Data generator

Stats

• stats

  • binning

    • sturges

      Sturges’ formula \(k = \lceil \log_2 n \rceil + 1\)

    • doane

      Doane’s formula \(k = 1+\log_2 (n) + \log_2 (1+\frac{|g_1|}{\sigma_{g_1}})\)

      where $g_1$ is the estimated 3rd-momentum skewness and

      \[\sigma_{g_1} = \sqrt{\frac{6(n-2)}{(n+1)(n+3)}}\]

    • scott

      Scott’s normal reference rule

      bin width $h$ is given by

      \[h = \frac{3.49\hat{\sigma}}{\sqrt[3]{n}}\]

    • freedman_diaconis

      Freedman-Diaconis’ choice

      bin width $h$ is given by \(h = 2\frac{IQR}{\sqrt[3]{n}}\) which is based on the interquartile range IQR.

  • frechet_inception_distance

    • Background

      \[d_F(\mu, \nu) := \left(\inf_{\gamma \in \Gamma (\mu, \nu)} \int _{\mathbb{R}\times \mathbb{R}} \Vert x-y\Vert^2 d\gamma(x,y)\right)^{1/2}\]

      Where $\Gamma(\mu, \nu)$ is teh setof all measures on $\mathbb{R}\times \mathbb{R}$ with marginals $\mu$ and $\nu$. In other words, it is the 2-Wasserstein distnce on $\mathbb{R}^n$

    • How to use

        import numpy as np
        from artemis7.stats.frechet_inception_distanec import FID
      
        x = np.random.normal(size = 1000)
        y = np.random.normal(size = 1000)
        fid = FID(x, y)
      

  • multivariate_sampling

  • piecewise_rejection_sampling

  • population_stability_index