Fast local linear regression with anchor regularization

The regression problem is an important problem in machine learning, data mining, and statistics, and several research works have investigated it in the past decades. Examples include stock price prediction [12, 25], age prediction from RNA-seq [6] or images [11], sentimental analysis [15, 18], or house prediction [7] to name a few. The most widely used regression approach is based on a linear model including the ordinary least squares (OLS), Ridge regression, least absolute shrinkage and selection operator (Lasso) [19], and elastic net [26]. Because these linear models are extremely simple and can be interpreted by simply checking the linear coefficients of the variables; these approaches are in particular used in practice. However, one of the limitations of linear models is that they cannot handle complex nonlinear data; the performance can be significantly degraded if we apply these linear methods to process complex data such as the gene expression data used heavily in biology and healthcare. To handle complex data, researchers tend to use kernel methods such as kernel ridge regression (KRR) and support vector regression (SVR) [16].