vignettes/example-docs/Example Experiment/docs/dgps/Linear DGP.md

In Yu-Group/simChef: Intensive Computational Experiments Made Easy

We simulate the (test and training) covariate/design matrix $\mathbf{X} \in \mathbb{R}^{n \times p}$ from a standard normal distribution and the response vector $\mathbf{y} \in \mathbb{R}^n$ from a linear model. Specifically,

\begin{align} \mathbf{y} = \mathbf{X} \boldsymbol{\beta} + \boldsymbol{\epsilon},\ \end{align}

where \begin{align} & \mathbf{X}_{ij} \stackrel{iid}{\sim} N\left(0, 1\right) \text{ for all } i = 1, \ldots, n \text{ and } j = 1, \ldots, p, \ & \boldsymbol{\epsilon}_i \stackrel{iid}{\sim} N(0, \sigma^2) \text{ for all } i = 1, \ldots, n. \end{align}

Default Parameters in DGP

• Number of training samples: $n_{\text{train}} = 200$
• Number of test samples: $n_{\text{test}} = 200$
• Number of features: $p = 2$
• Amount of noise: $\sigma = 1$
• Coefficients: $\boldsymbol{\beta} = (1, 0)^\top$

[In practice, documentation of DGPs should answer the questions “what” and “why”. That is, “what” is the DGP, and “why” are we using/studying it? As this simulation experiment is a contrived example, we omit the “why” here.]

Yu-Group/simChef documentation built on March 25, 2024, 3:22 a.m.