Research map / Probabilistic and scientific modeling / Variational and generative sampling
Variable Elimination in the Fourier Domain
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Fourier-domain variable elimination with coefficient truncation rather than Mini-bucket elimination | Fourier VE · UAI 2010 categories grids2/50-*, grids2/75-*, grids2/90-*, blockmap_05*, students_03*, mastermind_04*, mastermind_05*, mastermind_06* | median absolute log10 partition-function error: Fourier (max coef) vs Minibucket: 5.12 -> $3.67 \cdot 10^{-6}$; 18.34 -> $5.41 \cdot 10^{-4}$; 26.16 -> $2.23 \cdot 10^{ | Helped |
| Use Fourier-domain variable elimination with coefficient truncation rather than Mini-bucket elimination | Fourier VE · UAI 2010 categories bn2o-30-*, mastermind_03*, mastermind_10* | median absolute log10 partition-function error: 3.91 vs $1.21 \cdot 10^{-2}$; 7.83 vs 0.47; 275.82 vs 5.63 | Hurt |
| Use Fourier-domain variable elimination rather than HAK | Fourier VE · UAI 2010 categories grids2/50-*, grids2/75-*, grids2/90-*, blockmap_05*, students_03*, mastermind_04*, mastermind_05*, mastermind_06* | median absolute log10 partition-function error: grids2/50-* $1.53 \cdot 10^{-2}$ -> ${\bf 3.67 \cdot 10^{-6}}$; grids2/75-* $2.94 \cdot 10^{-2}$ -> ${\bf 5.41 \cdot 10^ | Mixed |
| Keep largest-absolute-value coefficients instead of lowest-degree coefficients (ablation) | Fourier VE · UAI 2010 categories | median absolute log10 partition-function error: The paper reports the versions work equally well; e.g. blockmap_05*: $4.34 \cdot 10^{-9}$ vs $4.34 \cdot 10^{-9}$; stude | No clear effect |
| Keep low-degree Fourier coefficients rather than largest-absolute-value coefficients (ablation) | Fourier VE · mastermind_03* and mastermind_10* | median absolute log10 partition-function error: 0.47 -> 0.36; 5.63 -> 2.98 | Helped |
| Keep largest-absolute-value Fourier coefficients rather than low-degree coefficients (ablation) | Fourier VE · grids2/90-* | median absolute log10 partition-function error: $5.71 \cdot 10^{-3}$ -> ${\bf 2.23 \cdot 10^{-3}}$ | Helped |
| Represent VE messages in the Fourier domain and truncate the coefficient representation | Variable elimination · 15-by-15 Ising models | absolute log-partition-function error | Helped |
| Use Fourier VE for inference rather than one-pixel Gibbs sampling, Mini-bucket, or mean field | Learned grid Ising model on synthetic images · Synthetic image marginals | marginal probability accuracy | Helped |
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