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COMP9418 – Advanced Topics in Statistical Machine Learning
创建日期：2024-06-05 17:17:11
标签： COMP9418
Advanced Topics in Statistical Machine Learning

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Assignment 

COMP9418 – Advanced Topics in Statistical Machine Learning
Instructions
Late Submission Policy: The penalty is set at 5% per late day for a maximum of 5 days. This is the
UNSW standard late penalty. For example, if an assignment receives an on-time mark of 70/100 and is
submitted three days late, it will receive a mark reduction of 70/100 ∗ 15%. After five days, the assignment
will receive a mark reduction of 100%.
Form of Submission: This is an individual or group of two students assignment. Write the name(s)
and zID(s) in this Jupyter notebook. If submitted in a group, only one member should submit the
assignment. Also, create a group on WebCMS by clicking on Groups and Create and include
both group members.
You can reuse any piece of source code developed in the tutorials.
You can submit your solution via WebCMS.
Alternatively, you can submit your solution using give. On a CSE Linux machine, type the following on the
command line:
$ give cs9418 ass1 solution.zip
Recall the guidance regarding plagiarism in the course introduction: this applies to this assignment. If
evidence of plagiarism is detected, it will result in penalties ranging from loss of marks to suspension.
The dataset and breast cancer domain description in the Background section are from the assignment
developed by Peter Lucas, Institute for Computing and Information Sciences, Radboud Universiteit.
Introduction
In this assignment, you will develop some sub-routines in Python to implement operations on Probabilistic
Graphical Models. You will code an efficient independence test, learn parameters from complete data,
and classify examples. Our classifiers will be based on Bayesian networks (Week 2), Naïve Bayes and
Tree-augmented Naïve Bayes classifiers (Week 3).
We will apply these classifiers to the diagnosis of breast cancer. We start with some background information
about the problem.
Background
Breast cancer is the most common form of cancer and the second leading cause of cancer death in women.
Every 1 out of 9 women will develop breast cancer in their lifetime. Although it is impossible to say what
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exactly causes breast cancer, some factors may increase or change the risk for the development of breast
cancer. These include age, genetic predisposition, history of breast cancer, breast density and lifestyle factors.
Age, for example, is the most significant risk factor for non-hereditary breast cancer: women aged 50 or older
have a higher chance of developing breast cancer than younger women. The presence of BRCA1/2 genes
leads to an increased risk of developing breast cancer, irrespective of other risk factors. Furthermore, breast
characteristics, such as high breast density, are determining factors for breast cancer.
The primary technique used currently for the detection of breast cancer is mammography, an X-ray image of
the breast. It is based on the differential absorption of X-rays between the various tissue components of the
breast, such as fat, connective tissue, tumour tissue and calcifications. On a mammogram, radiologists can
recognise breast cancer by the presence of a focal mass, architectural distortion or microcalcifications. Masses
are localised findings, generally asymmetrical to the other breast, distinct from the surrounding tissues.
Masses on a mammogram are characterised by several features that help distinguish between malignant and
benign (non-cancerous) masses, such as size, margin, and shape. For example, a mass with an irregular shape
and ill-defined margin is highly suspicious for cancer, whereas a mass with a round shape and well-defined
margin is likely to be benign. Architectural distortion is focal disruption of the normal breast tissue pattern,
which appears on a mammogram as a distortion in which surrounding breast tissues appear to be “pulled
inward” into a focal point, often leading to spiculation (star-like structures). Microcalcifications are tiny
bits of calcium that may show up in clusters or patterns (like circles or lines) and are associated with extra
cell activity in breast tissue. They can also be benign or malignant. It is also known that most cancers are
located in the upper outer quadrant of the breast. Finally, several physical symptoms of breast cancer are
nipple discharge, skin retraction, and palpable lump.
Breast cancer develops in stages. The early stage is in situ (“in place”), meaning that cancer remains confined
to its original location. When it has invaded the surrounding fatty tissue and possibly has spread to other
organs or the lymph, so-called metastasis is referred to as invasive cancer. It is known that early detection of
breast cancer can help improve survival rates.
