F22 - CS 439 - Final Exam - V1

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- SK 1< 125 F22 - CS 439 - Final Exam - V1 Prof. A.D. Gunawardena Administer Date: Wednesday Dec 21, 2022 4:00 PM - 7:00 PM e This test is based all topics from Introduction to Data Science course * You can use a cheat sheet during the exam, but labs, projects and quizzes cannot be used during the test. ¢ You are NOT allowed to any devices during the test e Please write the answers ONLY in the space provided. You may lose points for unnecessarily long answers. e Please scan the answer pages and upload to gradescope by pages. (entry code: DJZGPG https:/ /www.gradescope.com/courses/477236) o If you are unable to upload the exam to gradescope, please upload the exam to canvas. © You have 180 minutes to complete this exam plus 15 minutes to scan and submit to gradescope (195 minutes total) o Handover the paper exam to proctors. Your exam will not be graded w/o the paper copy. T understand that my work may not be graded without you signing below. I certify that the answers to this test represents my own work and I have read RU academic integrity policies https://www.cs.rutgers.edu/academic- integrity /introduction PRINT your name : Sa: Kucly; bhat la SIGN your name : netID : SKK 12.5 Exam Score Question | Points | Score | grader 1 10 2 10 3 10 4 10 5 10 6 20 7 15 8 15 Total 100

Question 1 - Sampling - 10 points a dataFrame restaurantX as follows. The name of the restaurant Restaurants in a city X is contained in he following table (String), Type of Cusine (String) and average number of customers per month (integer). T shows the first few rows of the dataFrame. name cuisine average Marufuku Japanese 2241 Jack in the Box Fast Food 1592 Thai Basil Thai 820 Tako Sushi Japanese 1739 McDonald’s Fast Food 1039 Wendy’s Fast Food 908 oo N\ 1. (3 pts) Complete the following function random_sample that takes a dataFrame df, a column name cname, and a sample size n, and returns a list containing a random sample of n entries from the column with cname. def random_sample(df, cname, n): vetumna 4. Sample (n=n) Cenane) 28 2. (2 pts) Complete the function that takes a series x and return the total null values. Call the function to get total null values in the cuisine column in restaurants. é&,\— ‘\‘&*ul o\_._lh(o' ( K) . Cosw = Y- IS (XC def total_null(x): W Tin ¥l (‘?n(hufi#‘) ' wfifi@m%rwo i Cil=>Trnuw : R E.\’a. 4 et e )) - “ccm/r +>= ) nwd = ‘(O‘st Cou »\k' . . / v - > 3. (2 pts) Suppose that the proEa ility of Thai Basil appears in the random sample is 1/12. What is the probability that Jack in the Box appears in the random sample? Briefly justify your answer. The proloalility S cjoivg @ e uniforin ol o they oveVaugue | so fe 4. (3 pts) A consultant wants to collect a random sample of restaurant names where the strata are the cuisine type, and the consultant wants to collect 10 restaurant names per strata. Write one/few lines of code to collect consultants desired stratified random sample.(hint: groupby, agg, and lambda functions can help) e Growy = &8 Gourly (lay = “Gsine ) - Coua } ) veTUvn &)}k\weoafDUzY). S“MV"Q((AﬂO)E“V\GMe”} Page ii

