Skip to content
fastlowess-wasm

Concepts

Understanding how LOWESS works and when to use it.

What is LOWESS?

Section titled “What is LOWESS?”

LOWESS (Locally Weighted Scatterplot Smoothing) is a nonparametric regression method that fits smooth curves through scatter plots without assuming a global functional form.

Unlike parametric methods (linear regression, polynomial fitting), LOWESS adapts locally to the data structure, making it ideal for:

  • Exploratory data analysis — Discover patterns without assumptions
  • Trend estimation — Extract signals from noisy time series
  • Baseline correction — Remove systematic effects in spectroscopy
  • Genomic smoothing — Smooth methylation, ChIP-seq, or expression data

How It Works

Section titled “How It Works”
![LOWESS Smoothing Concept](../assets/diagrams/lowess_concept.svg){ width="800" }
LOWESS fits local weighted regressions at each point, using a focused local window around each evaluation point

For each point in your data, LOWESS:

  1. Selects neighbors — Choose the nearest points (controlled by fraction)
  2. Assigns weights — Closer points get higher weights (using a kernel function)
  3. Fits locally — Perform weighted least squares regression
  4. Extracts value — Use the fitted value as the smoothed estimate
  5. Iterates (optional) — Reweight points based on residuals to reduce outlier influence

The Fraction Parameter

Section titled “The Fraction Parameter”

The fraction (also called bandwidth or span) is the most important parameter. It controls what proportion of data is used for each local fit.

![Fraction Effect](../assets/diagrams/fraction_comparison.svg){ width="1000" }
Small fraction vs large fraction — bandwidth controls how closely the fit follows local structure
Fraction Effect When to Use
0.1–0.3 Fine detail, follows data closely Rapidly changing signals
0.3–0.5 Balanced smoothing Most applications
0.5–0.7 Heavy smoothing Noisy data, trend extraction
0.7–1.0 Very smooth Strong noise, global trends

Robustness Iterations

Section titled “Robustness Iterations”

Standard LOWESS is sensitive to outliers. Robustness iterations downweight points with large residuals:

![Robustness Effect](../assets/diagrams/robust_iter_comparison.svg){ width="800" }
Non-robust LOWESS (iterations=0) vs robust LOWESS — outlier influence is suppressed through iterative reweighting
Iterations Effect When to Use
0 No robustness (fastest) Clean data, speed-critical
1–3 Moderate robustness Most applications
4–6 Strong robustness Data with outliers
7+ Very strong Heavy contamination

Confidence vs Prediction Intervals

Section titled “Confidence vs Prediction Intervals”
![Intervals](../assets/diagrams/intervals_comparison.svg){ width="800" }
Confidence intervals (narrow, mean curve uncertainty) vs Prediction intervals (wide, new-point uncertainty)
Interval Type What It Represents Width
Confidence Uncertainty in the mean curve Narrow
Prediction Uncertainty for new observations Wide
  • Use confidence intervals to show where the true trend likely lies
  • Use prediction intervals to show where new data points might fall

Execution Modes

Section titled “Execution Modes”

Choose the right mode based on your use case:

Mode Use Case Memory Features
Batch Complete datasets Entire dataset All features
Streaming Large files (>100K points) One chunk Residuals, robustness
Online Real-time data Fixed window Incremental updates

Quick Decision Guide

Section titled “Quick Decision Guide”
Situation Mode
Data fits in memory; needs intervals or CV Batch
Data too large for memory or arrives in chunks Streaming
Data arrives point-by-point in real time Online

Key Advantages

Section titled “Key Advantages”
Feature LOWESS Polynomial Regression Moving Average
No parametric assumptions ✓ ✗ ✓
Adapts to local structure ✓ ✗ Partial
Robust to outliers ✓ ✗ ✗
Uncertainty estimates ✓ ✓ ✗
Handles irregular sampling ✓ ✓ ✗

Next Steps

Section titled “Next Steps”