Residual Component Analysis: Generalising PCA for more flexible ...

More documents

Recommendations

Info

Dual PPCA (principal Coordinate analysis) (Lawrence, 06) ◮ Instead of the latent variable X, we can place a prior distribution on the mapping W. Marginalising W instead of X, � p(Y, W|X)dW = the PPCA dual solution can be obtained for likelihoods of the form p(Y|X) = p� j=1 N (y:,j|0, XX ⊤ + σ 2 I) ◮ Note the conditional independence is across features. Now, dual-PPCA solves for the latent coordinates, XML = U ′ ⊤ qLqR
From dual-PPCA to the GPLVM (Lawrence, 06) (Titsias & Lawrence, 10) (Damianou et. al, 11) ◮ Note the covariance is an inner-product term (of latent variables) plus spherical-Gaussian noise. p(Y|X) = p� j=1 N (y:,j|0, XX ⊤ + σ 2 I)
Page 1 and 2: Residual Component Analysis: Genera
Page 3 and 4: Probabilistic PCA (sensible PCA) (H
Page 5: Dual PPCA (principal Coordinate ana
Page 9 and 10: From dual-PPCA to the GPLVM (Lawren
Page 11 and 12: Residual Component Analysis ◮ Dis
Page 21 and 22: Residual Component Analysis (Kalait
Page 23 and 24: Low-rank + Sparse-Inverse Covarianc
Page 25 and 26: Optimising the LR + SI Covariance M
Page 27 and 28: Optimising the LR + SI Covariance M
Page 29 and 30: Simulations Precision 1 0.9 0.8 0.7
Page 31 and 32: Reconstructing the Human Form y 0.2
Page 33 and 34: Reconstructing the Human Form Confo
Page 35: Reconstruction of a protein-signall

Residual Component Analysis: Generalising PCA for more flexible ...

Create successful ePaper yourself

Delete template?

Save as template?