In gbonte/gbcode: Code from the handbook "Statistical foundations of machine learning"

Shiny dashboard "Statistical foundations of machine learning"

Conditional probability

Left panel:

• Number of samples
• 3D theta: angle defining the azimuthal direction in the 3D visualization
• 3D phi: angle defining the colatitude in the 3D visualization

Bivariate gaussian distribution

The dashboard illustrates a bivariate gaussian distribution in a 3D diagram. The user may change the contour axis size and their angle.

The slider x allows to change the value $x$ in the conditional probability $p({\bf y}=y|x)$. The bottom right panel plots both the marginal distribution $p({\bf y}=y)$ (invariant to the value of $x$) and the conditional distribution $p({\bf y}=y|x)$.

Regression function

The dashboard illustrates a bivariate distribution where ${\bf y}=f(x)+{\bf w}$ where ${\bf w} \sim {\mathcal N} (0,\sigma^2)$.

The function $f$ changes by moving the slider "Functions".

Top right: 3D visualization of the joint density $p({\bf x}=x,{\bf y}=y)$ Bottom left: 2D visualization of samples and function $f$

Sliders:

• Functions: by changing its value the user may change the function $f$: for values $p \ge 0$,
  $f(x)=x^p$; for $p<0$, $f(x)$ is a sinusoidal function with different frequencies.
• Cond sdev: conditional variance $\sigma$ of the noise
• x: value used to visualize $p({\bf y}=y|x)$ in the bottom right plot

gbonte/gbcode documentation built on Feb. 27, 2024, 7:38 a.m.