Gaussian mixture

sbisandbox.benchmarks.gaussian_mixture.GaussianMixtureBenchmark

Bases: UniformPriorMixin, Benchmark

Gaussian mixture benchmark task.

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

\[ \theta_i \sim \mathcal{U}([-1, 1]),\]

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

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

\[ \boldsymbol{x} \sim 0.5 \mathcal{N}(\mu=\boldsymbol{\theta}, \sigma_1 \boldsymbol{I}_n) + 0.5 \mathcal{N}(\mu=\boldsymbol{\theta}, \sigma_2 \boldsymbol{I}_n),\]

where \(\sigma_1 \gg \sigma_2 > 0\).