The following expression is known as the weighted average loss: [mathcal{L}=frac{1}{N} sum_{n=1}^{N} alpha_{n}left(t_{n}-mathbf{w}^{top} mathbf{x}_{n} ight)^{2}] where the influence of each data point is controlled by

The following expression is known as the weighted average loss:

\[\mathcal{L}=\frac{1}{N} \sum_{n=1}^{N} \alpha_{n}\left(t_{n}-\mathbf{w}^{\top} \mathbf{x}_{n}\right)^{2}\]

where the influence of each data point is controlled by its associated \(\alpha\) parameter. Assuming that each \(\alpha_{n}\) is fixed, derive the optimal least squares parameter value \(\widehat{\mathbf{w}}\).