fastLowess

High-performance parallel LOWESS (Locally Weighted Scatterplot Smoothing) for Rust — A high-level wrapper around the lowess crate that adds rayon-based parallelism and seamless ndarray integration.

[!IMPORTANT] For a minimal, single-threaded, and no_std version, use base lowess.

Features

• Parallel by Default: Multi-core regression fits via rayon, achieving multiple orders of magnitude speedups on large datasets.
• ndarray Integration: Native support for Array1<T> and ArrayView1<T>.
• Robust Statistics: MAD-based scale estimation and IRLS with Bisquare, Huber, or Talwar weighting.
• Uncertainty Quantification: Point-wise standard errors, confidence intervals, and prediction intervals.
• Optimized Performance: Delta optimization for skipping dense regions and streaming/online modes.
• Parameter Selection: Built-in cross-validation for automatic smoothing fraction selection.

Robustness Advantages

Built on the same core as lowess, this implementation is more robust than statsmodels due to:

MAD-Based Scale Estimation

We use Median Absolute Deviation (MAD) for scale estimation, which is breakdown-point-optimal:

s = median(|r_i - median(r)|)

Boundary Padding

We apply boundary policies (Extend, Reflect, Zero) at dataset edges to maintain symmetric local neighborhoods, preventing the edge bias common in other implementations.

Gaussian Consistency Factor

For precision in intervals, residual scale is computed using:

sigma = 1.4826 * MAD

Performance Advantages

Benchmarked against Python's statsmodels. Achieves 50-3800× faster performance across different tested scenarios. The parallel implementation ensures that even at extreme scales (100k points), processing remains sub-20ms.

Summary

Top 10 Performance Wins

Check Benchmarks for detailed comparisons.

Installation

Add this to your Cargo.toml:

[dependencies]
fastLowess = "0.2"

Quick Start

use fastLowess::prelude::*;
use ndarray::Array1;

fn main() -> Result<(), LowessError> {
    // Data as ndarray Array1
    let x = Array1::linspace(0.0, 10.0, 100);
    let y = x.mapv(|v| v.sin() + 0.1 * v);

    // Build the model (parallel by default)
    let result = Lowess::new()
        .fraction(0.5)
        .adapter(Batch)
        .parallel(true)
        .build()?
        .fit(&x, &y)?;

    println!("Smoothed values: {:?}", result.y);
    Ok(())
}

Builder Methods

use fastLowess::prelude::*;

Lowess::new()
    // Smoothing span (0, 1]
    .fraction(0.5)

    // Robustness iterations
    .iterations(3)

    // Interpolation threshold
    .delta(0.01)

    // Kernel selection
    .weight_function(WeightFunction::Tricube)

    // Robustness method
    .robustness_method(RobustnessMethod::Bisquare)

    // Zero-weight fallback behavior
    .zero_weight_fallback(ZeroWeightFallback::UseLocalMean)

    // Boundary handling (for edge effects)
    .boundary_policy(BoundaryPolicy::Extend)

    // Confidence intervals
    .confidence_intervals(0.95)

    // Prediction intervals
    .prediction_intervals(0.95)

    // Diagnostics
    .return_diagnostics()
    .return_residuals()
    .return_robustness_weights()

    // Cross-validation (for parameter selection)
    .cross_validate(&[0.3, 0.5, 0.7], CrossValidationStrategy::KFold, Some(5))

    // Convergence
    .auto_converge(1e-4)
    .max_iterations(20)

    // Execution mode
    .adapter(Batch)

    // Parallelism
    .parallel(true)

    // Build the model
    .build()?;

Result Structure

pub struct LowessResult<T> {
    /// Sorted x values (independent variable)
    pub x: Vec<T>,

    /// Smoothed y values (dependent variable)
    pub y: Vec<T>,

    /// Point-wise standard errors of the fit
    pub standard_errors: Option<Vec<T>>,

    /// Confidence interval bounds (if computed)
    pub confidence_lower: Option<Vec<T>>,
    pub confidence_upper: Option<Vec<T>>,

    /// Prediction interval bounds (if computed)
    pub prediction_lower: Option<Vec<T>>,
    pub prediction_upper: Option<Vec<T>>,

    /// Residuals (y - fit)
    pub residuals: Option<Vec<T>>,

    /// Final robustness weights from outlier downweighting
    pub robustness_weights: Option<Vec<T>>,

    /// Detailed fit diagnostics (RMSE, R^2, Effective DF, etc.)
    pub diagnostics: Option<Diagnostics<T>>,

    /// Number of robustness iterations actually performed
    pub iterations_used: Option<usize>,

    /// Smoothing fraction used (optimal if selected via CV)
    pub fraction_used: T,

    /// RMSE scores for each fraction tested during CV
    pub cv_scores: Option<Vec<T>>,
}

[!TIP] Using with ndarray: While the result struct uses Vec<T> for maximum compatibility, you can effortlessly convert any field to an Array1 using Array1::from_vec(result.y).

Streaming Processing

For datasets that don't fit in memory:

use fastLowess::prelude::*;

let mut processor = Lowess::new()
    .fraction(0.3)
    .iterations(2)
    .adapter(Streaming)
    .parallel(true)   // Enable parallel chunk processing
    .chunk_size(1000)
    .overlap(100)
    .build()?;

// Process data in chunks
for chunk in data_chunks {
    let result = processor.process_chunk(&chunk.x, &chunk.y)?;
}

// Finalize processing
let final_result = processor.finalize()?;

Online Processing

For real-time data streams:

use fastLowess::prelude::*;

let mut processor = Lowess::new()
    .fraction(0.2)
    .iterations(1)
    .adapter(Online)
    .parallel(false)  // Sequential for lowest per-point latency
    .window_capacity(100)
    .build()?;

// Process points as they arrive
for (x, y) in data_stream {
    if let Some(output) = processor.add_point(x, y)? {
        println!("Smoothed: {}", output.smoothed);
    }
}

Parameter Selection Guide

Fraction (Smoothing Span)

• 0.1-0.3: Local, captures rapid changes (wiggly)
• 0.4-0.6: Balanced, general-purpose
• 0.7-1.0: Global, smooth trends only
• Default: 0.67 (2/3, Cleveland's choice)
• Use CV when uncertain

Robustness Iterations

• 0: Clean data, speed critical
• 1-2: Light contamination
• 3: Default, good balance (recommended)
• 4-5: Heavy outliers
• >5: Diminishing returns

Kernel Function

• Tricube (default): Best all-around, smooth, efficient
• Epanechnikov: Theoretically optimal MSE
• Gaussian: Very smooth, no compact support
• Uniform: Fastest, least smooth (moving average)

Delta Optimization

• None: Small datasets (n < 1000)
• 0.01 × range(x): Good starting point for dense data
• Manual tuning: Adjust based on data density

Examples

Check the examples directory for advanced usage:

cargo run --example batch_smoothing
cargo run --example online_smoothing
cargo run --example streaming_smoothing

MSRV

Rust 1.85.0 or later (2024 Edition).

Validation

Validated against:

• Python (statsmodels): Passed on 44 distinct test scenarios.
• Original Paper: Reproduces Cleveland (1979) results.

Check Validation for more information. Small variations in results are expected due to differences in scale estimation and padding.

Related Work

• lowess (Rust core)
• fastLowess (Python wrapper)
• fastLowess (R wrapper)

Contributing

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

License

Dual-licensed under AGPL-3.0 (Open Source) or Commercial License. Contact <thisisamirv@gmail.com> for commercial inquiries.

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.