SLCP

sbisandbox.benchmarks.slcp.SLCPBenchmark

Bases: UniformPriorMixin, Benchmark

SLCP benchmark task.

The parameters \(\boldsymbol{\theta} \in \mathbb{R}^5\) are sampled independently from a uniform distribution,

\[ \theta_i \sim \mathcal{U}([-3, 3]),\]

for \(i \in \{1, \ldots, 5\}\).

The data \(\boldsymbol{x} \in \mathbb{R}^8\) are generated as follows:

\[ (\boldsymbol{x}_1, \boldsymbol{x}_2, \boldsymbol{x}_3, \boldsymbol{x}_4) \sim \mathcal{N}(\boldsymbol{\mu}, \boldsymbol{\Sigma}),\]

where

\[ \boldsymbol{\mu} = \begin{pmatrix} \theta_1 \\ \theta_2 \end{pmatrix}\]

and

\[ \boldsymbol{\Sigma} = \begin{pmatrix} \theta_3^4 & \theta_3^2 \theta_4^2 \tanh \theta_5 \\ \theta_3^2 \theta_4^2 \tanh \theta_5 & \theta_4^4 \\ \end{pmatrix}. \]