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15 Jan 2023: Modern Statistical MethodsRajen D. Shah r.shah@statslab.cam.ac.uk. Course webpage:http://www.statslab.cam.ac.uk/rds37/modern_stat_methods.html. In this course we will study a selection of important modern statistical methods. Thisselection is

27 Jan 2023: k2) = p(Di|Ti)p(Dj|Tj) where the probability of. a data set under a tree (e.g. ... Combiningterms we obtain:. p(Di|Ti)p(Dj|Tj)didjdk. =1. dk. . . v′VTi. αmv′m. v′.

27 Jan 2023: H. k2 ) = p(Di|Ti)p(Dj|Tj ) where the probability of a data set under. ... 3)Merge Dk Di Dj , Tk (Ti, Tj )Delete Di and Dj , c c 1.

27 Jan 2023: k2 ) = p(Di|Ti)p(Dj|Tj ) where the probability of. a data set under a tree (e.g. ... rk =πkp(Dk|Hk1 ). p(Dk|Tk). Merge Dk Di Dj , Tk (Ti, Tj )Delete Di and Dj , c c 1.

27 Jan 2023: 1. 2. 3. 4. 5. 6. tj on 1 0 1 2 3 4 5 60.511.52. ... 8. 7. 6. 5. 4. 3. 2. tj on 0 0.5 1 1.5 2 2.5 310987.

27 Jan 2023: rdeA1mnj!V yeTWZ]T B? YZc?;du Tj!deo[o]deA ikQ?=yes TWoÓdAZ[r;T!B? ... YA1B O S &O &O @ w{rJs oU@Ts o]ZmnQ8V s Z[Tj O S % $O!

27 Jan 2023: of the easier ones that do not depend on the RBF kernel :hxij = xj hzij = zjhxx>ij = xj x;Tj Cxxj hxz>ij = xj z;Tj Cxzjhzz>ij = zj z;Tj

27 Jan 2023: for j = i 1 to n. if sj {s<j} thenu(c) = u(c) wsj (tj )elseu(c) = u(c) α.

27 Jan 2023: where rj = φjC1j φ. Tj , uj = φjC. 1j mo, and Cj =. Λ1 m6=j φ. Tmφm. Here φj and φm are j. th and mth.

27 Jan 2023: O52O22O23. O53 O54 O55. O22O21O20O19O18O17. Ti=E. O52O51O50O49O48O47O46O45. Wsheet. Tj=E. anti-parallel dij=-1alignment aij=3.