3 Reasons Taguchi chose a squared Loss Function

In a previous post, we discussed the 𝗧𝗮𝗴𝘂𝗰𝗵𝗶 𝗟𝗼𝘀𝘀 𝗙𝘂𝗻𝗰𝘁𝗶𝗼𝗻:

Loss = k (x – 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:

▶️ A squared term is the first symmetric term in the 𝗧𝗮𝘆𝗹𝗼𝗿 𝗦𝗲𝗿𝗶𝗲𝘀 {remember those?} of functions that locally converge using a power series

💭 i.e., even if the ‘true’ loss function 𝘄𝗮𝘀 𝗻𝗼𝘁 squared, the squared function would still be an approximation of the ‘true’ function]

▶️ The statistical variance:

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

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

▶️ Since cost is additive (total cost = cost1 + cost2 +…), use of a variance-like (squared) function is appropriate since variance is also additive (total variance = variance1 + variance2+…) for uncorrelated random variables

It's important to know the 𝗪𝗛𝗬 of things.

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