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Discussion Ying Nian Wu UCLA Department of Statistics JSM 2011

Discussion Ying Nian Wu UCLA Department of Statistics JSM 2011. Population value decomposition. Latent variable models. Hidden. Observed. Learning:. Examples. Inference:. Latent variable models. Mixture model. Factor analysis. Computational neural science. Hidden. Observed.

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Discussion Ying Nian Wu UCLA Department of Statistics JSM 2011

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  1. Discussion Ying Nian Wu UCLA Department of Statistics JSM 2011 Population value decomposition

  2. Latent variable models Hidden Observed Learning: Examples Inference:

  3. Latent variable models Mixture model Factor analysis

  4. Computational neural science Hidden Observed Z: Internal representation by neurons Y: Sensory data from outside environment Connection weights Hierarchical extension: modeling Z by another layer of hidden variables explaining Y instead of Z Inference / explaining away

  5. Visual cortex: layered hierarchical architecture bottom-up/top-down V1: primary visual cortex simple cells complex cells Source: Scientific American, 1999

  6. Independent Component AnalysisBell and Sejnowski, 1996 Laplacian/Cauchy

  7. Hyvarinen, 2000

  8. Sparse codingOlshausen and Field, 1996 Laplacian/Cauchy/mixture Gaussians

  9. Sparse coding / variable selection Inference: sparsification, non-linear lasso/basis pursuit/matching pursuit mode and uncertainty of p(C|I) explaining-away, lateral inhibition Learning: A dictionary of representational elements (regressors)

  10. Olshausen and Field, 1996

  11. Restricted Boltzmann Machine Hinton, Osindero and Teh, 2006 hidden, binary visible P(H|V): factorized no-explaining away P(V|H)

  12. Visual cortex: layered hierarchical architecture bottom-up/top-down What is beyond V1? Hierarchical model? Source: Scientific American, 1999

  13. Hierarchical RBM Hinton, Osindero and Teh, 2006 V’ Unfolding, untying, re-learning H I V P(H)  P(V’,H) P(V,H) = P(H)P(V|H) Discriminative correction by back-propagation

  14. Hierarchical sparse coding Attributed sparse coding elements transformation group topological neighborhood system Layer above : further coding of the attributes of selected sparse coding elements

  15. Active basis model Wu, Si, Gong, Zhu, 10 Zhu, Guo, Wang, Xu, 05 n-stroke template n = 40 to 60, box= 100x100

  16. Learning and Inference Finding n strokes to sketch M images simultaneously n = 60, M = 9 Scan over multiple resolutions

  17. Scan over multiple resolutions and orientations (rotating template)

  18. Learning active basis models from non-aligned image EM-type maximum likelihood learning, Initialized by single image learning

  19. Learning active basis models from non-aligned image

  20. Learning active basis models from non-aligned image

  21. Hierarchical active basis High log-like Low log-likelihood

  22. Model based clustering MNIST 500 total

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