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Qualitative Induction
Dorian Šuc and Ivan Bratko
Artificial Intelligence Laboratory Faculty of Computer and Information Science
University of Ljubljana, Slovenia
Overview
• Learning of qualitative models
• Our learning problem: qualitative trees and qualitatively constrained functions
• Learning of qualitatively constrained functions
• Learning of qualitative trees (ep-QUIN, QUIN)
• QUIN in skill reconstruction (container crane)
• Conclusions and further work
Learning of qualitative models
Motivation: • building a qualitative model is a time-
consuming process that requires significant knowledge
• Learning from examples of system’s behaviour: – GENMODEL-Coiera, 89; KARDIO-Mozetič, 87; Bratko et al.,
89 – MISQ-Kraan et al., 91; Richards et al., 92– ILP approaches-Bratko et al., 91; Džeroski&Todorovski, 93
Learning of QDE or logical models
Our approach
• Inductive learning of qualitative trees from numerical examples; qualitatively constrained functions based on qualitative proportionality predicates (Forbus, 84)
• Motivation for learning of qualitative trees: experiments with reconstruction of human control skill and qualitative control strategies (crane, acrobot-Šuc and Bratko 99, 00)
Learning problem
• Usual classification learning problem, but learning of qualitative trees:
– in leaves are qualitatively constrained functions (QCFs); QCFs give constraints on the class change in response to a change in attributes
– internal nodes (splits) define a partition of the attribute space into areas with common qualitative behavior of the class variable
A qualitative tree example
• A qualitative tree for the function: z=x2-y2
z is monotonically increasing in its dependence on x and monotonically decreasing in its dependence on y
z is monotonically increasing in its dependence on x and monotonically decreasing in its dependence on y
z is positively related to x and negatively related to y
z is positively related to x and negatively related to y
z=M-,+(x,y) z=M
-,-(x,y) z=M+,+(x,y) z=M
+,-(x,y)
0
> 0
> 0
0
> 0
0
y
x
y
Qualitatively constrained functions (QCFs)
• M+(x) arbitrary monotonically increasing fn. of x
• A QCF is a generalization of M+, similar to qual. proportionality predicates used in QPT(Forbus, 84)
Gas in the container:
Pres = c Temp / Vol , c = n R > 0
Gas in the container:
Pres = c Temp / Vol , c = n R > 0Temp=std & Vol Pres
Temp & Vol Pres
Temp & Vol Pres
Temp=std & Vol Pres
Temp & Vol Pres
Temp & Vol Pres
QCF: Pres = M+,-(Temp,Vol)QCF: Pres = M+,-(Temp,Vol)
Temp & Vol Pres ?
Temp & Vol Pres ?
Temp & Vol Pres ?
Temp & Vol Pres ?
