仮説を立てて考えてみよう
Let's Hypothesize and Reason!
井上 克巳 Katsumi Inoue
アンドレイ・ドンチェスク Andrei Doncescu (LAAS-CNRS)
山本 泰生 Yoshitaka Yamamoto
オリヴァ－・レイ Oliver Ray (University of Bristol)
Automated hypothesis-finding through
deductively complete methods.
Intelligent machines --Thinking like human being.
Automated discovery of scientific knowledge,
in particular biological knowledge.
Induction of causal laws in action theories,
and applications to systems biology.
Web-based ILP system.
Background
How Intelligent Machines Think ?
How Human Beings Think ?
Observation
Induction
Everyday Life
Business
Science
Induction
Prediction
Hypothesizing
and
Reasoning
Abduction
Abduction
Deduction
Hypothesis
Generation
Deduction
The genius people are able to mix these
three fundamental modes of reasoning.
Combination of
Induction and
Abduction
Diagnosis
Design
Characterization
Discovery
Verification
One of the most powerful theoretical
answers for the next generation of
Intelligent Machine (Inoue 2001,2004)
Logic and Computation
IE for Abduction
Abduction and Induction: Logic
Input:
B : background theory
E : examples ／observations
Output:
H : hypothesis satisfying that
• SOLAR (Nabeshima, Iwanuma & Inoue 2003)
B: full clausal theory
E: conjunction of literals (￢ E is a clause)
H: conjunctions of literals (￢ H is a clause)
Example: graph completion problem – pathway finding
Find an arc which enables a path from a to d.
1. B ∧ H ⊨ E,
Axioms: [￢node(X),￢node(Y), ￢arc(X,Y), path(X,Y)].
2. B ∧ H is consistent.
[￢node(X), ￢node(Y), ￢node(Z), ￢arc(X,Y), ￢path(Y,Z), path(X,Z)].
[node(a)]. [node(b)]. [node(c)]. [node(d)].
Inverse Entailment (IE)
[arc(a,b)]. [arc(c,d)].
a
c
Computing a hypothesis H can be done deductively by: Negated Observation: [￢path(a,d)].
Production_field: [￢arc(_,_)].
B ∧￢E ⊨￢H
SOLAR outputs four consequences:
[￢arc(a, d)] , [￢arc(a, c)], [￢arc(b, d)], [￢arc(b, c)] b
d
We have good tools for this inverse computation.
IE for Induction
B
ILP
machine
E
ILP machine
H
• CFCF-induction (Inoue 2004: Yamamoto, Ray & Inoue 2007)
• fcfc-HAIL (Inoue & Ray 2007)
B, E, H:
full clausal theory
Note: CF-induction is the only existing ILP system that is
complete for full clausal theories.
Correspondence： 井上 克巳 （Katsumi Inoue）／ 国立情報学研究所 情報学ﾌﾟﾘﾝｼﾌﾟﾙ研究系 教授
TEL & FAX: 03-4212-2520
Email : ki@nii.ac.jp
推論による仮説発見とシステム生物学への応用
Inference-based Hypothesis-Finding for System Biology
アンドレイ・ドンチェスク Andrei Doncescu (LAAS-CNRS)
井上 克巳 Katsumi Inoue
山本 泰生 Yoshitaka Yamamoto
Discover hidden rules in systems biology.
Use Inductive Logic Programming (ILP).
Bridge between biologists and computer
scientists, due to the possibility to
represent biologist knowledge in the
form of logical formulas.
Explain the relationships between causes
and effects from genotype to phenotype.
Use generic models in biology,
Saccharomyces Cerevisiae and E-coli.
Modeling
Phenomenological
METABOLIC Analyzer
models
Yield PHB
5
4
3
2
Glucose
ATP
Glucose6-P
30
20
10
0
ª Simulation
0.91.0
0.70.8
0.6
0.5
0.4
0.3
0.2
0.1
0.0
Proteins
IsoCitrate CO
SH-CoA
aKglu
2
NADH,H+
NADPH,H+
CO2
Structural Models
Suc-CoA
CO2
GTP
SH-CoA
NADH,H+
ª Metabolic Constraints
ª Optimization
Phenotype
Metabolites
ANABOLISME
NADH,H+
Fumarate
FadH2 Succinate
ª Genomic Response
HS-CoA ATP
NADPH,H+ ATP
Citrate
OAA
Malate
40
RNA (microchips)
Pentose P
+ ATP
Fructose-P NADH,H
ATP
glycerol
GlycerolP
Sedoheptulose7 P TrioseP
+
NADH,H NADH,H+ H 0 + 4H+
2
ATP
Glycerate3P
Erythrose4P
NAD
1/2 O2
FADH2
H20 + 2H+
PEP
FAD
1/2 O2
ATP
3 H+
Pyruvate HS-CoAATP
NADH,H+
CO
2
NADPH,H+ ATP CO2
CO2
Acétate
Acetyl CoA
CO2
1
50
DNA
Genotype
2NADPH,H+
CO2
0
ªINTRACELLULARE
pools
ª Stoichiometric Modeling
Metabolic pathway: sequences of enzyme-catalyzed
reaction steps, converting substrate to a variety of
product to meet the needs of the cell.
Flux: the rate at which material is processed
trough a metabolic pathway.
Approach
Previously proposed methods
Our approach
Using the stoichiometric model
- dynamic behavior:
dC
= v in − v out − μ C
dt
Using the logical model (causal relations)
Observation: the concentration of B increases.
Background knowledge:
if the concentration of A increases,
the reaction A→B is accelerated and
the reaction B→C is inhibited, then
the concentration of B increases.
- steady states:
metabolite flux balancing
v1 = v 2 + rB
• Using the simple metabolic pathway (Pyruvate)
• Results obtained by CF-induction
B:
reaction(pyruvate, acetylcoa). reaction(pyruvate, acetaldehide).
reaction(glucose, glucosep). reaction(glucosep, pyruvate).
reaction(acetaldehide, acetate). reaction(acetate, acetylcoa).
reaction(acetaldehide, ethanol). concentration(glucose, up).
terminal(ethanol).
blocked(X)←reaction(X,Z), inhibited(X,Z).
blocked(X)←terminal(X).
X
E:
Z
X
concentration(X,up) ←reaction(Y,X), ￢inhibited(Y,X),
blocked(X).
A
Y
X
concentration(ethanol,up). concentration(pyruvate, up).
v1
C
B
rB
v2
Hypothesis:
the concentration of A increases,
the reaction A→B is accelerated and
the reaction B→C is inhibited.
¾ Not only estimating possible reaction states, but also discovering
new pathway rules that are missing in the current background theory
H1 :
￢Inhibited(glucosep, pyruvate).
￢inhibited(acetaldehide, ethanol).
inhibited(pyruvate, acetylcoa).
H2 :
￢inhibited(glucose, glucosep)
Glucose
Glucose-P
Pyruvate
Acetaldehide
Acetylcoa
Acetate
￢Inhibited(glucosep, pyruvate).
Glucose
￢inhibited(acetaldehide, ethanol).
Glucose-P
￢inhibited(pyruvate, acetaldehide).
concentration(X, up)← ￢inhibited(Y, X),
concentration(Y, up).
Pyruvate
Acetaldehide
Acetylcoa
Acetate
Correspondence： 井上 克巳 （Katsumi Inoue）／ 国立情報学研究所 情報学ﾌﾟﾘﾝｼﾌﾟﾙ研究系 教授
TEL & FAX: 03-4212-2520
Email : ki@nii.ac.jp
Ethanol
Ethanol