Least absolute deviations (LAD), also known as Least Absolute Errors (LAE), Least Absolute Value (LAV), or the L1 norm problem, is a mathematical optimization technique similar to the popular least squares technique that attempts to find a function which closely approximates a set of data. In the simple case of a set of (x,y) data, the approximation function is a simple "trend line" in two-dimensional Cartesian coordinates. The method minimizes the sum of absolute errors (SAE) (the sum of the absolute values of the vertical "residuals" between points generated by the function and corresponding points in the data). The least absolute deviations estimate also arises as the maximum likelihood estimate if the errors have a Laplace distribution.
Read more about Least Absolute Deviations: Formulation of The Problem, Contrasting Least Squares With Least Absolute Deviations, Other Properties, Variations, Extensions, Specializations, Solving Methods, See Also
Famous quotes containing the word absolute:
“The research on gender and morality shows that women and men looked at the world through very different moral frameworks. Men tend to think in terms of “justice” or absolute “right and wrong,” while women define morality through the filter of how relationships will be affected. Given these basic differences, why would men and women suddenly agree about disciplining children?”
—Ron Taffel (20th century)