In this section, you are going to implement the Gaussian Process and visualize the result.
● Training data o input.data is a 34x2 matrix. Every row corresponds to a 2D data point
(Xi,Yi).
o Yi = f(Xi) + 𝜖i is a noisy observation, where 𝜖i ~ N(∙|0, β-1). You can use β = 5 in this implementation.
● What you are going to do o Part1: Apply Gaussian Process Regression to predict the distribution of f and visualize the result. Please use a rational quadratic kernel to compute similarities between different points.
Details of the visualization:
- Show all training data points.
- Draw a line to represent the mean of f in range [-60,60].
- Mark the 95% confidence interval of f.
(You can use matplotlib.pyplot to visualize the result, e.g. use matplotlib.pyplot.fill_between to mark the 95% confidence interval, or you can use any other package you like.)
o Part2: Optimize the kernel parameters by minimizing negative marginal log-likelihood, and visualize the result again. (You can use scipy.optimize.minimize to optimize the parameters.)
