Table of Contents

Enum WeightFunction

Namespace
AiDotNet.Enums
Assembly
AiDotNet.dll

Defines different weight functions used in robust statistical methods and machine learning algorithms.

public enum WeightFunction

Fields

Andrews = 2

The Andrews weight function, which uses a sine wave to handle outliers.

For Beginners: The Andrews function uses a wave-like pattern (specifically, a sine wave) to determine how much weight to give to different data points.

How it works:

  • For data points close to the expected pattern, it gives them nearly full weight
  • As data points get farther from the pattern, their weight oscillates (goes up and down) but generally decreases
  • For very extreme outliers, it gives them zero weight

Think of Andrews as a "nuanced" approach - it doesn't just gradually reduce weight like Huber, or cut off outliers like Bisquare. Instead, it has a more complex pattern of weighting that can sometimes preserve more information from the data.

When to use Andrews:

  • In specialized statistical applications where you need the specific mathematical properties of the sine function
  • When dealing with periodic data or data with wave-like patterns
  • When recommended by a statistical expert for your specific application

The Andrews function is less commonly used than Huber or Bisquare but has useful properties in certain specialized applications.

Bisquare = 1

The Bisquare (also known as Tukey's biweight) weight function, which completely downweights extreme outliers.

For Beginners: The Bisquare function is more aggressive in handling outliers than Huber.

How it works:

  • For data points close to the expected pattern, it treats them normally (with full weight)
  • As data points get farther from the expected pattern, it reduces their weight more quickly than Huber
  • Beyond a certain threshold, it gives zero weight to extreme outliers (completely ignores them)

Think of Bisquare as a "strict" approach - it's willing to completely ignore data points that seem too unusual. It's like saying "If your opinion is too extreme, I'm not going to consider it at all."

When to use Bisquare:

  • When you know your data contains significant outliers that should have no influence
  • When you want to ensure extreme values don't affect your model
  • In situations where you need high robustness against outliers

The Bisquare function has a tuning parameter that determines the threshold beyond which outliers are completely ignored.

Huber = 0

The Huber weight function, which provides a balance between efficiency and robustness.

For Beginners: The Huber function is like a "middle ground" approach to handling outliers.

How it works:

  • For data points that are close to the expected pattern, it treats them normally (with full weight)
  • For data points that are far from the expected pattern, it reduces their importance (weight) gradually as they get more extreme

Think of Huber as a "diplomatic" approach - it doesn't completely ignore outliers, but it doesn't let them dominate either. It's like saying "I'll listen to unusual opinions, but I won't let them completely change my mind."

When to use Huber:

  • When you expect some outliers in your data but don't want to be too aggressive in removing their influence
  • When you want a good balance between accuracy and robustness
  • As a safe default choice when you're not sure which weight function to use

The Huber function has a tuning parameter that controls how quickly it starts to downweight outliers.

Remarks

For Beginners: Weight functions are special mathematical formulas that help AI models handle unusual or extreme data points (outliers).

In regular statistics, outliers can significantly throw off your results. For example, if you're calculating the average income in a neighborhood and one billionaire lives there, the average would be misleadingly high.

Weight functions solve this problem by automatically giving less importance (lower weight) to data points that seem unusual or extreme. This makes your AI models more robust and reliable when dealing with real-world data that might contain errors or unusual values.

Each weight function has different characteristics that make it suitable for different situations:

  • Some are gentler with outliers (like Huber)
  • Others are more aggressive in downweighting extreme values (like Bisquare)

Choosing the right weight function depends on how much you expect your data to contain outliers and how you want to handle them.

Edit this page