By Magnus Ekdahl.
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Additional info for Approximations of Bayes classifiers for statistical learning of clusters
10) time. 2 Tests The algorithm has been tested using 20000 randomly generated complete graphs against boost’s C++ implementation of MST . All random numbers were from the discrete uniform distribution (for # vertices [2,50], edge weights [0,RAND MAX]). 23 % was spent in DynamicMst. Two practical tests have also been performed to reduce chance that DynamicMst is implemented wrong. Both the Enterobacteriace 47bit data with up to 100 classes and the Vibrionaceae 994bit data with up to 5 classes have yielded the same result for the boost and dynamic version of MST.
36] extended the algorithm in  to include the possibility for searching for an optimal forest rather than an optimal tree. 4, equation (3)). ,d]SC(ξi ) 4: set the direction of all the edges in ei outwards from the root 5: for i = 1 to d − 1 do 6: (ξi , ξj ) ← ei 7: if SC(ξi |ξj ) > SC(ξi ) then 8: result ← result ∪ vi 9: else 10: result ← result ∪ ei 11: end if 12: end for 13: return result It is important that the result from the approximation is checked February 13, 2006 (13:19) 46 against the actual SC calculated under the locally independent parameter assumption.
8 Local parameter independence d qi gΘi |Πi (θi |j) gΘ (θ) = i=1 j=1 February 13, 2006 (13:19) 36 With the local parameter independence assumption we can calculate Jeﬀreys’ prior. Before doing that we introduce some notation. 1, where Proof for all j ∈ Πi , Pξi |Πi (l|j) ∝ l=1 ri −1 θijl . This yields θijri = 1 − l=1 ⎧ i) ⎨ − Ii 2(l) − Ii (r when l = m 2 δ θijl θijr i logPξi |Πi (l|j) ∝ Ii (ri ) ⎩ − θ2 δθijl δθijm otherwise ijri Now letting | . . | denote the determinant of a matrix I(θ) = ⎛ ⎞ Ii (ri ) Ii (1) Ii (ri ) Ii (ri ) ...
Approximations of Bayes classifiers for statistical learning of clusters by Magnus Ekdahl.