LOWESS Project

One LOWESS to Rule Them All

The fastest, most robust, and most feature-complete language-agnostic LOWESS (Locally Weighted Scatterplot Smoothing) implementation for Rust, Python, R, Julia, Node.js, C++, Go, Java, and WebAssembly.

The lowess-project also offers bindings for Rust, Python, R, Julia, Node.js, WebAssembly, C++, Go, and Java — see the full repository.

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Installation & Documentation

Currently available for R, Python, Rust, Julia, Node.js, WebAssembly, and C++. See the Installation Guide for detailed installation instructions.

📚 View the full documentation

GPU Backend

GPU acceleration (wgpu: Vulkan, Metal, DirectX 12, and GLES on Android) is also supported for high-throughput batch smoothing. See the GPU Backend guide for details.

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LOESS vs. LOWESS

Feature	LOESS	LOWESS (This Crate)
Polynomial Degree	Linear, Quadratic, Cubic, Quartic	Linear (Degree 1)
Dimensions	Multivariate (n-D support)	Univariate (1-D only)
Flexibility	High (Distance metrics)	Standard
Complexity	Higher (Matrix inversion)	Lower (Weighted average/slope)

Read more about how LOWESS works in the Concepts.

Note: For a LOESS implementation, use loess-project.

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Why this package?

Speed

It is on average 200-327x faster than Python's statsmodels.lowess and up to 7.8× faster than base R's stats::lowess on a tested large, wide-window workload. GPU fastLowess first beats CPU-parallel execution at 25K–50K points, depending on smoothing fraction, and reaches 4.7× speedup over parallel fastLowess CPU execution at 1M points in the tested workload. Small workloads can favor CPU because of GPU overhead; results vary by workload and hardware. See the Benchmarks page for details.

For more details on the performance comparison, see the Benchmarks page.

Robustness

This implementation is more robust than R's lowess and Python's statsmodels due to two key design choices:

MAD-Based Scale Estimation:

For robustness weight calculations, this crate uses Median Absolute Deviation (MAD) for scale estimation:

s = median(|r_i - median(r)|)

In contrast, statsmodels and R's lowess uses the median of absolute residuals (MAR):

s = median(|r_i|)

• MAD is a breakdown-point-optimal estimator—it remains valid even when up to 50% of data are outliers.
• The median-centering step removes asymmetric bias from residual distributions.
• MAD provides consistent outlier detection regardless of whether residuals are centered around zero.

Boundary Padding:

This crate applies a range of different boundary policies at dataset edges:

• Extend: Repeats edge values to maintain local neighborhood size.
• Reflect: Mirrors data symmetrically around boundaries.
• Zero: Pads with zeros (useful for signal processing).
• NoBoundary: Original Cleveland behavior

statsmodels and R's lowess do not apply boundary padding, which can lead to:

• Biased estimates near boundaries due to asymmetric local neighborhoods.
• Increased variance at the edges of the smoothed curve.

Features

A variety of features, supporting a range of use cases:

Feature	This package	statsmodels	R (stats)
Kernel	7 options	only Tricube	only Tricube
Robustness Weighting	3 options	only Huber	only Huber
Zero Weight Fallback	3 options	no	no
Boundary Padding	4 options	no padding	no padding
Scale Estimation	2 options	only MAR	only MAR
Auto Convergence	yes	no	no
Parallel Execution	yes	no	no
GPU Acceleration	yes	no	no
Confidence Intervals	yes	no	no
Prediction Intervals	yes	no	no
Cross-Validation	2 options	no	no
Streaming Mode	yes	no	no
Online Mode	yes	no	no
no-std Support	yes	no	no

Validation

All implementations are numerical twins of R's lowess:

Aspect	Status	Details
Accuracy	✅ EXACT MATCH	Max diff < 1e-12 across all scenarios
Consistency	✅ PERFECT	Multiple scenarios pass with strict tolerance
Robustness	✅ VERIFIED	Robust smoothing matches R exactly

Contributing

Contributions are welcome! Please see CONTRIBUTING.md for more information.

License

Licensed under MIT or Apache-2.0.

Citation

If you use this software in your research, please cite it using the CITATION.cff file or the BibTeX entry below:

@software{lowess_project,
  author = {Valizadeh, Amir},
  title = {LOWESS Project: High-Performance Locally Weighted Scatterplot Smoothing},
  year = {2026},
  url = {https://github.com/thisisamirv/lowess-project},
  license = {MIT OR Apache-2.0}
}