Introduction E R S V I T I N A U S Learning Bayesian - - PDF document

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Learning Bayesian Networks With Hidden Variables for User Modeling

Barbara Großmann-Hutter, Anthony Jameson, and Frank Wittig Department of Computer Science, University of Saarbrücken, Germany http://w5.cs.uni-sb.de/~ready/ (Slides, etc.)

Overview

• 1. Example domain and

experiment

• 2. Modeling the results by

learning Bayes nets Proposal 1 and issues Proposal 2 and issues ...

• 1. Conclusions
• 2. (Optional:) Why learn about

users−in−general?

Table of Contents

2

Introduction 1

[Title Page] 1 Table of Contents 2

Experiment: Method 3

✖

Experimental Setup 3 Stepwise vs. Bundled Instructions 5 Variables in Experiment 6

Experiment: Results 7

Main Results 7

Learning Bayes Nets 9

✗

1: Modeling Only Observable Variables 9 2: Hidden Theoretical Variable 11 3: Modeling Individual Differences 14 4: Constraining the Nature of Relationships 19 5: Choosing Learning Methods Flexibly 23

✘

Conclusions 25

✙

Conclusions 25

✘

Why Learn About Users-in-General? 26

Learning About Individual Users 26

✘

Learning About Users in General 27

✘

Which Approach to Use? 28

✘

SLIDE 2

3 Experiment: Method 4

Experiment: Method

Experimental Setup (1)

3

Experimental Setup (2)

4

SLIDE 3

5 Experiment: Method 6

Stepwise vs. Bundled Instructions

5

Stepwise:

✚

: Set X to 3

✛ : ... OK ✚

: Set M to 1

✛ : ... OK ✚

: Set V to 4

✛ : ... Done

Bundled:

✚

: Set X to 3, set M to 1, set V to 4

✛ : ... ... ... Done

Variables in Experiment

6

Independent variables

• 1. Presentation mode

✜

Stepwise vs. bundled

• 2. Number of steps in task

✜

2, 3 or 4 steps

• 3. Distraction by secondary task

✜

No secondary task vs. monitor the flashing lights

Dependent variables (selection)

• 1. Total time to execute an

instruction sequence Including "OK"s, etc.

• 2. Error in main task

✜

Buttons not pressed, or wrongly pressed

SLIDE 4

7 Experiment: Results 8

Experiment: Results

Main Results (1)

7

Distraction?

No Yes

Execution time (msec)

1000 2000 3000 4000 5000 6000

Three-step sequences:

Distraction?

No Yes

✢

Errors (%)

✣

10 20

✤

30

✥

40

Distraction?

No Yes

Execution time (msec)

1000 2000 3000 4000 5000 6000

Three-step sequences:

Main Results (2)

8 Distraction?

No Yes

Errors (%)

10 20

Distraction?

No Yes

Execution time (msec)

1000 2000 3000

Two-step

✦

sequences:

Distraction?

No Yes

Errors (%)

10 20 30 40

Distraction?

No Yes

Execution time (msec)

1000 2000 3000 4000 5000 6000

Three-step sequences:

Distraction?

No Yes

Errors (%)

10 20 30 40 50

Distraction?

No Yes

Execution time (msec)

1000 2000 3000 4000 5000 6000 7000

Four-step sequences:

SLIDE 5

9 Learning Bayes Nets 10

Learning Bayes Nets

1: Modeling Only Observable Variables (1)

9

Definition

✜

Structure is specified on the basis of theoretical considerations This holds for all nets discussed here

✜

Only observable variables of experiment are included in network

Positive points

✜

Learning can be done straightforwardly with many BN tools

✜

Learning is very fast (e.g., < 1 sec)

Negative points

✜

Little theoretical interpretability

✜

Relatively inefficient evaluation Too many parents per node

✜

Doesn’t take into account systematic individual differences

1: Modeling Only Observable Variables (2)

10

SLIDE 6

11 Learning Bayes Nets 12

2: Hidden Theoretical Variable (1)

11

Definition

✜

Hidden variable "Working Memory Load" added Basis: − Psychological theory − Previous experimental results

✜

Learning with Russell et al.’s APN algorithm ⇒

✧

Gradient descent

Positive points

✜

Better theoretical interpretability ⇒

✧

Easier to leverage existing psychological knowledge ⇒

✧

Possible to add or replace variables without relearning everything from scratch

✜

Relatively efficient evaluation

2: Hidden Theoretical Variable (2)

12

Negative points

✜

Learning times several orders of magnitude greater (hours or nights) Note: Partly due to current limitations of Netica, soon to be removed

✜

Some aspects of CPTs involving the hidden variable are implausible E.g., strangely nonmonotonic relationships

✜

Individual differences are still not taken into account

SLIDE 7

13 Learning Bayes Nets 14

2: Hidden Theoretical Variable (3)

13

3: Modeling Individual Differences (1)

