LOWESS Project

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

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

Installation

[!NOTE]

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

Documentation

[!NOTE]

📚 View the full documentation

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) |

[!TIP] Note: For a LOESS implementation, use loess-project.

Why this package?

Speed

The lowess project beats the competition in terms of speed, whether in single-threaded or multi-threaded parallel execution. It is on average 200-327x faster than Python's statsmodels.lowess and 2-3x faster than R's lowess.

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 | | Scale Estimation | 2 options | only MAR | only MAR | | Boundary Padding | 4 options | no padding | no padding | | Zero Weight Fallback | 3 options | no | no | | Auto Convergence | yes | no | no | | Online Mode | yes | no | no | | Streaming Mode | yes | no | no | | Confidence Intervals | yes | no | no | | Prediction Intervals | yes | no | no | | Cross-Validation | 2 options | no | no | | Parallel Execution | yes | no | no | | GPU Acceleration | 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 |

API Reference

import { Lowess } from "fastlowess-wasm"

const model = new Lowess({
    fraction: 0.5,
    iterations: 3,
    delta: 0.01,
    weight_function: "tricube",
    robustness_method: "bisquare",
    scaling_method: "mad",
    zero_weight_fallback: "use_local_mean",
    boundary_policy: "extend",
    return_se: true,
    confidence_intervals: 0.95,
    prediction_intervals: 0.95,
    return_diagnostics: true,
    return_residuals: true,
    return_robustness_weights: true,
    cv_fractions: [0.3, 0.5, 0.7],
    cv_method: "kfold",
    cv_k: 5,
    cv_seed: 123,
    auto_converge: 1e-4,
    parallel: true
})
const custom_weights = new Float64Array(x.length).fill(1)
const result = model.fit(x, y, custom_weights)

// Result structure:
result.x,
result.y,
result.standard_errors,
result.confidence_lower,
result.confidence_upper,
result.prediction_lower,
result.prediction_upper,
result.residuals,
result.robustness_weights,
result.diagnostics,
result.iterations_used,
result.fraction_used,
result.cv_scores

Contributing

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

Changelog

See CHANGELOG.md for a history of changes.

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}
}