Machine Learning Techniques Quiz 2: 6 August 2023 (May 2023 term)

Consider a training dataset of $n$ points for a regression problem. Assume that the model is linear. Let $\mathbf{w}_1$ and $\mathbf{w}_2$ be the optimal weight vectors obtained from solving the following optimization problems.

$\mathbf{w}_1 = \underset{\mathbf{w}}{\arg\min} \ \sum_{i=1}^{n} (\mathbf{w}^T\mathbf{x}_i - y_i)^2$

$\mathbf{w}_2 = \underset{\mathbf{w}}{\arg\min} \ \sum_{i=1}^{n} (\mathbf{w}^T\mathbf{x}_i - y_i)^3$

Choose the most appropriate answer.