Linear regression is a very simple regression model, However, the linear relation made by it is not realistic in many data mining application domains. Locally weighted linear regression and Model trees both combine locally learning and linear regression to imoprove linear regression. Our previous work called instance weighted linear regression is designed to improve the accuracy of linear regre...

This paper describes a machine learning method, called Regression by Selecting Best Feature Projections (RSBFP). In the training phase, RSBFP projects the training data on each feature dimension and aims to find the predictive power of each feature attribute by constructing simple linear regression lines, one per each continuous feature and number of categories per each categorical feature. Bec...

the gold standard to assess jaundice in neonates is the serum bilirubin measurement. blood sampling for the determination of total serum bilirubin (tsb) is painful for newborns and stressful for parents. the bilicheck®, a new transcutaneous bilirubinometer, is considered as a more accurate measurement of bilirubin compared to the previous bilirubinometers courtesy of its advanced technology. th...

This material is compiled for the course Empirical Modelling. Sections marked with a star (∗) are not central in the courses. The main source of inspiration when writing this text has been Chapter 4 in the book ”System Identification” by Söderström and Stoica (Prentice Hall, 1989) which also may be consulted for a more thorough treatment of the material presented here. The book is available for...

Linear regression is probably the most popular model for predicting a RV Y ∈ R based on multiple RVs X1, . . . , Xd ∈ R. It predicts a numeric variable using a linear combination of variables ∑ θiXi where the combination coefficients θi are determined by minimizing the sum of squared prediction error on the training set. We use below the convention that the first variable is always one i.e., X1...

Probablistic Model: We start with the assumption that prior to starting a sequence of experiments we have a family of random variables with means that vary linearly with respect to some deterministic independent variable. That is, there exist an intercept β0 and a slope β1 such that for each value of the independent variable x, we have a random variable Y with mean β0 + β1x. We are then given p...