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, JavaScript, C++, and WebAssembly.

Important

The lowess-project contains a complete ecosystem for LOWESS smoothing:

• lowess - Core single-threaded Rust implementation with no_std support
• fastLowess - Parallel CPU and GPU-accelerated Rust wrapper with ndarray integration
• R bindings - extendr-based R binding
• Python bindings - PyO3-based Python binding
• Julia bindings - Native Julia binding with C FFI
• JavaScript bindings - Node.js binding
• WebAssembly bindings - WASM binding
• C++ bindings - Native C++ binding with CMake integration

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Installation

Note

Currently available for R, Python, Rust, Julia, Node.js, WebAssembly, and C++. See INSTALLATION.md for detailed installation instructions.

Documentation

Note

📚 View the full documentation

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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)

Tip

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

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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 file.

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

* GPU acceleration is currently in beta and may not be available on all platforms.

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

R:

Lowess(
    fraction = 0.5,
    iterations = 3L,
    delta = 0.01,
    weight_function = "tricube",
    robustness_method = "bisquare",
    zero_weight_fallback = "use_local_mean",
    boundary_policy = "extend",
    confidence_intervals = 0.95,
    prediction_intervals = 0.95,
    return_diagnostics = TRUE,
    return_residuals = TRUE,
    return_robustness_weights = TRUE,
    cv_fractions = c(0.3, 0.5, 0.7),
    cv_method = "kfold",
    cv_k = 5L,
    auto_converge = 1e-4,
    parallel = TRUE
)$fit(x, y)

# 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

Python:

from fastlowess import Lowess

model = Lowess(
    fraction=0.5,
    iterations=3,
    delta=0.01,
    weight_function="tricube",
    robustness_method="bisquare",
    zero_weight_fallback="use_local_mean",
    boundary_policy="extend",
    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,
    auto_converge=1e-4,
    parallel=True
)
result = model.fit(x, y)

# 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

Rust:

Lowess::new()
    .fraction(0.5)
    .iterations(3)
    .delta(0.01)
    .weight_function(Tricube)
    .robustness_method(Bisquare)
    .zero_weight_fallback(UseLocalMean)
    .boundary_policy(Extend)
    .confidence_intervals(0.95)
    .prediction_intervals(0.95)
    .return_diagnostics()
    .return_residuals()
    .return_robustness_weights()
    .cross_validate(KFold(5, &[0.3, 0.5, 0.7]).seed(123))
    .auto_converge(1e-4)
    .adapter(Batch)
    .parallel(true)             // fastLowess only
    .backend(CPU)               // fastLowess only: CPU or GPU
    .build()?;

let result = model.fit(x, y);

// Result structure:
pub struct LowessResult<T> {
    pub x: Vec<T>,                           // Sorted x values
    pub y: Vec<T>,                           // Smoothed y values
    pub standard_errors: Option<Vec<T>>,
    pub confidence_lower: Option<Vec<T>>,
    pub confidence_upper: Option<Vec<T>>,
    pub prediction_lower: Option<Vec<T>>,
    pub prediction_upper: Option<Vec<T>>,
    pub residuals: Option<Vec<T>>,
    pub robustness_weights: Option<Vec<T>>,
    pub diagnostics: Option<Diagnostics<T>>,
    pub iterations_used: Option<usize>,
    pub fraction_used: T,
    pub cv_scores: Option<Vec<T>>,
}

Julia:

Lowess(;
    fraction=0.5,
    iterations=3,
    delta=NaN,  # NaN for auto
    weight_function="tricube",
    robustness_method="bisquare",
    zero_weight_fallback="use_local_mean",
    boundary_policy="extend",
    confidence_intervals=NaN,
    prediction_intervals=NaN,
    return_diagnostics=true,
    return_residuals=true,
    return_robustness_weights=true,
    cv_fractions=Float64[], # e.g. [0.3, 0.5]
    cv_method="kfold",
    cv_k=5,
    auto_converge=NaN,
    parallel=true
)

# 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

Node.js:

new Lowess({
    fraction: 0.5,
    iterations: 3,
    delta: 0.01,
    weightFunction: "tricube",
    robustnessMethod: "bisquare",
    zeroWeightFallback: "use_local_mean",
    boundaryPolicy: "extend",
    confidenceIntervals: 0.95,
    predictionIntervals: 0.95,
    returnDiagnostics: true,
    returnResiduals: true,
    returnRobustnessWeights: true,
    cvFractions: [0.3, 0.5, 0.7],
    cvMethod: "kfold",
    cvK: 5,
    autoConverge: 1e-4,
    parallel: true
}).fit(x, y)

// Result structure:
result.x,
result.y,
result.standardErrors,
result.confidenceLower,
result.confidenceUpper,
result.predictionLower,
result.predictionUpper,
result.residuals,
result.robustnessWeights,
result.diagnostics,
result.iterationsUsed,
result.fractionUsed,
result.cvScores

WebAssembly:

smooth(x, y, {
    fraction: 0.5,
    iterations: 3,
    delta: 0.01,
    weightFunction: "tricube",
    robustnessMethod: "bisquare",
    zeroWeightFallback: "use_local_mean",
    boundaryPolicy: "extend",
    confidenceIntervals: 0.95,
    predictionIntervals: 0.95,
    returnDiagnostics: true,
    returnResiduals: true,
    returnRobustnessWeights: true,
    cvFractions: [0.3, 0.5, 0.7],
    cvMethod: "kfold",
    cvK: 5,
    autoConverge: 1e-4,
    parallel: true
})

// Result structure:
result.x,
result.y,
result.standardErrors,
result.confidenceLower,
result.confidenceUpper,
result.predictionLower,
result.predictionUpper,
result.residuals,
result.robustnessWeights,
result.diagnostics,
result.iterationsUsed,
result.fractionUsed,
result.cvScores

C++:

fastlowess::LowessOptions options;
options.fraction = 0.5;
options.iterations = 3;
options.delta = 0.01;
options.weight_function = "tricube";
options.robustness_method = "bisquare";
options.zero_weight_fallback = "use_local_mean";
options.boundary_policy = "extend";
options.confidence_intervals = 0.95;
options.prediction_intervals = 0.95;
options.return_diagnostics = true;
options.return_residuals = true;
options.return_robustness_weights = true;
options.cv_fractions = {0.3, 0.5, 0.7};
options.cv_method = "kfold";
options.cv_k = 5;
options.auto_converge = 1e-4;
options.parallel = true;

fastlowess::Lowess model(options);
auto result = model.fit(x, y);

// Result structure:
result.x_vector(),
result.y_vector(),
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()

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Contributing

Contributions are welcome! Please see the CONTRIBUTING.md file 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}
}