Department of Computing and Information Systems

COMP90049

Introduction to Machine Learning

June 2021

Section A: Short answer Questions

 Answer each of the questions in this section as briefly as possible. Expect to answer each question in 1-3 lines, with longer responses expected for the questions with higher marks.

 Question 1:

(a) Name one classifier which can achieve perfect test performance on any linearly separable data set; and one classifier which cannot. [2 marks]

 (b) You trained a random forest for the task of geolocation classification. Your classifier achieves very high performance on the training set, but low performance on the test set. (i) What is the problem? (ii) Name two possible reasons for this behavior. [3 marks] 

(c) For each of the three feature selection methods Wrapper, Filter and Embedded Methods: 

(i) describe in your own words how it measures the “usefulness” of a feature; 

(ii) describe in your own words a scenario where it would be more appropriate than the other two methods. [6 marks] 

(d) Consider a multi-class classification problem over K classes, where for each instance we observe a label y as a K-dimensional 1-hot vector. We also assume a classifier which predicts ˆ y: a K- dimensional distribution over the same set of labels. y max is the true label of the instance and ˆ y max is the predicted label (i.e., the class with highest probability assigned by the classifier). 

Consider the following loss functions L a , L b and L c , defined for a single input instance,

(i) In your own words, describe how each of the loss function measures the quality of a model prediction. In other words: describe the intuition behind each loss function. [3 marks] 

(ii) Can all three loss functions be used to optimise a Multi-layer perceptron? Why (not)? [1 mark] 

(iii) Which of the three loss functions is the most appropriate for a classification task? Why? [1 mark]

(e) You are applying leave-one-out cross validation to evaluate your latest machine learning model. Your boss is concerned that your approach leads to high evaluation variance because of the very small test sets (just one instance). Is your boss right? Justify your answer. [2 marks]

(f) Connect the machine learning algorithms on the left with all concepts on the right that apply. (You may copy the answers onto your answer sheet. You do not need to justify your answer.) [3 marks]

 1-Nearest Neighbor                               Parametric model

 3-Nearest Neighbor                               Non-parametric model 

Naive Bayes                                           Probabilistic model

 Multi-layer perceptron                           Instance-based model 

Decision stump                                      Linear decision boundary 

Decision tree (depth: 3)                         Non-linear decision boundary

                                                              Generative model

(g) You are developing a model for diagnosing a highly contagious disease from a blood sample. Which of the following metrics is the most important to optimize:

 (a) precision;

(b) recall;

 (c) accuracy;

 (d) F-1 measure; (e) None of them. Justify your choice. [1 mark]

 (h) (i) Explain in your own words the problem of constrained optimization. (ii) Explain in your own words how this concepts relates to evaluating classifiers for fairness, naming both the target and the constraint(s). (N.B. no formula or calculations are necessary, providing the intuitions is sufficient.) [3 marks]

Section B: Method Questions

 In this section you are asked to demonstrate your conceptual understanding of the methods that we have studied in this subject.

 Question 2: Feature Selection 

You want to explore a data set of Nutrition information, where each instance is a fruit or vegetable characterized by three features: shape, color and sweetness. The target class is VITAMIN-C level.

Your favorite classifier accepts discrete features only. You want to compare three methods of feature discretization, and ultimately select the best one.

 (N.B. Show your mathematical working for each sub-question.)

 (a) Discretize the Sweetness feature into three equal-width bins [2 marks] 

(b) Discretize the Sweetness feature into three equal-frequency bins [2 marks] 

(c) Discretize the Sweetness using K-means clustering, with K=3 and L1 (Manhattan) distance. Your initial centroids are c 1 = 0.5,c 2 = 1.0,c 3 = 2.0, where c i refers to cluster i. Compute two rounds of updates. [6 marks]

 (d) (i) Compute the Mutual Information (MI) of the Sweetness feature after discretization by K- means (part (c)) with the class label. (N.B. as defined in the lectures, logarithms should be base 2.) [6 marks]

 (ii) The MI of Sweetness after equal-width discretization (part (a)) with the class label is 1.11, and the MI of Sweetness after equal-frequency discretization (part (b)) is 0.85. Which of the three discretization methods would you choose based on MI? [1 mark]

Question 3: Classification with Missing Features 

 Real world data sets very often have missing features, i.e., some instances do not have a value for one or more features. More formally, assume that for each data instance i, we observe a label y i , a set of features x i consisting of observed features o i = {o 1 i ...,o m i }, and missing features m i = {m 1 i ,...,m k i } with no associated value. 

Assume a trained, probabilistic classifier which predicts labels y i from features x i : P(y i |x i )

 (a) Using the statistical concept of marginalisation, and the notation introduced above, derive math- ematically (that is: write equations) a classifier which predicts y i using both observed features o i and missing features m i . (N.B. Show your mathematical working.) [6 marks]

(b) Is your classifier discriminative, generative, neither or both? Justify your answer by referring to your derivation in the first part of the question. [3 marks]

Question 4: Evaluation 

Consider the following two sets of plots. Plots (1)–(3) depict three decision boundaries (green), learnt by three different models over the same data set. The data set consists of instances, each described by two features (x 1 ,x 2 ) and a class label (x or o):

(a) Provide a plausible label for the x-axis, y-axis, and the two lines (red and blue) in plots (i)–(iii). [3 marks]

 (b) Find the most plausible 1:1 alignment of plots (1)–(3) with plots (i)–(iii). Justify your choice, referring to the concepts of bias and variance, and model complexity. [6 marks]

 (c) Out of models (1)–(3), which one would you choose? Justify your choice. [2 marks]

 Question 5: Fair Classification

 Consider the following data set consisting of 8 training instances, where each instance corresponds to an applicant for a job. Each instance has four features: work experience (in years), education (in years), LinkedIn page views, and gender encoded as binary female (value=1 if female, 0 if male). For the purpose of this question, we consider the female feature as a protected attribute. Each training instance has a true binary label y which denotes whether the applicant received a high (1) or low (-1) suitability score. We also have access to predicted labels from some classifier , ˆ y full , which was trained to automatically predict the label from all available features.

