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Introduction to mars_2009

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Matthew Magistrado

The document provides an introduction to MARS (Multivariate Adaptive Regression Splines), a tool developed by Jerome Friedman for regression analysis. MARS produces smooth curves and surfaces rather than step functions, handles continuous, binary, and censored target variables, and automatically selects important variables and transformations while protecting against overfitting. It works by constructing basis functions to represent the data and uses forward and backward stepwise selection to determine the optimal number of functions.

TecnologíaEducación
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Introduction to MARS Dan Steinberg Mykhaylo Golovnya [email_address] August, 2009
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Introduction
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Boston Housing Dataset
[object Object],[object Object],[object Object],Scatter Matrix                                             
[object Object],[object Object],[object Object],[object Object],MARS Model
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Challenge: Searching for Multiple Knots
[object Object],[object Object],[object Object],Example: Flat Top Function
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Basis Functions
[object Object],[object Object],[object Object],[object Object],The Set of All Basis Functions
Step-Wise Model Development using BFs ,[object Object],[object Object],[object Object],[object Object],[object Object]
Solution with 1 Basis Function ,[object Object]
Solution with 2 Basis Functions ,[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],Example: Solution with 3 Basis Functions
MARS Creates Basis Functions in Pairs ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],MARS Process
Example of Categorical Predictors ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Missing Value Handling ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Interaction Support in MARS ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Boston Housing – Conventional Regression ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],OLS Regression (R-squared 73%) MARS Regression (R-squared 87%)
Further Reading ,[object Object],[object Object],[object Object],[object Object],[object Object]

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Introduction to mars_2009

  • 1. Introduction to MARS Dan Steinberg Mykhaylo Golovnya [email_address] August, 2009
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