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3 Reasons Taguchi chose a squared Loss Function

In a previous post, we discussed the ๐—ง๐—ฎ๐—ด๐˜‚๐—ฐ๐—ต๐—ถ ๐—Ÿ๐—ผ๐˜€๐˜€ ๐—™๐˜‚๐—ป๐—ฐ๐˜๐—ถ๐—ผ๐—ป:

Loss = k (x โ€“ Target)^2

and how it is used to estimate losses; especially those associated with overly tight tolerances.

Here are 3 of the reasons Taguchi chose a square loss function:

โ–ถ๏ธ A squared term is the first symmetric term in the ๐—ง๐—ฎ๐˜†๐—น๐—ผ๐—ฟ ๐—ฆ๐—ฒ๐—ฟ๐—ถ๐—ฒ๐˜€ {remember those?} of functions that locally converge using a power series

๐Ÿ’ญ i.e., even if the โ€˜trueโ€™ loss function ๐˜„๐—ฎ๐˜€ ๐—ป๐—ผ๐˜ squared, the squared function would still be an approximation of the โ€˜trueโ€™ function]

โ–ถ๏ธ The statistical variance:

Variance = E [(x - mu)^2 }

(which is also a squared function), is a measure of risk

โ–ถ๏ธ Since cost is additive (total cost = cost1 + cost2 +โ€ฆ), use of a variance-like (squared) function is appropriate since variance is also additive (total variance = variance1 + variance2+โ€ฆ) for uncorrelated random variables

It's important to know the ๐—ช๐—›๐—ฌ of things.

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