Qualitative Induction Dorian Šuc and Ivan Bratko Artificial Intelligence Laboratory Faculty of Computer and Information Science University of Ljubljana,

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