[10 Marks] Task 1 – Efficient d-separation test
In this part of the assignment, you will implement an efficient version of the d-separation algorithm. Let us
start with a definition for d-separation:
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Definition. Let X, Y and Z be disjoint sets of nodes in a DAG G. We will say that X and Y are d-separated
by Z, written dsep(X,Z,Y), iff every path between a node in X and a node in Y is blocked by Z where a
path is blocked by Z iff there is at least one inactive triple on the path.
This definition of d-separation considers all paths connecting a node in X with a node in Y. The number of
such paths can be exponential. The following algorithm provides a more efficient test implementation that
does not require enumerating all paths.
Algorithm. Testing whether X and Y are d-separated by Z in a DAG G is equivalent to testing whether X
and Y are disconnected (ignoring edge direction) in a new DAG G′, which is obtained by pruning DAG G as
follows:
1. We delete any leaf node W from DAG G as long as W does not belong to X ∪ Y ∪ Z. This process is
repeated until no more nodes can be deleted.
2. We delete all edges outgoing from nodes in Z.
More detail on this algorithm can be found on page 66 (and surrounding pages) in the textbook (Darwiche).
Implement the efficient version of the d-separation algorithm in a function d_separation(G,X,Z,Y) that
returns a boolean: true if X is d-separated from Y given Z and false otherwise.
[5 Marks] Task 2 – Markov blanket
The Markov blanket for a variable X is a set of variables that, when observed, will render every other variable
irrelevant to X. If the distribution is induced by DAG G, then a Markov blanket for variable X can be
constructed using X’s parents, children, and spouses in G. A variable Y is a spouse of X if the two variables
have a common child in G.
You will implement a function Markov(G, X) that returns a Python set with the Markov blanket of X in G.
After implementing this function, you can use the d-separation test to assess the correctness of your Markov
blanked implementation and vice-versa. You can use the definition of Markov blankets below to understand
the connection between these two concepts.
A Markov blanket for a variable X ∈ X is the set of variables B ⊆ X such that X /∈ B and X ⊥
X \ (B ∪ {X})|B.
[5 Marks] Task 3 - Learning the outcome space from data
In this and the following tasks, we will implement three classifiers: Bayesian network, Naïve Bayes and a
Tree-augmented Naïve Bayes classifier. We will need to create an outcome space for all these implementations.
We defined the outcome space as a Python dictionary in the tutorials, and it maps each variable to a tuple
with its possible outcomes. In the tutorials, we manually defined the outcome spaces for our examples.
However, as we work with more extensive problems, learning the outcome space from data becomes more
efficient.
Thus, in this task, you will implement a function learn_outcome_space(dataframe) that learns the outcome
space from the pandas dataframe. Refer to our tutorials for more details about how we defined the outcome
space dictionary.
[5 Marks] Task 4 – Estimate Bayesian network parameters from
data
Estimating the parameters of a Bayesian Network is a relatively simple task if we have complete data. The
file bc.csv has 20,000 complete instances, i.e., without missing values. This task will estimate and store the
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conditional probability tables for each graph node. As we will see in more detail in the Naïve Bayes and
Bayesian Network learning lectures, the Maximum Likelihood Estimate (MLE) for those probabilities are
simply the empirical probabilities (counts) obtained from data.
In this task, you will implement a method model.learn_parameters(data, alpha) that learns the parame-
ters of the Bayesian network model. This method should work the same as the function built in tutorials,
except also implement additive smoothing with parameter α.
[5 Marks] Task 5 – Bayesian network classification
The Bayesian Network previously described has a variable that plays a central role in the analysis. The
variable BC (Breast Cancer) can assume the values No, Invasive and InSitu. Accurately identifying its
correct value would lead to an automatic system that could help early breast cancer diagnosis.
First, the variables metastasis and lymphnodes must be removed since they can be understood as pieces
of information derived from BC and may not be available when BC is classified. This is done for you at the
beginning of the notebook.
