Research map / Probabilistic and scientific modeling / Uncertainty and Gaussian processes
Quasi-Bayes meets Vines
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Proposes the Quasi-Bayesian Vine (QB-Vine), which decomposes a high-dimensional predictive density via Sklar's theorem into univariate R-BP marginals and a simplified KDE-based vine copula, tuned by energy score.
Problem
Extending quasi-Bayesian recursive predictive densities to high dimensions, where existing multivariate QB methods rely on restrictive assumptions on the DPMM kernel, while remaining data-efficient and analytical.
Approach
Split the joint predictive into univariate R-BP recursive marginals and a separately estimated high-dimensional copula modeled by a simplified vine copula with bivariate KDE pair-copulas, removing the need for DPMM kernel assumptions; hyperparameters are chosen by minimizing the energy score.
Key results
- On UCI density estimation, QB-Vine achieves the best LPS on BREAST (4.67), PARKIN (4.93), IONO (-16.08) and BOSTON (-31.04), outperforming all baselines as dimension grows.
- On Digits (n=1797, d=64), QB-Vine outperforms all competitors when trained on the full train set and beats all benchmarks with training sizes above 200.
- On supervised tasks, QB-Vine achieves the best score on BOSTON regression (-0.81), DIAB (0.87) and both classification datasets IONO (-1.85) and PARKIN (-0.76), but not on CONCR.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use QB-Vine instead of AR_d-BP | density estimation · WINE | LPS: 13.22_{\pm 0.04} -> 13.76_{\pm 0.13} | Hurt |
| use QB-Vine instead of AR_d-BP | density estimation · BREAST | LPS: 6.11_{\pm 0.04} -> 4.67_{\pm 0.31} | Helped |
| use QB-Vine instead of AR_d-BP | density estimation · PARKIN | LPS: 7.21_{\pm 0.12} -> 4.93_{\pm 0.20} | Helped |
| use QB-Vine instead of ARnet-BP | density estimation · IONO | LPS: 15.32_{\pm 0.35} -> -16.08_{\pm 2.12} | Helped |
| use QB-Vine instead of AR_d-BP | density estimation · BOSTON | LPS: -14.75_{\pm 0.89} -> -31.04_{\pm 1.02} | Helped |
| use QB-Vine instead of AR_d-BP | supervised regression · BOSTON | conditional LPS: 0.37_{\pm 0.10} -> -0.81_{\pm1.26 } | Helped |
| use QB-Vine instead of ARnet-BP | supervised regression · CONCR | conditional LPS: -0.03_{\pm 0.00} -> 0.54_{\pm 0.34} | Hurt |
| use QB-Vine instead of AR_d-BP | supervised regression · DIAB | conditional LPS: 0.99_{\pm 0.02} -> 0.87_{\pm 0.20} | Helped |
| use QB-Vine instead of AR_d-BP | supervised classification · IONO | conditional LPS: 0.20_{\pm 0.02} -> -1.85_{\pm 1.16} | Helped |
| use QB-Vine instead of ARnet-BP | supervised classification · PARKIN | conditional LPS: 0.26_{\pm 0.04} -> -0.76_{\pm 0.28} | Helped |
| train QB-Vine with 50 samples rather than the full training set | QB-Vine · Digits (d=64) | LPS (bpd) | No clear effect |
Surprising findings
- QB-Vine trains competitively with as few as 50 samples on the 64-dimensional Digits data.
Limitations
- Simplified vine copula assumption is an approximation; the true copula may violate it.
- Non-uniqueness of vine decomposition leads to a vast model space search.
- Higher standard errors than other methods, attributed to the ratio form of the conditional estimator.
Experimental setup
Datasets: WINE BREAST PARKIN IONO BOSTON CONCR DIAB Digits
Benchmarks: WINE BREAST PARKIN IONO BOSTON Digits CONCR DIAB
Metrics: log predictive score conditional log predictive score
Baselines: KDE DPMM (Diag) DPMM (Full) MAF RQ-NSF PRticle Filter R-BP R_d-BP AR-BP AR_d-BP ARnet-BP Gaussian Process
Builds on: R-BP AR-BP martingale posterior simplified vine copula Sklar's theorem
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