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Abstract:
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Monotonic Regression (MR) is a standard method for extracting a monotonic function from non-monotonic data, and it is used in many applications. However, a known drawback of this method is that its fitted response is a piecewise constant function, while practical response functions are often required to be continuous. We propose a method that achieves monotonicity and smoothness of the regression by introducing an L2 regularization term, and it is shown that the complexity of this method is O(n2). In addition, our simulations demonstrate that the proposed method has a higher predictive power than many other existing methods when large data are involved and the expected response is a complex function (which is typical in data science) or when there is a change point in the data. Our approach is probabilistically motivated and has connections to the Bayesian modeling.
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