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
- Partition
to
,
to
, where
are
observed noise-free observations. If observations are not adjacent data points, we can adjust
along with
- Then,
- Use formula, get conditional distribution, aka.,
's distribution
(unknown data's distribution)
- Generate
Noisy Observation
- Observed
noisy data
- Use selection matrix
, such that
- Now,
- Use theorem, get posterior distribution, aka.,
's distribution
(whole data's distribution)
- Generate
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