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al. Moreover,ery parsimose associatedng the tested
nt on the inhe Instructor
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tive manner.’e significant.
Lasso, we findal. (2017) isoin two parls (DCs) andne expression
iming to dehose two cellle. They end
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26 593 genes.
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lFDRのコントロールが可能
es in class c.
we are now lGithub

c,

Gene
ACTB
CD14
FCER1A
FCGR3AFTL
HLA-DPA1
IFI30

l 医療, 材料分野において科学的発⾒をサポートする機械学習基盤の構築
l 重要な特徴をデータから精度よく容易に⾒つけられる⼿法の研究開発
l 機械学習研究者以外でも容易に利⽤可能なソフトウェア開発

l 新規の科学的発⾒を容易にする基盤を確⽴し, ヘルスケア, 材料,
農業等の分野で⾰新を⽬指す
l 医療費の削減 (個別化医療, 疾病予測)l 材料発⾒の⼤幅な効率化

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l 少数特徴で⾼い予測性能l 特徴の信頼度がわかる （仮説検定）

l ⾮線形モデルは複雑 （誰も利⽤しない）
l ⾮凸最適化が利⽤される（最適化が難しい）

解釈性

教師あり⽊構造
Wasserstein距離 (ICML 2021)

チャレンジ

Wasserstein距離 (WD)は⾃然⾔語処理で盛んに利⽤されているが計算時間が⾮常に⼤きい問題がある。
WDと同等の性能を得られつつ、WDの数百倍⾼速に計算可能な教師あり⽊構造Wasserstein距離を提案。
Experimentp-value
0.961
0.026< 0.001
0.001
0.968< 0.001
0.002

Gene
IGJ
LYZ
MTRNR2L2
RPS3A
TMSB4X
TVAS5

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ript under review by AISTATS 2021

我々のチームでは2020年度までにカーネル法に基づ
The Turkish
confronted with a seriously high-dimensional problem
いた⾮線形選択的推論の確⽴をした。
where the number of features greatly exceeds thel選択的独⽴性検定
l選択的⼆標本検定
l選択的適合度検定

PeterJackNaylor/knockoff-MMD-HSIC

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Table 2: P-Values Of The Partial Target For The
Single-cell RNAseq Dataset

p-value< 0.001< 0.0010.420< 0.001
0.012
0.553

カーネル選択的推論(AISTATS 2022) A

lKnockoﬀ ﬁlterを初めてA
カーネル法(HSIC, MMD)に適⽤.

characteristics of monocytes is the expression of theCD14 protein; encouragingly, HSIC-Lasso selected
this gene as a discriminating feature. In fact, it also
selected six other genes which Villani et al. used in
multiple cell signatures: FCGR3A (DC4), FCER1A(DC2 and DC3), FTL (DC4), IFI30 (cDC-like), IGJ(pDC-like), and LYZ (cDC-like). Jointly, this shows
the ability of HSIC-Lasso to recover multiple genes
used to define the classes.
More exciting, however, are the genes which are
selected by HSIC-Lasso and were not used in theoriginal study. These might point to new molecularsignatures and functions that di↵erentiate these cell
types. For instance, one of these genes play a role
cMMD
Rawcells
in immunity: HLA-DPA1, which presenting(gaussian)like DCs use to present exogenous proteins to otherimmune cells. Another compelling example is ACTB,
which is involved in cell motility, a function relevantin migrating cells like monocytes or DCs.
Our method contributes to the detection of discriminatory features inasmuch it facilitates to formulateconfidence statements about the obtained results.

1−α

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Pearson B TR
2021)
(gaussian)(gaussian)
HSIC

DC

0.1

1−α

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(gaussian)

0.2

PC

0.0

0.3

0.1

0.4

0.2

0.5

Time Consumption

⽊構造Wasserstein距離: WdT (µi , µj ) = wv

sample size. Therefore, screening becomes more challenging and we consequently split the data evenly into
first and second fold. We screen 1 000 potentially influential features and apply the incomplete U-statistic
estimator of size 20. The remaining parameters wereset as in the previous experiment.
HSIC-Lasso in combination with screening allows for areasonably short computation time and selects 13 features. We find that all of the associated HSIC-targets
and most of the partial targets are significant, cf.
Table 2. Interestingly, one of the traditionally defining(AISTATS 2018, 2020)(ICLR 2019)(NeruIPS 2019)

本年度は我々のチームで開発しているHSIC Lasso法の選択的推論を提案しICML 2021にて報告。

遺伝⼦発現量データから重要な特徴を選択したところCD14, FCGR3A (DC4), FCER1A(DC2 and DC3), FTL (DC4), IFI30 (cDC-like), IGJ(pDC-like), LYZ (cDC-like) は重要であることが報告されていた (Science 2017). HLADPR1 は元論⽂では報告されておらず新規のバイオマーカーの可能性がある.

