LOESS Concepts

What is LOESS?

LOESS (Locally Estimated 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), LOESS 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

LOESS smoothing concept
LOESS smoothing concept

For each point in your data, LOESS:

  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

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

Effect of the fraction parameter
Effect of the fraction parameter
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

Tip: Start with fraction=0.67 (the default) and adjust based on visual inspection. Use cross-validation for automated selection.

Robustness Iterations

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

Effect of robustness iterations
Effect of robustness iterations
Iterations Effect When to Use
0 No robustness (fastest) Clean data, speed-critical
1–3 Moderate Most applications
4–6 Strong Data with clear outliers
7+ Very strong Heavy contamination

Confidence vs Prediction Intervals

Confidence and prediction intervals
Confidence and prediction intervals
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

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

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

Feature LOESS Polynomial Regression Moving Average
No parametric assumptions ✓ ✗ ✓
Adapts to local structure ✓ ✗ Partial
Robust to outliers ✓ ✗ ✗
Uncertainty estimates ✓ ✓ ✗
Handles irregular sampling ✓ ✓ ✗
Multivariate predictors ✓ ✓ ✗
Adjustable polynomial degree ✓ (0–4) ✓ ✗

Next Steps

  • vignette("quickstart", package = "rfastloess") — See it in action
  • ?Loess — All configuration options
  • vignette("degree", package = "rfastloess") — Constant, linear, quadratic fits
  • vignette("dimensions", package = "rfastloess") — 2D and n-D smoothing
  • vignette("boundary", package = "rfastloess") — Edge bias reduction strategies
  • vignette("robustness", package = "rfastloess") — Outlier downweighting methods
  • vignette("scaling", package = "rfastloess") — MAD, MAR, Mean scale estimation
  • vignette("merge", package = "rfastloess") — Chunk reconciliation in Streaming mode
sessionInfo()
#> R version 4.6.1 (2026-06-24)
#> Platform: x86_64-pc-linux-gnu
#> Running under: Ubuntu 26.04.1 LTS
#> 
#> Matrix products: default
#> BLAS:   /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3 
#> LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.32.so;  LAPACK version 3.12.0
#> 
#> locale:
#>  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
#>  [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8    
#>  [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
#>  [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
#>  [9] LC_ADDRESS=C               LC_TELEPHONE=C            
#> [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       
#> 
#> time zone: Etc/UTC
#> tzcode source: system (glibc)
#> 
#> attached base packages:
#> [1] stats     graphics  grDevices utils     datasets  methods   base     
#> 
#> other attached packages:
#> [1] rfastloess_3.0.0 rmarkdown_2.32  
#> 
#> loaded via a namespace (and not attached):
#>  [1] digest_0.6.39    R6_2.6.1         fastmap_1.2.0    xfun_0.61       
#>  [5] maketools_1.3.2  cachem_1.1.0     knitr_1.52       htmltools_0.5.9 
#>  [9] buildtools_1.0.0 lifecycle_1.0.5  cli_3.6.6        sass_0.4.10     
#> [13] jquerylib_0.1.4  compiler_4.6.1   sys_3.4.3        tools_4.6.1     
#> [17] evaluate_1.0.5   bslib_0.12.0     yaml_2.3.12      otel_0.2.0      
#> [21] jsonlite_2.0.0   rlang_1.3.0