(a) Define in your own words the fairness criterion of equal opportunity in the context of the above scenario. [2 marks] 

(b) Is the full model (column ˆ y full ) fair with respect to the concept of equal opportunity? (N.B. Show your mathematical working.) [3 marks] 

(c) (i) Define in your own words the concept of fairness through unawareness in the context of the above scenario. (ii) Would the resulting model be a truly fair classifier? Justify your answer [2 marks]

 (d) Train a Perceptron implementing fairness by unawareness , using the data set given above as training examples. Perform two training steps, i.e., process only the first two instances (ID 1 and 2) in the data set. Assume the following:

Question 6: Probability 

You developed a classifier which predicts whether a German movie will be successful in Australia, or not. ”Successful” here is defined as > 10,000 viewers in Australia within the first 4 weeks after release. From historical data it is known that 0.5% of all German movies turn out successful in Australia. After some development and evaluation, you find that your classifier has a false positive rate of 4%, and a false negative rate of 1%.

 (N.B. Show your mathematical working for each sub-question.) 

(a) What are the odds that a random novel German movie will be unsuccessful in Australia? [2 marks]

 (b) Your classifier predicts “successful” for a new German movie. What is the probability that the movie will indeed be successful? [4 marks]

Question 7: Ensembling 

The following graph shows the error of three classification models and a random baseline on 15 individual test instances (x 1 ,...,x 1 5). The error for each test instance is a continuous number between 0 and 1, where 0 is best.

(a) Explain the general concept of ensembling in the context of the above scenario. (N.B. you do not need to provide formulas or perform computations.) [2 marks]

 (b) Would you expect ensembling to improve performance? Why (not)? [3 marks] 

(c) Name an appropriate ensembling technique for the above scenario. Justify your choice. [1 mark] For the remainder of the question, consider a slighlty different scenario:

 A team of data scientists has access to a labelled training data set and found that several different classifiers lead to severe {overfitting, underfitting}. They consequently decided to apply Boosting using AdaBoost algorithm with Decision Stumps as their base classifiers. In doing so, they expects to obtain more {complex decision boundaries, stable predictions}.

 (d) Select the most appropriate term from the {options} (underfitting/overfitting and complex decision boundaries/stable predictions) in the text above. [1 mark] 

After t − 1 iterations, the data scientists obtained the following results for a set of N = 5 test instances (only the last base classifier shown):

(e) Compute the error rate ? t , classifier weight α t , and the new instance weights w t+1 . Use the following definitions of AdaBoost update formulas:

(f) (i) Compare the new weights w t+1 to the weights w t in the table above, and explain your observations in the context of the ideas underlying the AdaBoost algorithm. (ii) What are the two functions of the classifier weight α t ? [4 marks]

Section C: Design and Application Questions

In this section you are asked to demonstrate that you have gained a high-level understanding of the methods and algorithms covered in this subject, and can apply that understanding. Expect your an- swer to each question to be from one third of a page to one full page in length. These questions will require significantly more thought than those in Sections A–B, and should be attempted only after having completed the earlier sections.

Question 8: Plankton Classification 

Professor Shell is a marine biologist specialising in plankton. She has collected a large data base of plankton images, and would like to automatically classify the depicted instance into one of four plankton types (see Figure 1). For each image, she is able to obtain the following measurements which she wants to use as features: length, number of legs, number of eyes, circumference, and color intensity. She has labelled a small data set of 100 plankton images with the correct plankton type, and has an additional 2000 unlabeled images of varying quality (resolution), brightness, zoom and angle.

Professor Shell is an expert on plankton, but does not know much about machine learning. She requires input from a machine learning scientist to help her succeed in her classification task. Please answer the following questions.

(a) For each of the following algorithms, (a) indicate whether it is appropriate to use and (b) justify your decision. [2.5 marks]

– Multinomial Naive Bayes 

– Decision Tree 

– 30-nearest neighbor

 – K-means (K=8)

 – K-means (K=4)

You ultimately decide to design a neural network (NN).

(b) How many input units and output units would your NN have? [1 mark] 

(c) Would your NN have hidden units? Justify your answer. [1 mark]

 (d) What would be the activation function of the final layer? [1 mark]

 (e) What learning algorithm would you use? Justify your choice. [1.5 marks] 

(f) Considering your training set size(n = 100) how would you evaluate your model, making sure that you obtain a reliable estimate of its generalization performance? Describe all steps of your chosen evaluation strategy. [4 marks]

(g) After evaluation, performance is not quite satisfactory. You want to improve model performance using all the available resources mentioned above.

 (i) Select an appropriate machine learning algo- rithm and justify your choice. 

(ii) Explain the algorithm in the context of this data set. 

(iii) Justify any settings of the algorithm you may need to decide on. [5 marks] 

(h) Your classifier is working well, and you look forward to a break. However, all of a sudden Professor Shell presents you with a picture of a plankton unlike anything she has seen before! 

(i) Describe two reasons for why Professor Shell may be encountering a highly unusual data instance. 

(ii) Using all your machine learning knowledge, how would you help Professor Shell to make sense of the new data instance? [4 marks]

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