Gaussian Models

Basic Knowledge

• Normal Distribution / Multivariate Gaussian
  
• Eigenvalue Decomposition
• Estimate MLE for
• Same , Gaussian Distribution has Maximum Entropy
• Joint Gaussian Distribution

Interpolation

• 
  Data points: total , observed
• Suppose we can fit the data, then using smoothness assumption , we get

Noise-free Observation

1. Partition to , to , where are observed noise-free observations. If observations are not adjacent data points, we can adjust along with
2. Then,
3. Use formula, get conditional distribution, aka., 's distribution (unknown data's distribution)
4. Generate

Noisy Observation

1. Observed noisy data
2. Use selection matrix , such that
3. Now,
4. Use theorem, get posterior distribution, aka., 's distribution (whole data's distribution)
5. Generate