Loss Function - Quadratic Loss Function

Quadratic Loss Function

The use of a quadratic loss function is common, for example when using least squares techniques or Taguchi methods. It is often more mathematically tractable than other loss functions because of the properties of variances, as well as being symmetric: an error above the target causes the same loss as the same magnitude of error below the target. If the target is t, then a quadratic loss function is

for some constant C; the value of the constant makes no difference to a decision, and can be ignored by setting it equal to 1.

Many common statistics, including t-tests, regression models, design of experiments, and much else, use least squares methods applied using linear regression theory, which is based on the quadratric loss function.

The quadratic loss function is also used in linear-quadratic optimal control problems.

Read more about this topic:  Loss Function

Famous quotes containing the words loss and/or function:

    Unfortunately, I am involved in a freedom ride protesting the loss of the minority rights belonging to the few remaining earthbound stars. All we demanded was our right to twinkle.
    Marilyn Monroe (1926–1962)

    Our father has an even more important function than modeling manhood for us. He is also the authority to let us relax the requirements of the masculine model: if our father accepts us, then that declares us masculine enough to join the company of men. We, in effect, have our diploma in masculinity and can go on to develop other skills.
    Frank Pittman (20th century)