Lazy Learning for Nonparametric Locally Weighted Regression

Abstract

In this study, a newly designed local model called locally weighted regression model is proposed for the regression problem. This model predicts the output for a newly submitted data point. In general, the local regression model focuses on an area of the input space specified by a certain kernel function (Gaussian function, in particular). The local area is defined as a region enclosed by a neighborhood of the given query point. The weights assigned to the local area are determined by the related entries of the partition matrix originating from the fuzzy C-means method. The local regression model related to the local area is constructed using a weighted estimation technique. The model exploits the concept of the nearest neighbor, and constructs the weighted least square estimation once a new query is provided given. We validate the modeling ability of the overall model based on several numeric experiments.

Using machine learning techniques for predicting autogenous shrinkage of concrete incorporating superabsorbent polymers and supplementary cementitious materials

“…A good strategy is to apply weights to the contributions of the neighbors, such that closer neighbors contribute more to the average than the neighbors who are farther away. Neighbors-based regression is a sort of lazy learning in that it does not seek to build a generic internal model and instead just saves instances of the training data[92]. As an average or local linear approximation, the regression result is obtained from the k-nearest neighbors of each point.…”