IR-SBL-St: Reproduction Package for Implicit-Reparameterization Sparse Bayesian Learning with Student-t Emissions

# IR-SBL-St: Implicit-Reparameterization Sparse Bayesian Learning with Student-t Emissions Reproduction package for the manuscript *"IR-SBL-St: A Variational Sparse Bayesian Learning Framework with Student-t Emissions for Volatility Regime Identification on the Johannesburg Stock Exchange"* (submitted to *FinTech*, MDPI). This deposit contains the complete code, data, results, figures, and manuscript source needed to reproduce every table, figure, theorem-adjacent diagnostic, and numeric claim in the paper directly from the raw JSE return series. ## Repository structure ``` code/           All model code and experiment-runner scripts data/           Preprocessed JSE ALSI AR(1) residual series results/        Pickled/zipped output of the diagnostic experiments figures/        The five figures used in the manuscript, as submitted manuscript/     manuscript.tex, ref.bib, and the compiled manuscript.pdf ``` ### `code/` - `models.py` -- all six model implementations compared in Table 1   (Gaussian-HMM, GMM-ARD, MS-GARCH, BB-StM, HMM-St, and the proposed   IR-SBL-St), including the `nu_mode`/`estimator` ablation switches used   for Table 2. - `models_ext.py` -- extends `models.py` with the `kl_mode` (closed-form   vs. Monte Carlo KL) and `precondition_mode` (Fisher/`Nk` vs. literal   `Nk/2` vs. none) switches used for the Equations 16-17 empirical   validation. - `simulation.py` -- the Monte Carlo simulation study (known-truth   Student-t mixture: parameter recovery, runtime scaling, and the   duplicate-component merging logic reused by the power-curve analysis). - `run_all.py` -- driver script reproducing Tables 1-3 and Figures 2-4   end to end from the raw returns file. - `eq_validation.py` -- reproduces the Fisher-preconditioning and   closed-form-KL empirical validation (Section 6.7 / Table 6). - `stability_power.py`, `run_bootstrap_resumable.py`,   `run_power_resumable.py` -- the bootstrap stability analysis and Monte   Carlo power/null-specificity diagnostics (Section 6.8 / Table 8). - `IR_SBL_St_sensitivity.py` -- the hyperparameter sensitivity sweep over   `K_max`, ARD concentration `alpha0`, and learning rate (Section 6.9 /   Table 12, Figure 5). - `requirements.txt` -- Python package dependencies (CPU-only; no GPU   required for any experiment in this paper). ### `data/` - `resid_data.csv` -- the preprocessed AR(1)-residual JSE ALSI return   series (2015-01-05 to 2026-04-29), Eskom load-shedding stage, and   train/test split markers used throughout the paper. ### `results/` Pickled raw output from the diagnostic experiments reported in the paper, so the reported numbers can be inspected directly without re-running the (CPU-hours-scale) full experiment suite: - `eq_validation_results.pkl` -- Fisher-preconditioning / closed-form KL   validation (Table 6). - `bootstrap_stability_final.pkl` -- 12-resample bootstrap stability   analysis of the real JSE fit (Table 9). - `power_specificity_final.pkl` -- Monte Carlo power curve and   null-specificity check (Table 8). - `sensitivity_results.zip` -- the full 70-fit hyperparameter sensitivity   sweep (Table 12, Figure 5): `sensitivity_results.csv` (raw, per-fit),   `sensitivity_summary.csv` (aggregated), `fig_sensitivity.pdf`. ### `figures/` The five figures as they appear in the manuscript: `1.png` (model architecture), `2.png` (inferred regime probabilities), `3.png` (latent scale vs. squared residual), `4.png` (optimization trajectories), `5.pdf` (hyperparameter sensitivity). ### `manuscript/` `manuscript.tex` and `ref.bib` (MDPI FinTech class), plus the compiled `manuscript.pdf` as submitted. ## Setup ```bash cd code/ pip install -r requirements.txt ``` No GPU is required; every experiment in this paper runs on CPU. ## Reproducing the main results ```bash python run_all.py ``` Runtime: roughly 4-6 minutes on a standard laptop CPU for Tables 1-3 and Figures 2-4. For the additional diagnostics reported in Sections 6.7-6.9: ```bash python eq_validation.py              # Table 6 (~10 min) python run_bootstrap_resumable.py    # Table 9, run repeatedly to completion (~30-40 min total) python run_power_resumable.py        # Table 8, run repeatedly to completion (~10 min total) python IR_SBL_St_sensitivity.py      # Table 12 / Figure 5 (~35-40 min) ``` (`run_bootstrap_resumable.py` and `run_power_resumable.py` are checkpointed: each invocation makes partial progress and can be re-run to continue.) ## Reproducibility notes - Unless noted otherwise, all results use `seed=0` as the default; the   diagnostic experiments in `results/` were run across multiple seeds   per setting as described in the corresponding section of the paper.   Small differences in the last reported decimal can arise from   BLAS/threading nondeterminism in PyTorch across machines; the   qualitative conclusions (regime counts, model ranking, gradient-variance   ratios) are stable across runs. - All reported theorems, propositions, and the lemma in Section 5.4 are   proved analytically in the manuscript and are not themselves   "reproduced" by code, but every empirical claim used to illustrate or   validate them (e.g., the measured 4.0x gradient-variance ratio matching   the theoretical prediction of Proposition 3) is reproducible from the   scripts above. ## License Code: MIT License. Data: derived from public JSE market data and South Africa's public Eskom load-shedding schedule; redistributed here for research reproducibility. ## Citation If you use this code or data, please cite the manuscript (full citation to be added once published; see `manuscript/manuscript.pdf` for the current version) and this Zenodo deposit: ``` [Author name], (2026). IR-SBL-St reproduction package [Data set/Code]. Zenodo. doi.org to be assigned on publication] ``` ## Contact Prof. Ntebogang Dinah Moroke, North-West University, Mafikeng Campus, Faculty of Economic and Management Sciences, South Africa. ORCID: 0000-0001-8545-1860