Learning QCFs
Pres = 2 Temp / Vol Temp Vol Pres315.00 56.00 11.25315.00 62.00 10.16330.00 50.00 13.20300.00 50.00 12.00300.00 55.00 10.90
Pres = 2 Temp / Vol Temp Vol Pres315.00 56.00 11.25315.00 62.00 10.16330.00 50.00 13.20300.00 50.00 12.00300.00 55.00 10.90
Pre
s
Numeric examples (points in attribute space)
Learning of the “most consitent” QCF:
1) For each pair of examples form a qualitative change vector
2) Select the QCF with minimal error-cost
Learning of the “most consitent” QCF:
1) For each pair of examples form a qualitative change vector
2) Select the QCF with minimal error-cost
QCF Incons. Amb.M+(Temp)
M-(Temp)
M+(Vol)
M-(Vol)
M+,+(Temp,Vol)
M+,-(Temp,Vol)
M-,+(Temp,Vol)
M-,-(Temp,Vol)
QCF Incons. Amb.M+(Temp)
M-(Temp)
M+(Vol)
M-(Vol)
M+,+(Temp,Vol)
M+,-(Temp,Vol)
M-,+(Temp,Vol)
M-,-(Temp,Vol)
1: (zero,pos,neg)
4: (neg,neg,neg)
2: (pos,neg,pos)
Qual. change vectors at point (315, 56, 11.25)Numeric examples (points in attribute space)
3: (neg,neg,pos)
Pre
s
QCF Incons. Amb.M+(Temp) 3 1
M-(Temp)
M+(Vol)
M-(Vol)
M+,+(Temp,Vol)
M+,-(Temp,Vol)
M-,+(Temp,Vol)
M-,-(Temp,Vol)
QCF Incons. Amb.M+(Temp) 3 1
M-(Temp)
M+(Vol)
M-(Vol)
M+,+(Temp,Vol)
M+,-(Temp,Vol)
M-,+(Temp,Vol)
M-,-(Temp,Vol)
Learning QCFs
QCF Incons. Amb.M+(Temp) 3 1
M-(Temp) 2,4 1
M+(Vol) 1,2,3 /
M-(Vol) 4 /
M+,+(Temp,Vol) 1,3 2
M+,-(Temp,Vol) / 3,4
M-,+(Temp,Vol) 1,2 3,4
M-,-(Temp,Vol) 4 2
QCF Incons. Amb.M+(Temp) 3 1
M-(Temp) 2,4 1
M+(Vol) 1,2,3 /
M-(Vol) 4 /
M+,+(Temp,Vol) 1,3 2
M+,-(Temp,Vol) / 3,4
M-,+(Temp,Vol) 1,2 3,4
M-,-(Temp,Vol) 4 2
Select QCF with minimal
QCF error-cost
Select QCF with minimal
QCF error-cost
qTemp=neg
qVol=neg
qPres=pos
qTemp=neg
qVol=neg
qPres=pos
Learning qualitative tree
• For every possible split, split the examples into two subsets, find the “most consistent” QCF for both subsets and select the split minimizing tree-error cost (based on MDL)
• Algorithm ep-QUIN uses every pair of examples
• An improvement: heuristic QUIN algorithm that considers also locality and consistency of qualitative change vectors
Algorithm ep-QUIN, example
• 12 learning examples that correspond to 3 linear functions
Induced qual. tree does not correspond to the intuition
ep-QUIN does not consider the locality of qual. changes
Improvement: algorithm QUIN
• Heuristic QUIN algorithm considers the locality and consistency of qualitative change vectors
Human notices 3 groups of near-by points; QUIN considers the proximity of examples
Qualitative change vectors of near-by points are weighted more
QUIN considers the consistency of the class’s qual. change at k nearest neighbors of the point
QUIN: same algorithm as ep-QUIN but with the improved tree-error cost (weighted qualitative change vectors)
• Heuristic QUIN algorithm considers the locality and consistency of qualitative change vectors
Human notices 3 groups of near-by points; QUIN considers the proximity of examples
Improvement: algorithm QUIN
Experimental evaluation
• On a set of artificial domains:– Results by QUIN better than ep-QUIN– QUIN can handle noisy data– In simple domains QUIN finds qualitative
relations corresponding to our intuition
• QUIN in skill reconstruction:– QUIN used to induce qual. control strategies
from examples of the human control performance
– Experiments in the crane domain
Skill reconstruction and behavioural cloning
• Motivation: – understanding of the human skill– development of an automatic controller
• ML approach to skill reconstruction: learn a control strategy from the logged data from skilled human operators (execution trace). Later called behavioural cloning (Michie, 93).
