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Dimension reduction
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Classroom Contents
Manifold Learning with Noisy Data: Dimension Reduction and Support Estimation
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- 1 Intro
- 2 Dimension reduction
- 3 Manifold learning: some ideas (no noise)
- 4 Noisy data. What happens with noise? Geometric ideas
- 5 Additive noise: examples
- 6 Support estimation: deconvolution with Gaussian noise and (truncated) Hausdorff loss
- 7 Robustness to the assumptions on the noise
- 8 First question: identifiability
- 9 Identifiability theorem
- 10 When does HD hold? Simple facts.
- 11 When does HD hold? Geometrical condition
- 12 When does HD hold? Examples of supports
- 13 Second question: estimation (upper bound)
- 14 Take-home message
