Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 223 / 2 / a

Table of contents
- Solution a

Solution

Changing at most

n - h

observations leaves at least

h

original observations unchanged. At

θ = 0

, each unchanged observation has residual

y_{i}

and loss at most

ρ (M_{y})

. The sum of the

h

smallest losses cannot exceed the sum over any chosen

h

observations, so

L_{Z^{'}} (0) \leq h ρ (M_{y}) .

The

L^{1}

regularization term vanishes at zero.

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