ベイジアンネットワーク

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1 ( ) : ( ), ( ), ( ),,., imset., imset ( ) 3. ( ) 4. /7

2 n 0.,. N = f;:::;ng, X N. P(N) N :. a, b, c, d 2 N, X a a. A B C D 2P(N),,,,. A [ B AB. A? BC j D D :.. n A BC 2 /7

3 . a? b a? c a 6? bc b c,, ( ). a a b c b b c c a 6? bc b c? bc?. 3 /7

4 2. imset imset(, integer-valued multiset): Studeny( ). structural imset semi-elementary imset elementary imset elementary imset semi-elementary imset. structural imset. 4 /7

5 2. elementary imset semi-elementary imset u ha,b j Ci P(N)! R semi-elementary imset. u ha,b j Ci = ± ABC + ± C ± AC ± BC N = f; 2; 3g = fa; b; cg P(N) abc bc ac ab cb a ; u ha,b j ci ± E (S) = ( (S = E) 0 ( ) imset jp(n)j. A B, u ha;b j Ci a b elementary imset. 5 /7

6 2.2 imset P. a? b j c, P (a; b j c) =P (a j c)p (b j c) a? b j c., P (a; b; c) =P (a; c)p (b; c)=p (c), =P (a; b; c)p (c)=fp (a; c)p (b; c)g, 0=logP (a; b; c)+logp (c) log P (a; c) log P (b; c) imset. u ha;b j ci = ± abc + ± c ± ac ± bc multi-information function, imset,. 6 /7

7 2.3 structural imset u P(N)! R structural imset. u = X i i u hai ;b i j C i i i u hai ;b i j C i i, elementary imset. a? b; a? c; b? c structural imset,. u = u ha;b ji + u ha;c ji + u hb;c ji semi-elementary imset structural imset., semi-elementary imset elementary imset. 7 /7

8 u 2.4 imset structural imset. A? B j C[u], ( ) 9k 2 N, k u u ha,b j Ci is structural imset a? b; a? c; b? c structural imset. u = u ha;b ji + u ha;c ji + u hb;c ji. u u ha,b ji = u ha,c ji + u hb,c ji structural imset. u u ha,bc ji structural imset.,, a? b [u] a 6? bc [u] 8 /7

9 2.6 imset P. P, structural imset, P. a; b; c P a? b; a? c; b? c. 3 2 structural imset u = u ha;b ji + u ha;c ji + u hb;c ji, a.? b [u];a? c [u];b? c [u] [u],.., structural imset,. 9 /7

10 2.6 imset structural imset, 3 a; b; c structural imset. u = u ha,b ji + u ha,c j bi a? b; a? c j b a? c; a? b j c,.,. imset,. u ha,b ji + u ha,c j bi = u ha,c ji + u ha,b j ci, a? b; a? c j b, a? c; a? b j c. semi-graphoid. 0 /7

11 2.7 semi-graphoid. imset,. elementary imset configuration a? b j c; a? c j d; a? d j b, a? c j b; a? d j c; a? b j d a? c; b? d; a? d j bc; b? c j ad, a? d; b? c; a? c j bd; b? d j ac a? b; c? d j a; c? d j b; a? b j cd, c? d; a? b j c; a? b j d; c? d j ab semi-graphoid..,. /7

12 3 2 semi-graphoid. a? b; a? c j b, a? c; a? b j c 3. a? b j c; a? c j d; a? d j b, a? c j b; a? d j c; a? b j d semi-elementary imset elementary imset, semi-graphoid. semi-elementary imset, semi-graphoid. 2 /7

13 elementary imset : u ha,b j Ci ac 3. imset, a? b j C abc C bc semi-elementary imset : u ha,b j Ci AC C ABC BC, A? B j C semi-elementary imset elementary imset ( ) 3 /7

14 3.2 semi-graphoid semi-elementary imset elementary imset. semi-graphoid elementary imset u ha,b ji + u ha,c j bi = u ha,c ji + u ha,b j ci structral imset (semi-elementary imset ),. elementary imset. 4 /7

15 3.3 semi-elementary imset elementary imset. X u ha,b j Ci = i u hai,b i j C i i i,. 5 /7

16 4, imset. imset,. imset,.,, ( ( imset. imset imset (?). imset,.. 6 /7

17 . M. Studeny, Probabilistic Conditional Independence Structures (Springer-Verlag,London, 2005). 2. B. Grunbaum, Convex Polytopes, Graduate Texts in Mathematics, Vol. 22, second edn. (Springer-Verlag, New York, 2003). Prepared and with a preface by Volker Kaibel, Victor Klee and Gunter M. Ziegler. 3. T. Kashimura and A. Takemura, Standard imsets for undirected and chain graphical models, arxiv: v, (20). 4. B. Sturmfels, Gr obner Bases and Convex Polytopes, University Lecture Series, ol. 8 (American Mathematical Society, Providence, RI, 996). 5. T. Kashimura, T. Sei, A. Takemura and K. Tanaka, Properties of semielementary imsets as sums of elementary imsets, Journal of algebraic statistics, 2, (20). 6. R. Hemmecke, J. Morton, A. Shiu, B. Sturmfels and O. Wienand, Combin. Probab. Comput. 7, 239 (2008). 7. M. Studeny, R. R. Bouckaert and T. Kocka, Extreme supermodular set functions over five variables, Research report n. 977, Institute of Information Theory and Automation, Prague, (2000). 8. M. Drton, B. Sturmfels and S. Sullivant, Lectures on algebraic statistics, Oberwolfach Seminars, 39 (Birkh auser Verlag, Basel, 2009). 9. H. Ohsugi, J. Herzog and T. Hibi, Osaka J. Math. 37, 745 (2000). 0. H. Ohsugi, Comment. Math. Univ. St. Pauli. 56, 27 (2007).. H. Ohsugi and T. Hibi, Ann. Inst. Statist. Math. 62, 639 (200). 2. 4ti2 team, 4ti2 - a software package for algebraic, geometric and combinatorial problems on linear spaces Available at 7 /7

山东2014第四季新教材《会计基础》冲刺卷第三套

山东2014第四季新教材《会计基础》冲刺卷第三套 2016 年会计从业考试会计基础冲刺卷 3 一单项选择题 ( 本题共 20 小题, 每小题 1 分, 共 20 分在下列每小题的备选项中, 有且只有一个选项是最符合题目要求的, 请将正确答案前的英文字母填入题后的括号内, 不选错选均不得分 ) 1.

ベイジアン ネットワーク

ベイジアンネットワーク