Pattern Recognition and Machine Learning
Citations
767 citations
747 citations
Additional excerpts
...p(x|z = 0, y = 1) = N([1, 2], [5, 2; 2, 5]) p(x|z = 1, y = 1) = N([2, 3], [10, 1; 1, 4]) p(x|z = 0, y = −1) = N([0,−1], [7, 1; 1, 7]) p(x|z = 1, y = −1) = N([−5, 0], [5, 1; 1, 5])...
[...]
...15 for a logistic regression classifier [5]....
[...]
...p(x|z = 0, y = 1) = N([2, 0], [5, 1; 1, 5]) p(x|z = 1, y = 1) = N([2, 3], [5, 1; 1, 5]) p(x|z = 0, y = −1) = N([−1,−3], [5, 1; 1, 5]) p(x|z = 1, y = −1) = N([−1, 0], [5, 1; 1, 5])...
[...]
745 citations
Cites background from "Pattern Recognition and Machine Lea..."
...Additionally, it has to be kept in mind, that the different algorithms can be combined to maximize the classification power (Bishop, 2006)....
[...]
...that the different algorithms can be combined to maximize the classification power (Bishop, 2006)....
[...]
734 citations
Cites background or methods from "Pattern Recognition and Machine Lea..."
...where the expectation is taken with respect to h, thenL ≤ lnP (D) with equality holding iffQ(h) is the exact posterior P (h|D) [7]....
[...]
...This complication can be avoided by assuming a variational approximation of the form lnP (x1, x2|D) ≈ lnQ(x1) + lnQ(x2) and iteratively applying the standard variational Bayes update formulas [7] lnQ(x2) ≡ Ex1 [lnP (D,x1, x2)] lnQ(x1) ≡ Ex2 [lnP (D,x1, x2)] ....
[...]
...See the section on Bayesian PCA in [7]....
[...]
...(The Student’s t distribution is defined in the Appendix; see also [7]....
[...]
...s L1(s); this is the auxiliary function in Bishop’s formulation of the EM algorithm [7]....
[...]
726 citations
Cites background from "Pattern Recognition and Machine Lea..."
...where Nr represents a regularization term, which behaves as a uniform Dirichlet prior [4] over feature values....
[...]