# High dimensional Bayesian Optimization Algorithm for Complex System in Time Series

arXiv: https://arxiv.org/abs/2108.02289 · HTML: https://mlsanity.com/paper/2108.02289/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 31 references that are in the map.
- First posted on arXiv 4 Aug 2021.

## Builds on (most cited first, 7 of 7)

- [Local Gaussian process approximation for large computer experiments](https://mlsanity.com/paper/1303.0383/) (2013)
- [High Dimensional Bayesian Optimization Using Dropout](https://mlsanity.com/paper/1802.05400/) (2018)
- [High Dimensional Bayesian Optimization via Supervised Dimension Reduction](https://mlsanity.com/paper/1907.08953/) (2019)
- [A deterministic global optimization using smooth diagonal auxiliary functions](https://mlsanity.com/paper/1509.04518/) (2015)
- [A New Bayesian Optimization Algorithm for Complex High-Dimensional Disease Epidemic Systems](https://mlsanity.com/paper/2108.00062/) (2021)
- [On strong homogeneity of a class of global optimization algorithms working with infinite and infinitesimal scales](https://mlsanity.com/paper/1801.05306/) (2018)
- [Pymc-learn: Practical Probabilistic Machine Learning in Python](https://mlsanity.com/paper/1811.00542/) (2018)

## Built on by (most cited first, 2 of 2)

- [High-dimensional Bayesian Optimization Algorithm with Recurrent Neural Network for Disease Control Models in Time Series](https://mlsanity.com/paper/2201.00147/) (2022)
- [An Improved Mathematical Model of Sepsis: Modeling, Bifurcation Analysis, and Optimal Control Study for Complex Nonlinear Infectious Disease System](https://mlsanity.com/paper/2201.02702/) (2022)

## Abstract (arXiv)

At present, high-dimensional global optimization problems with time-series models have received much attention from engineering fields. Since it was proposed, Bayesian optimization has quickly become a popular and promising approach for solving global optimization problems. However, the standard Bayesian optimization algorithm is insufficient to solving the global optimal solution when the model is high-dimensional. Hence, this paper presents a novel high dimensional Bayesian optimization algorithm by considering dimension reduction and different dimension fill-in strategies. Most existing literature about Bayesian optimization algorithms did not discuss the sampling strategies to optimize the acquisition function. This study proposed a new sampling method based on both the multi-armed bandit and random search methods while optimizing the acquisition function. Besides, based on the time-dependent or dimension-dependent characteristics of the model, the proposed algorithm can reduce the dimension evenly. Then, five different dimension fill-in strategies were discussed and compared in this study. Finally, to increase the final accuracy of the optimal solution, the proposed algorithm adds a local search based on a series of Adam-based steps at the final stage. Our computational experiments demonstrated that the proposed Bayesian optimization algorithm could achieve reasonable solutions with excellent performances for high dimensional global optimization problems with a time-series optimal control model.