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A loss function quantifies the cost of an event, such as inaccurate estimation or performance variation. The Taguchi loss function is a well-known example, which shows that reducing performance variation can result in a disproportionately large reduction in losses. Loss functions can be used to estimate potential losses and make objective decisions.
A loss function is a way of expressing the effects of an event numerically. This formula and the resulting number represent the cost to those involved compared to other events that may have taken place, such as making a different decision: Using wood to make a door creates a loss as wood cannot be used to make a table. The loss function can also represent the effects of an inaccurate estimate. You can predict potential loss functions in advance and use this information to make an objective decision.
One of the best-known loss functions is a Taguchi loss function, named after its creator, Genichi Taguchi. A Taguchi loss function deals with the effects of a performance variation, such as a machine designed to produce a widget of a certain size that does not meet this specification. The function states that the loss this causes to the firm varies in proportion to the square of the proportion by which actual performance varies from actual output.
The Taguchi loss function is most commonly demonstrated in graphical form. In this way it becomes clear that a minor performance variation results in a relatively small loss. As the variation in performance increases, the loss increases at a much faster rate. This model is generally interpreted as demonstrating that, at any stage, achieving a reduction in performance variation should result in a disproportionately large reduction in losses. This in turn encourages continued attempts to perfect a manufacturing process.
A loss function can exist as a purely statistical tool. In this content attempts to measure the loss caused by inaccurate estimation. The function tries to establish the relationship between the degree of inaccuracy and the degree of loss.
Another use of loss functions is in estimating the potential losses caused by a change in a particular measurement. For example, using a loss function a mobile food stall owner could influence the effects of temperature changes on the sales of ice cream and hot soup. There are several ways to make decisions using these predictions. One would be to choose the option that causes the least loss in their respective worst-case scenarios: the stall owner could unexpectedly wind up cold that would cause more damage to ice cream sales than unexpectedly hot would cause hot soup sales, and then decide what soup is the safest option. Alternatively, he could look at their respective loss functions and decide that ice cream sales are less likely to fluctuate overall and that this will give him greater security in buying stocks.
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