Predicting Flatfish Growth in Aquaculture Using Bayesian Deep Kernel Machines
Abstract
1. Introduction
2. Backgrounds
2.1. Bayesian Kernel Machine Regression
2.2. Artificial Neural Network
3. Materials and Methods
3.1. Data Description
3.2. Bayesian Deep Kernel Machine Regression
3.2.1. Model Specification
3.2.2. Posterior Inference
Algorithm 1. Laplace approximation for BDKMR. |
|
3.3. Evaluation Metrics
4. Results
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
BDKMR | Bayesian Deep Kernel Machine Regression |
BKMR | Bayesian Kernel Machine Regression |
GP | Gaussian Process |
KRR | Kernel Ridge Regression |
Appendix A
Appendix A.1. Data Summary
Item | Description |
---|---|
Study period | March 2023–July 2024 (coverage varies by tank) |
Regions/farms/tanks | Wando (2 farms), Jeju (3 farms); total tanks: 7 |
Observations (monthly) | [fill in N total]; by region: [Wando nW], [Jeju nJ]; by tank: [] |
Seasonal coverage | Spring–summer–autumn–winter represented; duration per tank is unbalanced |
Predictors used | Water temperature (minutely sensor), dissolved oxygen (minutely sensor), feed quantity (daily tank-level; per-fish normalization), initial log weight, region/tank indicators |
Outcome | Log-mean monthly weight (average of 50 randomly sampled fish per farm) |
Preprocessing | Align exposures to weight window ; average temperature and DO over the window; aggregate daily feed within the window and convert to per-fish; log-transform 50 weights and average; use heteroscedastic likelihood |
Excluded variables | Salinity, pH, stocking density (stable/controlled or not consistently available across tanks) |
Appendix A.2. Conceptual Comparison with Other Nonlinear Models
Model | Interpretability | Interaction Modeling | Uncertainty | Nonlinearity | Comp. Cost | Scalability |
---|---|---|---|---|---|---|
BKMR | Moderate | Strong | Yes | Strong | High | Moderate |
BDKMR (ours) | Moderate | Strong | Yes | Very Strong | High | Moderate |
Random Forest | Moderate | Limited | No | Moderate | Low | High |
SVM (RBF kernel) | Low | Limited | No | Strong | Moderate | High |
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Model | MAE | MSE |
---|---|---|
KRR | 1.1141 | 3.5665 |
BKMR | 0.6977 | 0.9447 |
BDKMR (Equal) | 0.2006 | 0.0721 |
BDKMR | 0.1895 | 0.0629 |
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Kim, J.; Seo, S.-W.; Jung, H.-J.; Jang, H.-S.; Lim, H.-K.; Jo, S. Predicting Flatfish Growth in Aquaculture Using Bayesian Deep Kernel Machines. Appl. Sci. 2025, 15, 9487. https://doi.org/10.3390/app15179487
Kim J, Seo S-W, Jung H-J, Jang H-S, Lim H-K, Jo S. Predicting Flatfish Growth in Aquaculture Using Bayesian Deep Kernel Machines. Applied Sciences. 2025; 15(17):9487. https://doi.org/10.3390/app15179487
Chicago/Turabian StyleKim, Junhee, Seung-Won Seo, Ho-Jin Jung, Hyun-Seok Jang, Han-Kyu Lim, and Seongil Jo. 2025. "Predicting Flatfish Growth in Aquaculture Using Bayesian Deep Kernel Machines" Applied Sciences 15, no. 17: 9487. https://doi.org/10.3390/app15179487
APA StyleKim, J., Seo, S.-W., Jung, H.-J., Jang, H.-S., Lim, H.-K., & Jo, S. (2025). Predicting Flatfish Growth in Aquaculture Using Bayesian Deep Kernel Machines. Applied Sciences, 15(17), 9487. https://doi.org/10.3390/app15179487