Multivariate Adaptive Regression Splines (MARS)
Also known as: multivariate adaptive regression splines, earth algorithm, MARS regression, çok değişkenli uyarlamalı regresyon spline'ları
Multivariate adaptive regression splines, introduced by Jerome Friedman in 1991, is a flexible nonparametric regression method that automatically models nonlinearities and interactions by combining piecewise-linear 'hinge' functions. It builds the model in a forward stagewise pass that adds basis functions where they help most, then prunes back the overgrown model, yielding an interpretable additive-plus-interaction form that adapts its complexity to the data.
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When to use it
Use MARS when you expect nonlinear effects and interactions among continuous predictors but want a model that discovers them automatically and remains more interpretable than a black box. It handles moderate-to-high dimensions, mixes additive and interaction terms, requires little preprocessing (it is insensitive to monotone transformations and handles different scales), and runs quickly. It is a strong middle ground between GAMs (which need interactions specified) and tree ensembles. Its piecewise-linear fits can be less smooth than spline-based GAMs, it can be unstable (small data changes alter selected knots), and modern gradient-boosted trees often predict better on large, complex datasets; for purely additive smooth effects a GAM may be cleaner.
Strengths & limitations
- Automatically discovers nonlinearities and interactions without manual specification.
- Produces an interpretable form as a sum of hinge functions and their products.
- Handles many predictors and different scales with minimal preprocessing.
- Automatic complexity control via forward selection and GCV-based pruning.
- Piecewise-linear fits are less smooth than spline-based methods like GAMs.
- Greedy selection can be unstable: small data changes alter chosen knots and terms.
- Often less accurate than gradient-boosted trees on large, complex problems.
- Higher-order interactions and very high dimensions strain the forward search.
Frequently asked
What is a hinge function?
A hinge (or truncated linear) function is zero on one side of a knot and increases linearly on the other, like max(0, x − t). Pairing a hinge with its mirror image lets the model bend at the knot. MARS builds its fit by combining many such hinges, and products of hinges across variables represent interactions.
How does MARS differ from a regression tree?
Both partition the predictor space adaptively, but a regression tree produces piecewise-constant (step) predictions, whereas MARS produces continuous, piecewise-linear predictions via hinge functions. MARS therefore captures smooth trends and interactions more gracefully while retaining an interpretable structure.
How does MARS avoid overfitting?
It deliberately overfits in a forward pass that adds many basis functions, then prunes them in a backward pass, selecting the subset that minimizes the generalized cross-validation (GCV) criterion. GCV penalizes model complexity, so the final model keeps only the terms that improve out-of-sample fit.
Sources
- Friedman, J. H. (1991). Multivariate adaptive regression splines. The Annals of Statistics, 19(1), 1–67. DOI: 10.1214/aos/1176347963 ↗
How to cite this page
ScholarGate. (2026, June 2). Multivariate Adaptive Regression Splines (MARS). ScholarGate. https://scholargate.app/en/machine-learning/mars
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
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- Generalized Additive ModelMachine learning↔ compare
- Gradient BoostingMachine learning↔ compare
- Regression SplinesMachine learning↔ compare