LOESS / LOWESS Local Regression
Local Regression (LOESS / LOWESS) · Also known as: LOWESS, local regression, locally weighted scatterplot smoothing, yerel regresyon
LOESS (locally estimated scatterplot smoothing), introduced by William Cleveland in 1979 and extended with Susan Devlin in 1988, fits a smooth curve through data by performing a separate weighted polynomial regression in the neighbourhood of each point. Nearby observations count more than distant ones, so the method follows local structure without assuming any global functional form, making it a popular exploratory smoother for scatterplots.
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When to use it
Use LOESS as an exploratory smoother to visualize the relationship between two variables when you do not want to assume a functional form — for example, adding a trend line to a scatterplot, smoothing a noisy time series, or inspecting residuals for structure. It is intuitive and flexible, and the robust variant handles outliers gracefully. Its costs are computational (a separate regression per evaluation point), poor behaviour in high dimensions (the curse of dimensionality limits it to one or two predictors), unreliable extrapolation, and the absence of a compact closed-form equation. When you need an interpretable parametric summary, a global model is preferable; for many predictors, splines within a GAM or other methods scale better.
Strengths & limitations
- Flexible, assumption-free smoothing that follows local structure in the data.
- Excellent for exploratory visualization and trend lines on scatterplots.
- A robust variant resists the influence of outliers.
- Only a span and local degree to choose, with intuitive effects.
- Computationally expensive, requiring a local regression at each evaluation point.
- Suffers from the curse of dimensionality; practical only for one or two predictors.
- Produces no compact equation and extrapolates poorly beyond the data.
- Sensitive to the span: too large oversmooths, too small overfits.
Frequently asked
What is the span in LOESS?
The span (or bandwidth) is the fraction of the data used in each local regression. A larger span produces a smoother but more biased curve; a smaller span captures more local detail but is noisier. It is the primary tuning parameter and is usually chosen to balance smoothness against fidelity, sometimes via cross-validation.
What is the difference between LOESS and LOWESS?
They refer to closely related local-regression smoothers from Cleveland's work; LOWESS classically denotes the robust locally weighted scatterplot smoother, while LOESS often denotes the more general local-regression framework allowing higher-degree local polynomials and multiple predictors. In practice the names are frequently used interchangeably.
Why shouldn't I use LOESS with many predictors?
LOESS relies on having enough neighbouring points near each target. In high dimensions data become sparse — neighbourhoods are either nearly empty or so large they are no longer local — so the method breaks down. It is best limited to one or two predictors; for more, use additive splines or other scalable methods.
Sources
- Cleveland, W. S. (1979). Robust locally weighted regression and smoothing scatterplots. Journal of the American Statistical Association, 74(368), 829–836. DOI: 10.1080/01621459.1979.10481038 ↗
- Cleveland, W. S., & Devlin, S. J. (1988). Locally weighted regression: an approach to regression analysis by local fitting. Journal of the American Statistical Association, 83(403), 596–610. DOI: 10.1080/01621459.1988.10478639 ↗
How to cite this page
ScholarGate. (2026, June 2). Local Regression (LOESS / LOWESS). ScholarGate. https://scholargate.app/en/machine-learning/loess
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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