Practice question · Multiple choice
Least squares minimises squared error, which makes it sensitive to outliers. Why is that sensitivity accepted so widely?
Hints
- Ask which objective has a derivative you can set to zero and solve directly.
- Where is |x| non-differentiable, and what does that do to an optimiser?
Show the answer
B. Because squaring makes the objective smooth, convex and solvable directly
Why
Squaring buys a differentiable convex objective with an exact solution via the normal equations; absolute error has a corner at zero and needs iteration. The outlier sensitivity is the price, which is why robust regression exists and is used where outliers are expected rather than exceptional.
Practise Complex Numbers
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