Part 14 (5 points, non-coding task)
Prove that L \left( \mathbf{\beta} \right) is a (weakly) concave function.
- Reasoning is required.
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Because \sigma \left( \cdot \right) \in \left[ 0 , 1 \right] and \mathbf{x}^{(n)} \mathbf{x}^{(n)^\top} is a positive semidefinite matrix, we have that \nabla_{\mathbf{\beta}}^2 \ L \left( \mathbf{\beta} \right) is a positive semidefinite matrix.
Therefore, L \left( \mathbf{\beta} \right) is (weakly) concave.
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