• Used in domains as: – pole balancing (Miche et al., 90)– piloting (Sammut et al., 92; Camacho 95)– container cranes (Urbančič & Bratko, 94)
Learning problem for skill reconstruction
• Execution traces used as examples for ML to induce:– a control strategy (comprehensible, symbolic)– automatic controller (criterion of success)
• Operator’s execution trace: – a sequence of system states and
corresponding operator’s actions, logged to a file at a certain frequency
Container crane
X0=0 L0=20
load
trolley
X
L
Xg=60 Lg=32
Used in ports for load transportation
Used in ports for load transportation
Control forces: Fx, FL
State: X, dX, , d, L, dL
Control forces: Fx, FL
State: X, dX, , d, L, dL
Based on previous work of Urbančič(94)
Control task: transport the load from the start to the goal position
Learning problem, cont.
Fx FL X dX d L dL 0 0 0.00 0.00 0.00 0.00 20.00 0.00 2500 0 0.00 0.00 -0.00 -0.01 20.00 0.00 6000 0 0.00 0.01 -0.01 -0.02 20.00 0.00 10000 0 0.02 0.10 -0.07 -0.27 20.00 0.00 14500 0 0.12 0.31 -0.32 -0.85 20.00 0.00 14500 0 0.35 0.59 -0.95 -1.49 20.00 0.01 ….… … … … … … …….
Fx FL X dX d L dL 0 0 0.00 0.00 0.00 0.00 20.00 0.00 2500 0 0.00 0.00 -0.00 -0.01 20.00 0.00 6000 0 0.00 0.01 -0.01 -0.02 20.00 0.00 10000 0 0.02 0.10 -0.07 -0.27 20.00 0.00 14500 0 0.12 0.31 -0.32 -0.85 20.00 0.00 14500 0 0.35 0.59 -0.95 -1.49 20.00 0.01 ….… … … … … … …….
Usual approach: induce decision trees;
COMPREHENSIBILITY
Usual approach: induce decision trees;
COMPREHENSIBILITY
QUIN in skill reconstruction, crane domain
• Qualitative trees induced from execution traces• Experiments with traces of 2 operators using
different control styles• Crane control requires trolley and rope control
Ldes= M+( X )
bring down the load as the trolley moves from the start to the goal position
Ldes= M+( X )
bring down the load as the trolley moves from the start to the goal position
Rope control• QUIN: Ldes= f(X, dX, , d, dL)
• Often very simple strategy induced
Trolley control
• QUIN: dXdes= f(X, , d)
• More diversity in the induced strategies
M-(X)M-(X) M+()M+()
X < 20.7X < 20.7
X < 60.1X < 60.1M+(X)M+(X)
yes
yes
no
no
First the trolley velocity is increasing
First the trolley velocity is increasing
From about middle distance from the goal (X=20.7) until the goal
(X=60.1) the trolley velocity is decreasing
From about middle distance from the goal (X=20.7) until the goal
(X=60.1) the trolley velocity is decreasing
At the goal reduce the swing of the rope (by
acceleration of the trolley when the rope angle
increases)
At the goal reduce the swing of the rope (by
acceleration of the trolley when the rope angle
increases)
Trolley control
• QUIN: dXdes= f(X, , d)
• More diversity in the induced strategies
M-(X)M-(X) M+()M+()
X < 20.7X < 20.7
X < 60.1X < 60.1
X < 29.3X < 29.3
M+(X)M+(X) d < -0.02d < -0.02
M-(X)M-(X) M-,+(X,)M-,+(X,)
M+,+,-(X, , d)M+,+,-(X, , d)
yes
yes
yes
yes
no
no
no
no
Enables reconstruction of individual
differences in control styles
Enables reconstruction of individual
differences in control styles
QUIN in skill reconstruction
Qualitative control strategies:
• Comprehensible
• Enable the reconstruction of individual differences in control styles of different operators
• Define sets of quantitative strategies and can be used as spaces for controller optimization
QUIN is able to detect very subtle and important aspect of human control strategies
Further work
• Qualitative simulation to generate possible explanations of a qualitative strategy
• (Semi-)Qualitative reasoning to find the necessary conditions for the success of the qual. strategy
• Reducing the space of admissible controllers by qualitative reasoning
• QUIN is a general tool for qualitative system identification; applying QUIN in different domains