14

Procedure

Add to each observation in the dataset a new observable feature: "Overall average execution time of the user in question" Distinction

✜

Variables that are naturally observable in an application setting

✜

Variables that can be made observable in an experimental setting How to do this: Exploit possibilities for measuring and controlling variables Ensure an appropriate number of observations from each subject and/or in each condition

SLIDE 8

15 Learning Bayes Nets 16

3: Modeling Individual Differences (2)

15

Positive points

✜

Accuracy of learned net is greater Here: 50% (vs. 44%) accurate prediction of

★

’s execution time in training set (Not in itself surprising or significant)

✜

When the individual-speed variable can be assessed (with uncertainty) in an application situation, prediction accuracy will be improved

Negative points

✜

CPTs are still sometimes implausible

3: Modeling Individual Differences (3)

16

SLIDE 9

17 Learning Bayes Nets 18

3: Modeling Individual Differences (4)

17

3: Modeling Individual Differences (5)

18

SLIDE 10

19 Learning Bayes Nets 20

4: Constraining the Nature of Relationships (1)19

Basic idea

✜

Formulate theoretically motivated qualitative constraints E.g., "More steps ⇒ Higher WM load"

✜

Ensure that only networks that (almost) satisfy these constraints can be learned

Procedure

• 1. Translate qualitative formulations of constraints into quantitative

inequalities concerning conditional probabilities See Druzdzel & van der Gaag (UAI95)

• 2. Define a corresponding penalty term for nets that violate a constraint
• 3. Factor in the penalty term when determining the next step in the

gradient descent

• 4. (Strategy tried up to now:)

Give the penalty term less weight as the search proceeds Motivation: Otherwise it might take forever to find a solution

4: Constraining the Nature of Relationships (2)20

✩

Positive points

✜

The learned nets do satisfy the constraints better

Negative points

✜

There are still some constraint violations

SLIDE 11

21 Learning Bayes Nets 22

4: Constraining the Nature of Relationships (3)21

✩

4: Constraining the Nature of Relationships (4)22

✩

SLIDE 12

23 Learning Bayes Nets 24

5: Choosing Learning Methods Flexibly (1)

23

✩

Basic idea

Each CPT can be seen as a learning problem with its own specific features So why not choose the most suitable learning technique for each CPT (cf. Musick, KDD96)? Example: If you think that A and B have a linear influence on C, use linear regression to estimate the parameters

Simple application here

• 1. For CPTs that involve only observable variables, use simple

methods

• 2. Then fix these CPTs before starting to use gradient descent

Positive points

✜

Saves a lot of learning time Here: about 1/3

✜

Perhaps better prediction of extreme observations?

5: Choosing Learning Methods Flexibly (2)

24

✩

SLIDE 13

25 Conclusions 26

Conclusions

25

✩

What

✪

have we done?

✜

First(?) example of learning an BN with a hidden variable for user modeling

✜

Example of using BN learning to explain results of a psychological experiment

✜

Identification of several problems that seem especially important for BN learning in this context

✜

Outline of briefly tested possible solutions to these problems

What

✪

do we have to do now?

✜

Investigate possible answers more thoroughly

✜

In particular perform thorough and systematic evaluations

✜

Look into further issues of this sort E.g., What is the best criterion here for evaluating a learned net? Should it be evaluated in terms of success at the particular tasks for which the net is to be used?

• Cf. Greiner et al. (UAI97); Kontkanen et al. (UAI99)

Why Learn About Users-in-General?

Learning About Individual Users

26

✩

USAGE DATA FROM A SINGLE USER

✫

DECISION-RELEVANT PREDICTIONS FOR

✫ ✫

’S PREFERENCES OR BEHAVIORAL REGULARITIES LEARNING ABOUT

✫

APPLICATION OF LEARNED KNOWLEDGE ABOUT

✫

SLIDE 14

27 Why Learn About Users-in-General? 28

Learning About Users in General

27

✩

USAGE DATA FROM A REPRESENTATIVE SAMPLE OF USERS MODEL EMBODYING KNOWLEDGE OF USERS IN GENERAL LEARNING ABOUT USERS IN GENERAL

USAGE DATA FROM A SINGLE USER

✬

DECISION-RELEVANT PROPERTIES OF

✬

GENERALLY RELEVANT PROPERTIES OF

✬

INTERPRETATION OF

✬

’S DATA WITH GENERAL MODEL PREDICTIONS FOR

✬

ON BASIS OF GENERAL MODEL

Which Approach to Use?

28

✩

When

✪

to learn for users in general?

✜

Useful generalizations can be made about all users

✜

These generalizations are not obvious but must be learned from data

✜

Only limited data is available about any given user

When to learn for each individual user?

✜

There are few nontrivial generalizations

✜

Individual users differ not only in details but in their overall structure, strategies, etc.

✜

A reasonably large about of data is available for each user