An Efficient Approach to Learning Inhomogenous Gibbs Models

1. An Efficient Approach to Learning Inhomogenous Gibbs Models Ziqiang Liu, Hong Chen, Heung-Yeung Shum Microsoft Research Asia CVPR 2003 Presented by Derek Hoiem

2. Overview • Build histograms for projections to 1-D • Feature selection: max KL divergence between estimated and true distribution • 1-D histograms for a feature computed from training data and MCMC sampling • Fast solution with good starting point and importance sampling

3. Maximum Entropy Principle • p(x) and f(x) should have same stats over observed features but p(x) should be as random as possible over other dimensions

4. Gibbs Distribution and KL-Divergence • The solution: Gibbs distribution Λ minimizes the KL divergence:

5. Inhomogeneous Gibbs Model • Gaussian and MoG deemed inadequate • Use vector-valued features (histograms)

6. Approximate Information Gain and KL-Divergence • Effectiveness of feature defined by reduction in KL-divergence: • Approximate information gain given by (old params constant): • For a vector-valued feature: Key Contribution! gain starting point

7. Estimating Λ: Importance Sampling • Obtain reference samples xref by MCMC from starting point • Update Λ by: Good starting point Bad starting point

8. A Toy Success Story True Reference (Initial) Optimized Estimate

9. Caricature Generation: Representation • Learn mapping from photo to caricature • Active appearance models: • Photos: shape + texture (44-D after PCA) • Caricature: shape (25-D after PCA)

10. Caricature Generation: Learning • Gain(1)=.447 Gain(17)=.196 • 100,000 reference samples • 8 hours on 1.4GHz 256MB • vs 24 hours on 667MHz 18-D • Estimate: • Draw samples from: • Approximate to:

11. Caricature Generation: Results

12. Caricature Generation: Results

13. Comments • Claims 100x speedup from efficiency analysis (33% speedup in reality)