The example with spiral

[pawel-czyz]

We apply the "spiral" diffeomorphism to the $X$ variable and observe how the $I(X; Y)$ changes.

[pawel-czyz]

python scripts/ksg_spiral.py
Settings:
Namespace(dim_x=3, dim_y=2, rho=0.8, n_points=5000, seed=42)
True MI: 0.511
KSG(X; Y) without distortion: 0.486
-------------------
speed KSG(spiral(X); Y)
0.00 0.486
0.02 0.487
0.10 0.478
0.50 0.358
1.00 0.248
10.00 0.071

python scripts/ksg_spiral.py --rho 0.5 --dim-x 2
Settings:
Namespace(dim_x=2, dim_y=2, rho=0.5, n_points=5000, seed=42)
True MI: 0.144
KSG(X; Y) without distortion: 0.135
-------------------
speed KSG(spiral(X); Y)
0.00 0.135
0.02 0.136
0.10 0.136
0.50 0.111
1.00 0.079
10.00 0.000

python scripts/ksg_spiral.py --rho 0.5 --dim-x 2 --dim-y 1
Settings:
Namespace(dim_x=2, dim_y=1, rho=0.5, n_points=5000, seed=42)
True MI: 0.144
KSG(X; Y) without distortion: 0.140
-------------------
speed KSG(spiral(X); Y)
0.00 0.140
0.02 0.139
0.10 0.135
0.50 0.124
1.00 0.098
10.00 0.020