Gaussian linear

sbisandbox.benchmarks.gaussian_linear.GaussianLinearBenchmark

Bases: Benchmark

Gaussian linear benchmark task.

The parameters \(\boldsymbol{\theta} \in \mathbb{R}^n\) are sampled from

\[ \boldsymbol{\theta} \sim \mathcal{N}(\mu=\boldsymbol{0}_n, \Sigma_1=\sigma \boldsymbol{I}_n),\]

where \(\sigma > 0\), \(\boldsymbol{I}_n\) is the n x n identity matrix and \(\boldsymbol{0}_n = \begin{pmatrix} 0 & \ldots & 0 \end{pmatrix}^T \in \mathbb{R}^n\).

The data \(\boldsymbol{x} \in \mathbb{R}^n\) are generated as follows:

\[ \boldsymbol{x} \sim \mathcal{N}(\mu=\boldsymbol{\theta}, \Sigma_2=\sigma \boldsymbol{I}_n) \]