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Pablo Silva LZ1LUZ [email protected] | Artificial Intelligence | December 13, 2013

Knowledge and data

engineering with BayesiannetworksREPORT HOMEWORK


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Task 1 Domain description

My model is about AI classes. The purpose of the model is to find out the probability that an AI

class be interesting under some situations.

Task 2 Variable definitions

VARIABLES:

Lecturer:o Represents: the lecturer of the AI class in someday.o Value Range: Peter Lang, Pter Antal.o Depends on:nothing.

Winter:o Represents: the current season is autumn.o Value Range:binary (true, false).o Depends on:nothing.

Place:o Represents: the building where the classes are on.o Value Range:E504, Q408.o Depends on:nothing.

Subject:o Represents: the subject taught in class.o Value Range: Bayesian networks, another.o Depends on: Lecturer.

Delay:o Represents: the lecturer comes in time for the class.o Value Range:binary (true, false).o Depends on:Lecturer, Winter, Place.

Agreeableness:o Represents: how interesting was the class for the students.o Value Range: excellent, good, bado Depends on: Subject and Delay.

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Task 3 Structure of the Bayesian network

Figure 1 - Structure of the BN

If the student likes or not the class depends on whether there is a delay to start the lesson and which

the subject was taught. Some late in class could happens if the lecturer does not come in time and

this could be affected by the place and the weather or not. Finally the subject only depends on aboutwhat the lecturer thinks that is good for teaching for his students.

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Task 4 Quantify the Bayesian network

P(Lecturer) Peter Antal Another0.9 0.1

Peter is the official lecturer of the AI classes, therefore just in specials occasions will be not him to

be a lecturer.

P(Winter) True False

0.25 0.75

In Hungary, its winter about 25% of the time.

P(Place) E504 Q408

0.5 0.5

There are two classes per week and on Mondays it is in E504 and on Wednesday it is in Q408.

P(Subject) BNs Another

Lecturer=Peter Antal 0.7 0.3

Lecturer=Another 0.5 0.5

Peter seems to like of BNs and the others times that was not him teaching, the classes were middle

about BNs.

P(Delay) True False

Lecturer=Another,Winter=False,Place=Q408 0.1 0.9

Lecturer=Another,Winter=False,Place=E504 0.3 0.7

Lecturer=Another,Winter=True,Place=Q408 0.1 0.9

Lecturer=Another,Winter=True,Place=E504 0.3 0.7Lecturer=Peter Antal,Winter=False,Place=Q408 0.2 0.8

Lecturer=Peter Antal,Winter=False,Place=E504 0.3 0.7

Lecturer=Peter Antal,Winter=True,Place=Q408 0.3 0.7

Lecturer=Peter Antal,Winter=True,Place=E504 0.4 0.6

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Delays occur with greater intensity when the classes are at building E504 because the lecturer need

get the projector far from that building. Despite this, most of the classes are in time.

P(Agreeableness) Bad Good Excellent

Subject=Another,Delay=True 0.2 0.5 0.3

Subject=Another,Delay=False 0.1 0.4 0.5

Subject=BNs,Delay=True 0.2 0.4 0.4

Subject=BNs,Delay=False 0.1 0.4 0.5

In general the students do not complain about the AI classes, just in case of some delay, but

nevertheless are just few ones. The best classes are when does not have a delay and the subject is

BNs.

Task 5 Inference and sensitivity analysis

My inferences are as follows:

What is the probability that the class will be excellent when nothing else is given? P(Agreeableness=Excellent) = 0.464

If the class start late, which is the chance of the class being excellent? P(Agreeableness=Excellent|Delay=true) = 0.368

Peter needed miss the class because the winter and then the class was in building E504,which is the probability of the one has been excellent?

P(Agreeableness=Excellent|Lecturer=Another,Winter=true,Place=E504) = 0.455

Because of the rigorous winter Peter could not go to class and the substitute lecturer taughtsearch methods because him did not liked BNs. What the students though about the class?

P(Agreeableness|Lecturer=Another,Subject=Another,

Winter= true)

Bad Good Excellent

0.12 0.42 0.46

If the class was excellent, what is the chance of the lecture has been Peter Antal?

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P(Lecturer=Peter Antal|Agreeableness=Excellent) = 0.898

The Sensitivity Analysis of P(Agreeableness=excellent|Subject,Delay). Such analysis could be seen

on Figure 1:

Figure 2 - Example of Sensitivity Analysis

Computing the values using normal inference:

P(Agreeableness|Delay) Excellent

Delay=true 0.368

Delay=False 0.5

Difference is: ~0.132

P(Agreeableness|Subject) Excellent

Subject=BNs 0.473

Subject=Another 0.447

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Difference is: ~0.026

As we can see, the value of Delay has a greater impact on the random variable Agreeableness than

Subject.

Task 6 Compare Differences of constructed and learnt models

The parameters I used for sample generation and learning:

Sample Size: 10000Prior: CHMax. parent count: 5Max. permutation: 80

The learnt structure:

Figure 3 - Learning with 10000 samples

As we can see, the structure resembles the original except for the Winter random variable. The

CPTs are changed accordingly the new model which can be seen in the attached

PHAS_LZ1LUZ_HW_AI2013_learning_structure_10000s.xml.

