Multivariate Adaptive Regression Splines


MARS (Multivariate Adaptive Regression Splines) is one of the most important tools used in modern Data Mining, Machine Learning and Predictive Analytics. Applicable for both Classification and Regression problems. The MARS algorithm is an extension of linear models that makes no assumptions about the relationship between the target variable and the predictor variables. In other words, it is a non-parametric regression method that builds multiple linear regression models across the range of predictor values. It is ideal for users who prefer results in a form similar to traditional regression while capturing essential nonlinearities and interactions. The MARS methodology’s approach to regression modelling effectively uncovers important data patterns and relationships that are difficult, if not impossible, for other regression methods to reveal. The MARS modelling engine builds its model by piecing together a series of straight lines with each allowed its own slope. This permits the MARS modelling engine to trace out any pattern detected in the data.

What is MARS (Multivariate Adaptive Regression Splines)?

Multivariate Adaptive Regression Splines or MARS model is a regression model that automatically constructed using an adaptive spline algorithm, partitioning the data and run a linear regression model on each different partition. MARS provides a great stepping stone into nonlinear modelling and it is closely related to multiple regression techniques. MARS is actually an adaption of CART that allows for additive terms to be entered onto the model.

In order to construct a CART decision tree, there are two main steps –
      • Grow a large tree
      • Prune the large tree
The process for constructing a MARS model is similar and involves two steps –
      • Forward step (add terms to the model)
      • Backward step (delete terms from the model)

Features of Multivariate Adaptive Regression Splines (MARS)

      • Automatic variable selection – MARS automatically select the variables used in the model via the forward and backward step.
      • Automatic nonlinear modelling – MARS automatically models nonlinear functions via piecewise linear approximations.
      • Automatic variable interaction – Determine interactions between predictor variables.
      • Automatic missing value handling – Handling missing values with new nested variable techniques.
      • Automatic numeric and categorical predictor handling – MARS automatically handles both categorical and numeric predictors directly.

Multivariate Adaptive Regression Splines (MARS) in Salford Predictive Modeler

Salford Predictive Modeler is an integrated suite of Machine learning and Predictive Analytics Software. It includes various data mining techniques like classification, clustering, association and prediction. Some of the other methods are regression, survival analysis, missing value analysis, data binning and many more. SPM is a highly accurate and ultra-fast platform for developing predictive, descriptive, and analytical models from databases and datasets of any size, complexity, or organisation. The Salford Predictive Modeler software suite includes CART, MARS, TreeNet, Random Forests, as well as powerful new automation and modelling capabilities not found elsewhere.

Multivariate Adaptive Regression Splines (MARS) was developed in the early 1990s by world-renowned Stanford physicist and statistician Jerome Friedman and has become widely known in the data mining and business intelligence worlds. The only commercial version of MARS software is distributed by Minitab. It includes a number of proprietary features, extensions, and enhancements developed by Salford Systems, Jerome Friedman which is exclusive to Salford Predictive Modeler software.

MARS is an innovative and flexible modelling tool that automates the building of accurate predictive models for continuous and binary dependent variables. It excels at finding optimal variable transformations and potential interaction within any regression-based modelling solution and easily handles the complex data structure that often hides in high-dimensional data. In doing so, this new approach to regression modelling effectively uncovers important data patterns and relationships that are difficult, if not impossible, for other methods to reveal. With the advent of MARS, regression models can now be routinely and automatically developed for the most complex data structures.


Multivariate Adaptive Regression Splines (MARS) in Salford Predictive Modeler

Why use Multivariate Adaptive Regression Splines (MARS)?

      • Given a target variable and a set of candidate predictor variables, MARS automates all aspects of model development and model deployment.
      • Multivariate adaptive regression splines (MARS) enables you to rapidly search through all possible models and quickly identify the “optimal” solution.
      • MARS performs regression techniques along with the search for nonlinearities in the data that helps to maximise the predictive accuracy of the model.
      • Multivariate adaptive regression splines (MARS) have useful features to effectively reduce the number of terms in a model.
      • MARS can automatically select and transform variables and can identify potential interactions between variables.

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