Optimization Under Uncertainty: Gaussian Process Regression (GPR) and Gekko Optimization
This video walks through the process of setting up, training, and optimizing a GPR model to handle uncertainty in predictions, ideal for tasks requiring uncertainty-aware decision-making.
Outline:
1. Introduction to Gaussian Process Regression (GPR)
- Understanding GPR as a probabilistic model
- Benefits of GPR in making predictions with well-defined uncertainty
- Detailed mathematical description available in the "Machine Learning for Engineers" course
2. Setting Up the Environment
- Importing essential libraries: NumPy, Matplotlib, Gekko, and Scikit-learn's Gaussian Process Regressor and kernels
- Installation guide for Gekko if not already installed
3. Data Generation and Visualization
- Generating noisy data samples
- Visualizing true functions and measured data points
4. Data Preparation
- Splitting data into training and testing sets using scikit-learn’s `train_test_split`
5. GPR Model Training
- Creating and training a GPR model
- Evaluating model performance using the R-squared metric
6. Model Visualization
- Plotting trained GPR model predictions and confidence intervals against true functions and noisy measurements
7. Optimization with Gekko
- Using Gekko to perform optimization
- Minimizing predicted values and uncertainties using the trained GPR model
8. Uncertainty Optimization
- Minimizing uncertainty with Gekko
9. Multi-Objective Optimization
- Minimizing both expected values and uncertainties as a weighted sum
10. Results Visualization
- Visualizing optimization results
- Highlighting points of optimized predicted values and uncertainties
Check out the detailed mathematical description on the Gaussian Process Regression learning page in the "Machine Learning for Engineers" course for more insights. Code Blocks Available:
- Import Libraries
- Generate Data
- Data Preparation
- GPR Model Training
- Model Visualization
- Optimization with Gekko
- Uncertainty Optimization
- Multi-Objective Optimization
- Results Visualization