Pearson

0.3

TR

Due to the high number of possible customisations, this work can only be the starting point fora more in-depth analysis of our presented approachfor PSI with HSIC-Lasso. Besides, the definition andanalysis of more targets and the expansion of thepresented approach to other regularisation terms areinteresting topics for future work.

lK個の特徴を選択
lKnockoﬀ ﬁlterを⽤いて
検定を⾏う

0.4

1.00

0.5

0.75

0.50

0.00

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(gaussian)

DC

0.1
0.15

0.2
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α

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(gaussian)
HSIC(gaussian)

0.3
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measure
0.1
0.2
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DC

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(I
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Association measureHSIC(gaussian)Pearson0.15 0.50.25 0.6 0.350.7 0.450.8 0.55
0.4
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0.75
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0.4

illK:M

主要成果２: 最適輸送

構造のある最適輸送

我々のチームでは最適輸送の研究に取り組んでおり
特に構造のある最適輸送の研究に取り組んでいる

l複数⽊に基づいた⽊構造Wasserstein距離 NeurIPS 2019l不均衡⽊構造最適輸送の研究 NeurIPS 2020, AISTATS 2021
lNeural Architecture Search (NAS)への応⽤ NeurIPS2021
l異なるドメイン間の⽊構造最適輸送 AISTATS 2021
l密度⽐推定に基づいた最適輸送 ECML 2021
l⽊構造データにおけるBarycenter推定 arXiv 2019, 2021
l⾼次元データのための最適輸送 arXiv 2020
lWasserstein距離の再評価 arXiv 2021

✓

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0.5

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HSIC Lassoの選択的推論(ICML 2021)

⽊構造Gromov-Wasserstein
U
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9(AISTATS
2021)

NIVERSITY

l超⾼速に異なる空間の距離を測る⽅法

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Opt. Error (log scale)

主要成果１：高次元非線形特徴選択

⼭⽥ 誠

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⽬標

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High-Dimensional Statistical Modeling Team
Makoto Yamada
Centerfor
Advanced lntelligence Project

高次元統計モデリングチームの研究概要

2021年度主要成果

l カーネル選択的推論 （重要な特徴の選択）
l HSIC Lassoの選択的推論 (ICML 2021)l Knockoff filterに基づいた選択的推論 (AISTATS 2022)l 最適輸送（⾼次元データの類似度計算）

l ⾼次元・構造データの学習

l 教師あり⽊構造Wasserstein距離 (ICML 2021)
l 不均衡⽊構造最適輸送の研究 (AISTATS 2021)
l NASへの応⽤ (NeurIPS2021)
l 異ドメイン間の⽊構造最適輸送 (AISTATS 2021)
l ⽊構造Barycenter推定 (AISTATS 2022)

l 機械学習応⽤

l へシアン⾏列近似⼿法の提案 (arXiv 2021)
l Lassoの⾼速スクリーニング法 (NeurIPS 2021)
l ランダム特徴量に基づいた学習 (SDM 2021)
l 医療画像データからの学習

By Guillaume Paumier, from https://commons.wikimedia.org/wiki/File:DNA_microarray.svg

主要成果３：高次元・構造データの学習

背景:
GNN には万能近似能力がない
GNNの限界と克服⽅法を⽰した
しかし、GNN は特定のグラフ対をどんなパラメータを用いても区別できない、という問題がある
GNN は特定のグラフ対をどんなパラメータを⽤いても区↔ 標準的なニューラルネットワークは万能近似能力がある
別で きない、という問題が知られている。

(NeurIPS2019, SDM2021)

lGNNと局所分散アルゴリズムの類似性を指摘しGNNの近似度を⽰した。

GNNはどのような構造を区別できる・できないか？
l局所分散アルゴリズムでは決定的なものよりも乱択ア
ルゴリズムの⽅が良い近似度を達成できることを利⽤GNNはどのグラフ関数（グラフ x 頂点 → ラベル）を表現できるか？
しノード特徴量に乱数を連結する⽅法を提案。
あるパラメータが存在して GNN の出力が関数と一致する

グラフニューラルネットワーク (GNN) というモデルの限界を⽰し、その限界を克服する⽅法を⽰した。

5 / 24

Nystrom近似ニュートン法(arXiv 2021)
KYOTO UNIVERSITY

lNystrom近似に基づいたニュートン法⌘(Z ⌧ Z ⌧ + ⇢I)

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主要成果４：機械学習応用

解釈可能な組織
プロファイリングと分類

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2022年度の目標l
⾼次元データからの因果推論⽅法の提案
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l 最適輸送技術の医療応⽤
0.8
0.9
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l 新規バイオマーカーの発⾒