Discrete Structural Statistics
for Cancer Science:
2016 Progress

Koji Tsuda (U. Tokyo)
Kenji Kadomatsu (Nagoya U.)
Ichiro Takeuchi (Nagoya Inst. Tech.)
Jun Sese (AIST)
Ryo Yamada (Kyoto U.)1New)Statistical)Test,)Cancer)ScienceHypotheses)Set
Discrete(MathematicsZDD,)SAT,)WISH)etc
Statistics
FDR,Permutation

Discrete)StructuralStatistics)

Structure)Introduced)Cancer(Science(Closure)Operator
Statistical)Pruning2

2016)Highlights• New)statistical)principle:)Selective)inference)– Suzumura et)al.,)in)submission• Improved)efficiency)in)pattern)mining)(POSTER)– Nakagawa)et)al.,)KDD)2016.

• Neuroblastoma)SingleRCell)RNARSeq experiments– OnRgoingTesting)after)selection• Select)features)by)LASSO)and)compute)pRvalues– Selection)bias:)pRvalues)are)too)good!)• Remedy)1:)Consider)unselected)features)as)well)(e.g.,)LAMP)• Remedy)2:)Condition)on)the)selection)event

Selection)by)
LASSOComputing)pRvalue(X, y) ! (x2 , x7 )corr(x2 , y) = 0.90
Comparecorr(x2 , ỹ1 ) = 0.10
corr(x2 , ỹ2 ) = 0.82
corr(x2 , ỹ3 ) = 0.23
corr(x2 , ỹ4 ) = 0.30
corr(x2 , ỹ5 ) = 0.92
With)permutated)outcomesSelection)by)
LASSOComputing)pRvalue(X, y) ! (x2 , x7 )corr(x2 , y) = 0.90
Compare(X, ỹ1 ) ! (x1 , x9 )(X, ỹ2 ) ! (x2 , x7 )(X, ỹ3 ) ! (x3 , x4 )(X, ỹ4 ) ! (x8 , x9 )(X, ỹ5 ) ! (x2 , x7 )corr(x2 , ỹ1 ) = 0.10
corr(x2 , ỹ2 ) = 0.82
corr(x2 , ỹ3 ) = 0.23
corr(x2 , ỹ4 ) = 0.30
corr(x2 , ỹ5 ) = 0.92
With)permutated)outcomesSelection)by)
LASSOComputing)pRvalue(X, y) ! (x2 , x7 )corr(x2 , y) = 0.90
Compare(X, ỹ1 ) ! (x1 , x9 )(X, ỹ2 ) ! (x2 , x7 )(X, ỹ3 ) ! (x3 , x4 )(X, ỹ4 ) ! (x8 , x9 )(X, ỹ5 ) ! (x2 , x7 )corr(x2 , ỹ1 ) = 0.10
corr(x2 , ỹ2 ) = 0.82
corr(x2 , ỹ3 ) = 0.23
corr(x2 , ỹ4 ) = 0.30
corr(x2 , ỹ5 ) = 0.92Use)them)only)!

With)permutated)outcomes2016)Highlight)1:)Selective)inference)in)pattern)mining• Computation)of)selective)null)distribution)needs)reference)to)all)features• Impossible)in)combinatorial)cases)• New)bound)for)disregarding)large)patterns)!

HIV)drug)resistance2016)Highlight)3:)
Single)cell)RNARseq for)Neuroblastoma• 2014:)Bulk)analysis)=)Average)of)many)cells• 2014:)Single)cell)analysis)(10x)Genomics)

Plan)of)experiments
0R1w
Other)cell

2R3w

1Ganglion)cell

5R6w

10R20w

11/1

WT
Neuroblast

1MYCN (+))cell

2/8

220%

MYCNRTg

280%

Tumor

Cancer)cells)detected)clearly••••••Cluster)1:)Neuroblastoma)cells)(MYCN))
Cluster)2:)Ganglion)cells)(Npy,)Dbh,)Ntrk1)
Cluster)3:)Glial)cells)?)(Dbi,)
Fabp7,)Arpc1b)
Cluster)4:)Fibroblasts)?)(Dcn,
Col3a1,)Lum,)Igfbp6,)Acta2)
Cluster)5:)Myeloid)cells,)
probably)macrophages)(Lyz2,)C1qa,)C1qb,)C1qc,)
Ftl1)
Cluster)6:)Endothelial)cells)?)(Egfl7,)Id3,)Plvap,)Esam,)
Cldn5)

Summary• New)directions)emerged)in)2016• Biological)experiments)going)well• 2017:)New)discoveries)in)cancer)science• Awareness: Invited)session)in)MCP)2017)!

Safe Pattern Pruning:
An Efficient Approach for Predictive Pattern Mining
中川和也(名工大), 鈴村真矢(名工大), 烏山昌幸(名工大), 津田宏治(東大), 竹内一郎(名工大) KDD2016 採択論文
 グラフの性質を特徴づける部分構造を見つけたい-1-1

 スパース学習を行う+1

データベースf=

w1 +w2 +w3 +w4 + …

Safe Pattern Pruning

𝑆𝑐𝑜𝑟𝑒 𝑡 < 1t∗
𝑤𝑡 ′ = 0

 最適解においてスパースとなる部分木を同定・プルーニングできる
 各ノードにおけるscore計算には最適解を必要としない (近似解を使う)

LAMPLINK: detection of statistically significant
SNP combinations from GWAS data
発表者: 寺田愛花（JST さきがけ/東京大学）

がん患者
...
...
...

...
...
...
...

...
... SNP単体 − 疾患発症
...
...

健常者

SNP pair − 疾患発症
c5?

nQQ

Epistatic
pair effect1.5

Test statistic

Q-ee

Individual QTL

QqEe

Individual QTL

0Genomic location (M)0.5

QTL pairs
Test statistic between 1 and 2
Test statistic between 0 and 1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

1

1.5

Test statistic

Test statistic between 2 and 34-log10(P)疾患発症に関与するSNPδ

...
...
...

qqee

SNP: 数万〜数百万カ所

Marginal effects

1• FastANOVA(Zhang, X., et al. 2008)

Kochi et al., Nat. Genet., 2010 を一部改変

3個以上のSNP − 疾患発症
MTRR(Chr 5)

FREM2(Chr 13)• PLINK(Purcell, S., et al. 2007)

0.5

0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Genomic location (M)itative trait loci and epistatic quantitative trait locus mapping. Quantitative trait locus (QTL) mapping aims to
it into the effects of individual loci. a | The F2 design for QTL mapping uses a three-generation pedigree, and requires
and a linkage map of polymorphic molecular markers. The hybrid F1 generation derived from the parental lines ise, one full sibling family of n individuals that differ in the proportion of markers that they have inherited from the parental
statistically to determine whether there is a difference in phenotype between marker genotype classes. If there is, thened to the marker. b | In principle, individual QTL mapping searches for the partitioning of the F2 individuals according to thec variation within the genotype classes and the largest differences among the genotype classes. Epistatic QTL mappinggenotypes at multiple loci (for example, Q and E), which ensures a better fit if the phenotype depends on the genotypes
ults in a statistical support curve for the individual effects of a QTL at each tested location in the genome (two greens results in a statistical support surface for all potential combinations of QTL locations in the genome (centre panel). QTLs
high peaks in the individual QTL support curve and as ridges in the QTL-pair support surface. A stepwise approach forCarlborg & Haley,
Nat. Rev. Genet. (2004).

Terada, A et al. Bioinformatics 32(22), 3513–3515