Checkered Regression

Abstract. This paper introduces the checkered regression model, a nonlinear generalization of logistic regression. More precisely, this new binary classifier relies on the multivariate function $\frac{1}{2}\left( 1 + \tanh(\frac{z_1}{2})\times\dots\times\tanh(\frac{z_m}{2}) \right)$, which coincides with the usual sigmoid function in the univariate case $m=1$. While the decision boundary of logistic regression consists of a single hyperplane, our method is shown to tessellate the feature space by any given number $m\ge 1$ of hyperplanes. In order to fit the model’s parameters to some labeled data, we describe a classic empirical risk minimization framework based on the cross entropy loss. A multiclass version of our approach is also proposed.

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