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.

[!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 package

Python bindings - PyO3-based Python package

Julia bindings - Native Julia package with C FFI

JavaScript bindings - Node.js package

WebAssembly bindings - WASM package

C++ bindings - Native C++ package with CMake integration

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.

Documentation

[!NOTE]

📚 View the full documentation

Why this package?

Speed

The lowess project crushes the competition in terms of speed, wether in single-threaded or multi-threaded parallel execution.

Speedup relative to Python's statsmodels.lowess (higher is better):

Category	statsmodels	R (stats)	Serial	Parallel	GPU
Clustered	163ms	83×	203×	433×	32×
Constant Y	134ms	92×	212×	410×	18×
Delta (large–none)	105ms	2×	4×	6×	16×
Extreme Outliers	489ms	106×	201×	388×	29×
Financial (500–10K)	106ms	105×	252×	293×	12×
Fraction (0.05–0.67)	221ms	104×	228×	391×	22×
Genomic (1K–50K)	1833ms	7×	9×	20×	95×
High Noise	435ms	133×	134×	375×	32×
Iterations (0–10)	204ms	115×	224×	386×	18×
Scale (1K–50K)	1841ms	264×	487×	581×	98×
Scientific (500–10K)	167ms	109×	205×	314×	15×
Scale Large* (100K–2M)	—	—	1×	1.4×	0.3×

*Scale Large benchmarks are relative to Serial (statsmodels cannot handle these sizes)

The numbers are the average across a range of scenarios for each category (e.g., Delta from none, to small, medium, and large).

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

Installation

Currently available for R, Python, Julia, and Rust:

R (from R-universe, recommended):

install.packages("rfastlowess", repos = "https://thisisamirv.r-universe.dev")

Python (from PyPI):

pip install fastlowess

Or from conda-forge:

conda install -c conda-forge fastlowess

Rust (lowess, no_std compatible):

[dependencies]
lowess = "0.99"

Rust (fastLowess, parallel + GPU):

[dependencies]
fastLowess = { version = "0.99", features = ["cpu"] }

Julia (from Julia General Registry):

using Pkg
Pkg.add("fastLowess")

Node.js (from npm):

npm install fastlowess

WebAssembly (from npm):

npm install fastlowess-wasm

Or via CDN:

<script type="module">
  import init, { smooth } from 'https://unpkg.com/fastlowess-wasm@latest';
  await init();
</script>

C++ (build from source):

make cpp
# Links against libfastlowess_cpp.so

Quick Example

library(rfastlowess)

x <- c(1, 2, 3, 4, 5)
y <- c(2.0, 4.1, 5.9, 8.2, 9.8)

result <- fastlowess(x, y, fraction = 0.5, iterations = 3)
print(result$y)

Python:

import fastlowess as fl
import numpy as np

x = np.array([1.0, 2.0, 3.0, 4.0, 5.0])
y = np.array([2.0, 4.1, 5.9, 8.2, 9.8])

result = fl.smooth(x, y, fraction=0.5, iterations=3)
print(result["y"])

Rust:

use lowess::prelude::*;

let x = vec![1.0, 2.0, 3.0, 4.0, 5.0];
let y = vec![2.0, 4.1, 5.9, 8.2, 9.8];

let model = Lowess::new()
    .fraction(0.5)
    .iterations(3)
    .adapter(Batch)
    .build()?;

let result = model.fit(&x, &y)?;
println!("{}", result);

Julia:

using fastlowess

x = [1.0, 2.0, 3.0, 4.0, 5.0]
y = [2.0, 4.1, 5.9, 8.2, 9.8]

result = fit(Lowess(fraction=0.5, iterations=3), x, y)
println(result.y)

Node.js:

const { Lowess } = require('fastlowess');

const x = [1.0, 2.0, 3.0, 4.0, 5.0];
const y = [2.0, 4.1, 5.9, 8.2, 9.8];

const model = new Lowess({ fraction: 0.5, iterations: 3 });
const result = model.fit(x, y);
console.log(result.y);

WebAssembly:

import init, { smooth } from 'fastlowess-wasm';

await init();

const x = new Float64Array([1.0, 2.0, 3.0, 4.0, 5.0]);
const y = new Float64Array([2.0, 4.1, 5.9, 8.2, 9.8]);

const result = smooth(x, y, { fraction: 0.5, iterations: 3 });
console.log(result.y);

C++:

#include <fastlowess.hpp>

std::vector<double> x = {1.0, 2.0, 3.0, 4.0, 5.0};
std::vector<double> y = {2.0, 4.1, 5.9, 8.2, 9.8};

fastlowess::LowessOptions options;
options.fraction = 0.5;
options.iterations = 3;

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

for (double val : result.y_vector()) std::cout << val << " ";

API Reference

fastlowess(
    x, y,
    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
)

Python:

fastlowess.smooth(
    x, y,
    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
)

Rust:

Lowess::new()
    .fraction(0.5)              // Smoothing span (0, 1]
    .iterations(3)              // Robustness iterations
    .delta(0.01)                // Interpolation threshold
    .weight_function(Tricube)   // Kernel selection
    .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)             // or Streaming, Online
    .parallel(true)             // fastLowess only
    .backend(CPU)               // fastLowess only: CPU or GPU
    .build()?;

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
)

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)

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
})

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$x, result$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:

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:

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:

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

Node.js:

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:

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++:

result.y_vector()              // std::vector<double>
result.confidence_lower()      // std::vector<double>
result.confidence_upper()      // std::vector<double>
result.prediction_lower()      // std::vector<double>
result.prediction_upper()      // std::vector<double>
result.residuals()             // std::vector<double>
result.robustness_weights()    // std::vector<double>
result.diagnostics()           // Diagnostics struct
result.iterations_used()       // size_t
result.fraction_used()         // double

Contributing

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

License

Licensed under either of:

Apache License, Version 2.0 (LICENSE-APACHE or https://www.apache.org/licenses/LICENSE-2.0)
MIT license (LICENSE-MIT or https://opensource.org/licenses/MIT)

at your option.

References

Cleveland, W.S. (1979). "Robust Locally Weighted Regression and Smoothing Scatterplots". JASA.
Cleveland, W.S. (1981). "LOWESS: A Program for Smoothing Scatterplots". The American Statistician.

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}
}

fastLowess 0.99.9

LOWESS Project

LOESS vs. LOWESS

Documentation

📚 View the full documentation

Why this package?

Speed

Robustness

Features

Validation

Installation

Quick Example

API Reference

Result Structure

Contributing

License

References

Citation