We consider the classical problem of heteroscedastic linear regression, where
we are given $n$ samples $(\mathbf{x}_i, y_i) \in \mathbb{R}^d \times
\mathbb{R}$ obtained from $y_i = \langle \mathbf{w}^{*}, \mathbf{x}_i \rangle +
\epsilon_i \cdot \langle \mathbf{f}^{*}, \mathbf{x}_i \ran