Pattern Recognition and Machine Learning
Citations
281 citations
280 citations
Cites background or methods from "Pattern Recognition and Machine Lea..."
...Within training cross-entropy (CE) error function is minimized (Bishop, 2006) E(w) = − ln p(T|w) = − N∑ n= 1 K∑ k= 1 tnk ln ynk (1) where E(w) is the CE error function that depends on the neurons’ weight coefficients w, T is the set of vectors of target outputs in the training set composed of N…...
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...One disadvantage of the DT classifier is the considerable sensitivity to the training dataset, so that a small change to the training data can result in a very different set of subsets (Bishop, 2006)....
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...An important property of SVMs is that the determination of the model parameters corresponds to a convex optimization problem, and so any local solution is also a global optimum (Bishop, 2006)....
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...The main difference from other models and algorithms is the outcome score that could be considered as a probability value (Bishop, 2006; Haykin, 2008)....
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...Within training cross-entropy (CE) error function is minimized (Bishop, 2006)...
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279 citations
Cites background from "Pattern Recognition and Machine Lea..."
...It can potentially reduce the burden on radiologists in the practice of radiology[57], which can learn complex relationships or patterns from empirical data and make accurate decisions[58]....
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279 citations
Additional excerpts
...Skipping the derivation (see Bishop 2006 or Jaakkola and Jordan 2000 for details), the lower bound on the logarithm of the sigmoid function is logψ(x) ≥ logψ(η) + 12 (x− η) − u2 (x 2 − η2), (17) where we have defined u = 1η (ψ(η) − 12 )....
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279 citations
Cites background or methods from "Pattern Recognition and Machine Lea..."
...The posterior distribution is analytic and given by (Bishop, 2006) S−1θ = X TC−1y X+C −1 θ mθ = Sθ X TC−1y y+C −1 θ μθ ð27Þ Please cite this article as: Penny, W.D., Comparing Dynamic Causal Mode j.neuroimage.2011.07.039 These parameter values can then be plugged into Eqs....
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...This is equivalent to the statement that BIC is equal to the Free Energy under the infinite data limit, and when the priors over parameters are flat, and the variational posterior is exact (see section 2.3 in (Attias, 1999) and page 217 in (Bishop, 2006))....
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...1053-8119/$ – see front matter © 2011 Elsevier Inc. Al doi:10.1016/j.neuroimage.2011.07.039 Please cite this article as: Penny, W.D., Com j.neuroimage.2011.07.039 a b s t r a c t a r t i c l e i n f o...
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...A generic approach for statistical inference in this context is Bayesian estimation (Bishop, 2006; Gelman et al., 1995) which provides estimates of two quantities....
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