Design a new method model.predict(class_var, evidence) that implements the classification with com-
plete data. This function should return the MPE value for the attribute class_var given the evidence. As
we are working with complete data, evidence is an instantiation for all variables in the Bayesian network
model but class_var. Implement the efficient classification procedure discussed in the lectures.
Assure that you only join the necessary factors.
[5 Marks] Task 6 - Bayesian network accuracy estimation
In this task, you will implement a function to measure the accuracy of the Bayesian network classifier. Design
a new function assess_bayes_net(model, dataframe, class_var) that uses the test cases in dataframe
to assess the performance of the Bayesian network. Such a function should return the classifier accuracy (a
value between 0 and 1) defined as:
Acc = TP + TN
TP + TN + FP + FN
where TP are the true positives, TN are the true negatives, FP are the false positives, and FN are the false
negatives.
[5 Marks] Task 7 - Bayesian network assessment with cross-validation
We will use k-fold cross-validation to generate training and test set pairs to assess our classifiers. In this
task, you will implement a function called cross_validation_bayes_net(G, dataframe, class_var, k)
to compute and report the average accuracy of the Bayesian network classifier specified by the graph G over
k = 10 cross-validation runs as well as the standard deviation.
We provide a scaffold for this function that uses the Scikit-learn class KFold.
[5 Marks] Task 8 - Naïve Bayes classifier structure
Let’s work now on the Naïve Bayes classifier. This classifier is a Bayesian network with a pre-defined graph
structure. This pre-defined structure can be directly learned from the dataset definition, i.e., the class
attribute and the features.
You will start creating a function learn_naive_bayes_structure(dataframe, class_var) that learns the
Naïve Bayes graph structure from a pandas dataframe using class_var as the class variable. This function
should return a graph object with the learned graph. The graph class was implemented in the first tutorial.
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[5 Marks] Task 9 – Naïve Bayes classification
As the Naïve Bayes classifier is a Bayesian network, we can use the existing BayesNet class to create a new
class NaiveBayes. Thus, the Naïve Bayes class will inherit all the methods we implemented for the Bayesian
networks.
In this task, we will also implement a new method for the Naïve Bayes class. The method
model.predict_log(class_var, evidence) implements the classification with complete data. It
differs from the implementation in Task 5 by using the log probability trick discussed in the lectures.
The method should return the MPE value for the attribute class_var given the evidence. As we work with
complete data, evidence is an instantiation for all variables but class_var.
[5 Marks] Task 10 - Naïve Bayes accuracy estimation
This task is similar to Task 6. You should implement a function assess_naive_bayes(model, dataframe,
class_var) that uses the test cases in dataframe to assess the performance of the Naïve Bayes classifier
model for the class variable class_var. This function will return the accuracy of the classifier according to
the test examples in dataframe.
[5 Marks] Task 11 - Naïve Bayes assessment with cross-validation
This task is similar to Task 7. You will implement a function called cross_validation_naive_bayes(dataframe,
class_var, k), compute and report the average accuracy and standard deviation of a Naïve Bayes classifier
over k = 10 cross-validation runs. We provide a scaffold for this function that uses the Scikit-learn class
KFold.
[15 Marks] Task 12 - Tree-augmented naïve Bayes structure
Let’s work now with the Tree-augmented Naïve Bayes classifier (TAN). The TAN classifier is a mid-term
between a Naïve Bayes and a Bayesian network, and it allows a richer graph structure learned directly from
data using mutual information.
We will start by creating a new function, learn_tan_structure(dataframe, class_var), that learns the
Tree-augmented graph structure from a pandas dataframe. Refer to Lecture 6, slide 24 for the algorithm
that describes the steps to learn the graph structure from data. Remind that mutual information (MI) was
defined in Lecture 3, slide 29.
Also, observe that the TAN classifier is a Bayesian network. Therefore, we can use the existing BayesNet
class to help implement this classifier.
[5 Marks] Task 13 - Tree-augmented naïve Bayes assessment with
cross-validation
In our final task, we will implement a function called cross_validation_tan(dataframe, class_var, k),
compute and report the average accuracy and standard deviation over k = 10 cross-validation runs. This
task is similar to Tasks 7 and 11. Notice we are not asking you to implement an assess_tan function since
it would be the same implemented for the Bayesian network classifier.