Proper examination whether the two models are the same is out of this works reach but let us retry

some queries:

P(Agreeableness=Excellent) = 0.472 (prev.: 0.464) P(Agreeableness=Excellent|Delay=true) = 0.365 (prev.: 0.368)

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P(Agreeableness=Excellent|Lecturer=Another,Winter=true,Place=E504) = 0.447 (prev.:0.455)

As we can see, even the model learnt does not be exactly identical to the designed the queries had

almost the same result which indicates the resemblance.

Task 7 Analysis estimation biases

OVERCONFIDENCE

I have changed the Lecturer and Delay variables to make my model overconfident.

P(Lecturer) Peter Antal Another

0.915 0.0842

P(Delay) True False




Lecturer=Another,Winter=True,Place=E504 0.2584 0.7416

Lecturer=Peter Antal,Winter=False,Place=Q408 0.1702 0.8298




Rerunning my queries, I got the following result:

P(Agreeableness=Excellent) = 0.469 (prev.: 0.464)

P(Agreeableness=Excellent|Delay=true) = 0.368 (prev.: 0.368)


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Winter= true)

Bad Good Excellent

0.117

(prev.:0.12)

0.417 (prev.:

0.42)

0.466 (prev.:

0.46)

P(Lecturer=Peter Antal|Agreeableness=Excellent) = 0.914 (prev.: 0.898)It is possible see that the probability of the class be excellent if the lecturer is Peter Antal increases.

This happens because before the variable Delay had a greater bias that associated the delay on classes

with the Lecturer Peter Antal and with overconfidence the delay associated with Peter decreased.

UNDERCONFIDENCEI have changed the Lecturer and Delay variables to make my model underconfident.

P(Lecturer) Peter Antal Another

0.5626 0.4374

P(Delay) True False




Lecturer=Another,Winter=True,Place=E504 0.4557 0.5443

Lecturer=Peter Antal,Winter=False,Place=Q408 0.4438 0.5562




Rerunning my queries, I got the following result:

P(Agreeableness=Excellent) = 0.437 (prev.: 0.464)

P(Agreeableness=Excellent|Delay=true) = 0.361 (prev.: 0.368)

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Winter= true)

Bad Good Excellent

0.145(prev.:0.12)

0.445 (prev.:0.42)

0.410 (prev.:0.46)

P(Lecturer=Peter Antal|Agreeableness=Excellent) = 0.567 (prev.: 0.898)We can see for all queries about Agreeableness had a lower excellent value. This is due to the

previously values for the Lecturer and Delay had a bias in the sense that the lecturer be almost always

Peter Antal and the Delay in classes happens in very few quantities. When the Peter is the lecturer

the chance of has a class about BNs is higher and has less delays and seems that the students likemore to learn about BNs and when the classes starts on time. With this two facts underconfidents,

the positive effect in Agreeableness was lower.

On the last query about which the chance of the lecturer be Peter if the class was excellent had a big

decrease once previously had a bias in the variable Delay in sense that when the lecturer was Peter

Antal the delay happens with less frequency and then the classes were better and also had a bias on

the variable Lecturer that in the most part of the classes the lecturer was Peter Antal and combined

with less Delay the class were nicer. Therefore the effect of the Peter in the Agreeableness of the

classes is lower now.

Task 8 Effects of model uncertainty and sample size on learning

Undersampled model:


Sample Size: 1000Prior: CH

Max. parent count: 5Max. permutation: 80


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We can see that the model learnt has significant differences compare with the original one. Thearrows now indicate dependencies that didnt have before. In this sense we can make a few queriesto discover how much this changes influence in the knowledge of the model:

Original Learnt (10000samples)

Learnt (1000samples)

P(Agreeableness=Excellent)0.464 0.472 0.476

P(Agreeableness=Excellent|Delay=true)0.368 0.365 0.391

P(Agreeableness=Excellent|Lecturer=Another,Winter

=true,Place=E504)0.455 0.447 0.457

Analyzing the results we can see that the role of the samples has a big influence on the results. Aswe can see Agreeableness is an independent variable and because this it tends to be greater without

influence of the evidences.

Underconfident model:


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Sample Size: 10000Prior: CHMax. parent count: 5Max. permutation: 80


Analyzing the structured learned we can see that in this time there are no isolated nodes, but there

are serious problems with the dependencies and the newer structure does not remember the original

one. Lets check how it is accurate comparing the queries:

Originalunderconfident

Learntunderconfident

P(Agreeableness=Excellent)0.437 0.467

P(Agreeableness=Excellent|Delay=true)0.361 0.369

P(Agreeableness=Excellent|Lecturer=Another,Wint

er=true,Place=E504)

0.431 0.467

Looking in the table we can see that the queries had similar answers without big discrepancies but

of course was expected that the accuracy would be lower than the original one.

Analyzing both test realized we can conclude that the models probability distributions (CPTs) and

sample size make a big difference when learning is being talked about. In the first one, with few

samples, the entire structure was prejudiced and in the second one the dependencies were big

influenced by the probabilities distributions.

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