Part 3 — Iterative Gaussianization (RBIG)

The classical, non-parametric Gaussianization algorithm. Part 1 built the marginal transforms and Part 2 the rotations; Rotation-Based Iterative Gaussianization Laparra et al. (2011) simply alternates them — marginal → rotate → marginal → rotate … — until any distribution flows to $\mathcal{N}(0,I)$. Each block is fit once, greedily, and never revisited (the parametric, end-to-end-trained version is Part 4). This part builds the loop, proves it converges, shows the rotation sets the speed, and adds the numerical care that makes it robust — grounded in rbig (the iterative algorithm and its information measures) and gauss_flows (the smooth, exact-log-det version used for density and sampling).

Notebooks¶

The two tools, and when to use each¶

Part 3 deliberately uses both packages for what each does best:

• rbig (NumPy, sklearn-style) — the canonical iterative algorithm (AnnealedRBIG, MarginalGaussianize, the rotation zoo) and the information-theoretic measures (total_correlation, tc_per_layer_, negentropy, score, entropy) that drive convergence and stopping.
• gauss_flows (JAX) — the smooth, differentiable RBIG (fit_rbig) with mixture-CDF marginals and an exact autodiff log-det, used wherever sample or density quality matters (notebook 00 shows histogram marginals generate diffuse samples; the smooth version generates crisp ones).

Threads¶

• The change-of-variables machinery (Part 0) makes the forward/inverse and log-det of the whole stack concrete; the marginal (Part 1) and rotation (Part 2) halves are the per-layer pieces.
• Why rotation matters (Part 2 00) — marginal-only stalls — is the reason RBIG interleaves a rotation; notebook 02 here quantifies how the rotation choice sets convergence speed.
• Warm-starting a trainable flow from a greedy RBIG fit (master-list 3.7–3.8) is deferred to Part 4, where it belongs: it only matters once there is a parametric flow to initialise.

Running¶

Same uv environment as the earlier parts (rbig + gauss_flows + a Jupyter stack):

cd projects/gaussianization
.venv-tutorials/bin/jupyter nbconvert --to notebook --execute --inplace \
  notebooks/03_iterative_rbig/0*.ipynb --ExecutePreprocessor.timeout=600

Notebooks are paired (jupytext, py:percent) and kept light enough to execute in seconds (small samples, low layer counts).