[20 Marks] Task 14 – Report
Write a report (with less than 500 words) summarising your findings in this assignment. Your report
should address the following:
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a. Make a summary and discussion of the experimental results. You can analyse your results from different
aspects such as accuracy, runtime, coding complexity and independence assumptions.
b. Discuss the time and memory complexity of the implemented algorithms.
Use Markdown and Latex to write your report in the Jupyter Notebook. If you want, develop some plots
using Matplotlib to illustrate your results. Be mindful of the maximum number of words. Please be concise
and objective.
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COMP2013 IB9X60 INVP001 EMATM0051 COMP220 BLAW1002 E20 TCP8001 ECON61001 EART40005 ECONM1022 MATH 365 MATH 367 ELEC6218 COMP 5812M EDUC 5061M ELEC ENG 1101 equation MATH6174 ST334 C4 EC9570 A33648 EBUS603 ECON47815 stata WFMS0001 PEM102 INF6060 ionically ELECTRICAL MATH 375 MMW 12 MKTG860 ECON60401 ALY6010 SOST20131 Introduction COM3524 MME2 GGR305 JNB 538 EECS101 COMM5030 IEOR E4601 2B CSC336 EN2315 LAW 432 CSC263 MATH2001 OLET1143 CSCB63 SIT772 COMM1170 STAT 441 MS930 INFT3050 GLBH0030 Stat 120B MAST10007 MGEC61 Machine GGR 252H1S ECON7030 Financial Marketing MGMT30019 ECON5120 SDSC 8009 CSC165H1S DSCI 551 3081W ACM41000 ECA 5304 MATH 1064 ECSE444 DATA 604 COMP7105 MIE1615 ECON4004 ENV200H1S EC481 MKT 306 EC1B1 MATH08051 ALY6140 CS260C CSE30 MSIN0226 CS4103 CSC3064 AM16 COMP11212 CSE4101 PSTAT 174 Math 380W CNT 5106C STAT 310 FIN2028 CS5014 STAT 425 COMP 4102A ELEC2140 MANF9544 QRM 9 QRM 8 ECON 457 COMPSCI 4091 MATH 523 DNSC-4211 PEAS 6000 MSIN0180 COMP2119 A2A HT 2022 IB93F0 MAS316/414 ACCT2522 MSIN0181 ATMS 201 COMP3425 MATH7861 SOLA2060 MA 325 7CCEMCTH ECON 432 INFT2051 SOLA 2060 ECOS2002 Stats141XP BIOA02H3 S2022 MA4601 K5 COMP5329 EG 284 IB3A70 WECO1020 COMP3027 Energy ACS61011 MAST20026 STAT 533 MATA31 ENVS257 BEM2031 EC 486 COMP0172 CS3214 EECE5644 IB2B20 COSC2536 COSC1147 COMP6214 5CCM242A COMP0130 AMME2000 MTMG50: EG238 ACF6006 QBUS2810 COSC2391 ECON7560 MATH377 STA305 CS 486 COMP1117B EL648 ELEC3909 ECON 241 COMP 4901W BUSI4428 ENEN20002 ENGN4524 ELEC3115 CSC 413 PSYC 100B ECON1002 MATH256 ANSC20005 MTHS2008 MATH40082 COSC 2406 FIT3174 STA 238 CMT202 Differential Equations MTHM017 GARCH 101 MATH2069 CSC336S ACSC12 ETF2121 CEME 2001 DB B474F ARHT1001 EECS 3311 3220 STATS 786 CS 484 COMP20008 MATH4091 ECE 455 CSCI 204 BUS B200F BA 875 BU5562 COSC 1147 X11 GEOG 101 IMM250F CSE 584A MATH38172 LAB 4 ELEC5882M FINS5523 EE 430 COMP 465 6CCS3PRE 7CCSMNSE FINANCE ACMB02H3 ENGG2112 ELEC5616 SCM B371 CHEM3120 CS22 ECMT2130 MAST30011 ADSPBF706 CENG0013 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