Least Absolute Deviation Regression

TL;DR

A regression method that fits predictions by minimizing the absolute deviations (L1) between observed and predicted values.
Less sensitive to outliers than least squares (L2) regression.
Commonly applied when outliers may distort least squares estimates, for example in housing-price or stock-price prediction tasks.

Definition

Least absolute deviation regression, also known as L1 regression, is a type of regression analysis that minimizes the absolute difference between the observed values and the predicted values.

Explanation

This approach finds model parameters that reduce the sum of absolute errors between predictions and observations. Because it optimizes absolute deviations rather than squared deviations, L1 regression is less sensitive to the influence of outliers than least squares regression. The method can be used to predict target values from input features while prioritizing robustness to atypical observations.

Examples

Housing prices

A real estate agent has a dataset of 100 houses with corresponding prices and square footage. Using L1 regression, the agent can predict the price of a new house based on its square footage while minimizing the absolute deviation between predicted and observed prices. This can improve price predictions when some houses in the dataset are significantly over- or underpriced compared to the others.

Stock prices

An investor has a dataset of daily stock prices for a particular company over a period of time. Using L1 regression, the investor can predict future stock prices based on historical data while minimizing the absolute deviation between predicted and observed prices. This can help make decisions even if there are outliers in the data, such as a sudden market crash or spike.

Use cases

Situations where outliers are present and a regression method less sensitive to those outliers is desired.

L1 regression (alternate name)
Least squares regression