LOESS Project

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

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

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

LOESS vs. LOWESS

| Feature | LOESS (This Crate) | LOWESS | | --- | --- | --- | | 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 LOESS works in the Concepts.

Note: For a LOWESS implementation, use lowess-project.

Why this package?

Speed

fastLoess beats the competition by being 47.3× faster than R's stats::loess in serial mode and 236.4× faster in parallel compared to R's stats::loess; speedups vary by workload, and parallel execution is not always faster. For datasets of 1,000 points or fewer, serial execution is advised.

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

Robustness

This implementation is more robust than R's loess 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, R's loess 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

R's loess does 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 | R (stats) | |-------------------------------|:-------------:|:----------------:| | Polynomial Degree | 5 (0–4) | 2 (1 or 2) | | Kernel | 7 options | only Tricube | | Robustness Weighting | 3 options | only Bisquare | | Scale Estimation | 3 options | only MAR | | Distance Metric | 6 options | normalized only | | Boundary Padding | 4 options | no padding | | Zero Weight Fallback | 3 options | no | | Auto Convergence | yes | no | | Online Mode | yes | no | | Streaming Mode | yes | no | | Confidence Intervals | yes | no | | Prediction Intervals | yes | no | | Diagnostics (RMSE, R2, AIC) | yes | no | | Cross-Validation | 2 options | no | | Parallel Execution | yes | no | | no-std Support | yes | no |

Validation

All implementations are numerical twins of R's loess:

| 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{loess_project,
  author = {Valizadeh, Amir},
  title = {LOESS Project: High-Performance Locally Estimated Scatterplot Smoothing},
  year = {2026},
  url = {https://github.com/thisisamirv/loess-project},
  license = {MIT OR Apache-2.0}
}