Sampling Playground
Compare sampling algorithms on uniform sets or continuous targets $\pi(x) \propto e^{-f(x)}$.
Initialize
Count $N$
Spread $\sigma_0$
Center $\mu_x$
Center $\mu_y$
Spawn $X_0 \sim \mathcal{N}(\mu, \sigma_0^2 I)$
For Uniform(X), points are rejected if they fall outside the set.
Run Dynamics
Step size $\sigma$:
15
Proposal scale (pixels/units). For ULA/MALA, $\eta \propto \sigma^2$.
Speed:
6
steps/sec
Step (1)
Run
Step-by-step (Educational)
Cycle: Forward / Backward / Update
Ready to start.
Visuals
3D surface view
Show $-\nabla f(x)$ vector field
Show $\nabla^2 f(x)$ Hessian ellipses
Highlight rejected proposals (Red)
Auto-scale plot Y-axis
Show grid overlay
Target and algorithms
Target
Uniform on a drawn set X
Gaussian (standard)
Mixture of two Gaussians
Banana-shaped
Ring / donut
Funnel
Draw a region. Click 'Finish' to commit.
Finish shape
Clear drawing
Algorithms:
Prox (RGO / In-and-Out)
Math
MRW (Metropolis random walk)
Math
MALA (Metropolis-adjusted Langevin)
Math
ULA (unadjusted Langevin)
Math
Time $t$:
0
IDLE