Research map / Probabilistic and scientific modeling / Uncertainty and Gaussian processes
Analysis of Variational Bayesian Factorizations for Sparse and Low-Rank Estimation
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Gaussian scale mixture (VB-GSM) instead of bilinear Gaussian (VB-BG) factorization for sparse estimation (ablation) | sparse linear estimation with correlated design · synthetic sparse estimation, correlation parameter eta in [0,2] | normalized MSE and avg. # nonzeros | Helped |
| Non-informative prior on bilinear factorization (VB-BG) with increasing design correlation (ablation) | VB-BG sparse estimation · synthetic sparse estimation, eta > 0.6 | avg. # nonzeros: approaching 100 nonzeros vs. 50 max required | Hurt |
| Strongly informative prior on VB-BG (large alpha, lambda scaled) (ablation) | VB-BG sparse estimation · synthetic sparse estimation | normalized MSE and avg. # nonzeros | No clear effect |
| Empirical Bayes learned prior on VB-BG instead of fixed non-informative prior (ablation) | VB-BG sparse estimation · synthetic sparse estimation | normalized MSE and avg. # nonzeros | Hurt |
| Matrix recovery: VB-GSM instead of VB-BG | affine matrix recovery · matrix recovery experiments (Xin & Wipf, 2015, cited) | recovery performance | Helped |
| Row-wise factorization of posterior in VB-BG (needed for tractability) | VB-BG matrix recovery · theory (Section 3.2) | local minima / penalty structure | Hurt |
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