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An introduction to multivariate adaptive regression splines
1Department of Statistics and Stanford Linear Accelerator Center, Stanford University, CA 94305-4065, USA.
Statistical Methods in Medical Research
|September 1, 1995
Summary
Multivariate Adaptive Regression Splines (MARS) offers flexible modeling for complex, high-dimensional data by automatically determining model components from data. This method effectively captures interactions and produces continuous models, with extensions for various data types.
Area of Science:
- Statistics
- Machine Learning
- Data Mining
Background:
- High-dimensional data presents challenges for traditional modeling techniques.
- Existing methods may struggle with capturing complex interactions and ensuring model continuity.
Purpose of the Study:
- To introduce and explain the Multivariate Adaptive Regression Splines (MARS) method.
- To detail the automatic determination of model components and its advantages over recursive partitioning.
- To present extensions and practical application of MARS.
Main Methods:
- MARS utilizes an expansion in product spline basis functions.
- Model parameters (basis functions, product degree, knot locations) are data-driven.
- The procedure is inspired by recursive partitioning (e.g., CART) but offers enhanced flexibility.
Main Results:
- MARS captures high-order interactions and models nearly additive relationships effectively.
- It produces continuous models with continuous derivatives.
- The model structure allows for separate identification of additive and interaction effects.
Conclusions:
- MARS provides a powerful and flexible approach for modeling high-dimensional data.
- Extensions enhance its applicability to diverse data scenarios, including binary responses and missing values.
- The paper offers guidance on interpreting MARS output and demonstrates its utility with clinical data.