Correctness and Predictive Uncertainty in Bayesian TSK Fuzzy Regression: A Reproducible Evaluation on Tabular and Building-Meter Data

Abstract

Uncertainty estimates from fuzzy regression are informative only when the implementation is correct and the comparison protocol makes the sources of variation visible. We revisit a first-order Takagi--Sugeno--Kang (TSK) regression implementation and rebuild its dense, conjugate Bayesian, BIC-based, and rule-level spike-and-slab estimators using corrected code. The corrected pipeline freezes the Gaussian membership partition at training time, uses a scaled conjugate prior, evaluates firing strengths in the log domain, and reports direct posterior-predictive quantiles for Bayesian methods. Across 30 outer 80/20 splits on three targets from two UCI regression datasets, corrected TSK-LS obtains $R^2=0.957$, $0.923$, and $0.786$ on Energy-Heating, Energy-Cooling, and Concrete, respectively; rule-level Gibbs sampling with Bayesian model averaging obtains $0.957$, $0.922$, and $0.784$. We then evaluate the same workflow on a bounded chronological sample of the Building Data Genome 2 meter data that covers 158 buildings across 17 sites. In a common-unit evaluation, every method is scored on the same 47,400 test rows and every trained model uses 94,800 train--validation rows. Persistence has RMSE $27.710$, compared with $29.083$ for both TSK-LS and Bayesian TSK; the pre-specified building-level mean RMSE difference between Bayesian TSK and persistence is $+0.0447$ with a 95% site-cluster bootstrap interval of $[-1.5536,1.5665]$. The Bayesian TSK 90% intervals have PICP $0.980$ and MPIW $116.469$. Taken together, the evidence supports a narrower conclusion: spike-and-slab model averaging is a reproducible implementation option, but it does not provide a demonstrated accuracy or calibration advantage across the tested tabular and building-meter settings.