is high: wrong label changes would completely change the information contained in the data. In this work, we tackle the construction of monotone datasets by removing the wrong or noisy examples that violate monotonicity restrictions. We propose two monotonic noise filtering algorithms to preprocess the ordinal datasets and improve the monotonic relations between instances. The experiments are carried out over eleven ordinal datasets, showing that the application of the proposed filters improve the prediction capabilities over different levels of noise

Choquistic Regression: Generalizing Logistic Regression using the Choquet Integral

In this paper, we propose a generalization of logistic regression based on the Choquet integral. The basic idea of our approach, referred to as choquistic regression, is to replace the linear function of predictor variables, which is commonly used in logistic regression to model the log odds of the positive class, by the Choquet integral. Thus, it becomes possible to capture non-linear dependencies and interactions among predictor variables while preserving two important properties of logistic regression, namely the comprehensibility of the model and the possibility to ensure its monotonicity in individual predictors. In experimental studies with real and benchmark data, choquistic regression consistently improves upon standard logistic regression in terms of predictive accuracy

Axiomatic Attribution for Multilinear Functions

We study the attribution problem, that is, the problem of attributing a change in the value of a characteristic function to its independent variables. We make three contributions. First, we propose a formalization of the problem based on a standard cost sharing model. Second, we show that there is a unique attribution method that satisfies Dummy, Additivity, Conditional Nonnegativity, Affine Scale Invariance, and Anonymity for all characteristic functions that are the sum of a multilinear function and an additive function. We term this the Aumann-Shapley-Shubik method. Conversely, we show that such a uniqueness result does not hold for characteristic functions outside this class. Third, we study multilinear characteristic functions in detail; we describe a computationally efficient implementation of the Aumann-Shapley-Shubik method and discuss practical applications to pay-per-click advertising and portfolio analysis.Comment: 21 pages, 2 figures, updated version for EC '1