Interactive 3D LASSO geometry: prediction ellipsoids centred on the OLS solution expand until they touch the L1 constraint ball, determining coefficient selection
SOLUTION INFO
Tangent ellipsoid
Inner ellipsoids
L1 constraint ball
OLS β*
LASSO β̂
β₁* =
1.45
β₂* =
1.42
β₃* =
0.12
λ (L1 ball radius) =
1.00
ρ (corr β₁–β₂) =
0.00
Near tipping point
3 predictors (stable)
Single predictor
OLS inside ball