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

R:

library(rfastlowess)

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

model <- Lowess(fraction = 0.5, iterations = 3)
result <- model$fit(x, y)
print(result$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

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)

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

R:

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}
}