Question 2 - Visualization - 10 points L (2 ptS)' For each of the following cases, choose the ideal plot type from : 1D : Bar chart, Histogram,2D: Scatter plot, line plot, box-whisker heatmap, 3D: scatter matrix, bubble chart. You do not need to write the code. Just briefly justify what plot may be appropriate. (a) Plot 10,000 employees labeled male, female, other versus their salaries DoX-WisKey ~ C wa m:j:l;:i (b) Plots midterm and final exam scores of 100 students with course grades color coded by 5 colors (A,B,C,D,F). Saxkler ot~ namai wh VS - mumerical dak, Colofivg € @nbe dong in Code (¢) Compare the average, median, max and min temperature in 3 different countics Doxahisker (d) Visualize the Density of traffic in NY city map during rush hour. @x‘i""_le_c L‘“‘ 1_/ "(“f_ Mf st 2. (2 pts) Sam has suggested that, given any numerical data set, the mean and standard deviation are reliable metrics to understand the shape of the distribution of any data set. Sam argues that there is no need to plot the data. Explain briefly arguments for or against this statement. Answer should be brief and to the point. The wean D stondard dujabion ave wekrics thal can be wsed Aoua ik W Otlers to wadovstand + W dishibubioa Jouk— \,lo-\'Hlv e Sresidools Cud help 48 uideytand it dionibbon. 59/ wo JUH&\' %MA Li‘hoh 3 [T ove not e»oq%/ ' 3. (2 pts) Consider the following plot that shows the relationship between cancer screenings and abortions from 2006 to 2013. “ ~~._Cancer Screeni ey ng ~ 327000 2007371 289750 935573 - T T T T T T 1 2006 2007 2008 2009 2010 2011 2012 2013 (a) interpret the plot and make a statement about cancer screenings and abortions (eg. how they have changed as a percentage) T %cems/ s abovHon 1 wCEases p Conta v $erecuniny ecureays, canay SCreew#9s bowe doyeascd Yy ¥ Kin !7 Co/, hyorti g s Tincreased L.,}'(?;’.»?-a e .4 le ~elo 323 -4 gt MB e e B % 0 *T0 10 ¥ Page iii o — = 77“>§-

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(b) A lawmaker claims that by looking at the plots, abortions have dramatically increased during this period compared to cancer screenings. Do you agree or disagree with that statement? Provide a brief explanatior o o &ngrfecj 4 Le S(nrl for abocjon 1S lesg flaw 14‘4-’ S(c\oe for Camcar SCrcu\,;yaJG, Whorken ncrecsed %VA/ \F/ N0 /L 70&1ar5 wile canmcey S Oreening \”"}f €0l /(—'1(»/.5- 4. (4 pts) Consider the Kernel density function K (z) = i(l — |a]) where |z| < 1. Show that K(z) satisfies the 3 properties of a KDE. Identify the 3 properties clearly and explain why you think the function satisfies the property. Clearly identify the limits of integration. (a) property 1: _S x-]»‘»f/@r{f awd. IIK(‘( o&r X ;‘t( | =) = Thven andw ae = () S;_{' i dx => (x +2D] O 3 [A+1) 4 Le-) de = e Sl A T 000 j'f’m’s) o K‘)_A P Jo = k” ?’} Lv = @’d’ (b) property 2: 124 : A Queg, =) (g)wm}nc T KCRy =K(X) Heuce, Seh 'Sy = g = (x| BAARDR (c) property 3: V>\£C"K\ = \"(_)\‘ = (_lx‘ = “‘CGCG/ \(\"a(&/“ gobjf;ed S (x| & \/ the lawesy valug o EX) = ='=0 treuce, pvorefin Sakigied pee) =0 ") {= K\ =D

Question 3 - Text Processing - 10 points 1. (2 pts) [Regex] A Java variable name must start with an alpha-character {A-Z,a-z} or underscore _and cannot start with a digit and has a maximum of 32 characters chosen from alpha-numeric characters (includes A-Z a-z 0-9) or underscopre _ Write a regular expression to describe any Java variable name === r2 a-e\ ") &ﬂ (42a-2 o~ -’3 %32?7 2. Consider the following 4 sentences. e S1 = "Sam I am Sam” e 52 = "I Sam like Fish Chips” e 53 = "Sam Sam Fish” o S4 = "Fish Chips like Sam Chips” (a) (4 pts) Create the term-frequency matrix TF where rows are sentences and columns are words. I am Fish Chips like st 2 VI o o 0 S35 1 @ Lie ) \ $3 8 o0 © | o o S4 \ 0o 0 \ £ L | 3. (4 pts) Using L1 or Manhattan distance between two sentence vectors in the TF matrix, create the 4x4 distance matrix. Using the matrix of distances, group Sentences into two clusters where sentences are "similar”. Use any tie breaking rule and clearly describe your algorithm. S1 S2 S3 S84 {00V DT s(%1=lo-5\+ls~ol t3-ql 2] = 18 —(o-atlsd t( 3ol |3y = e 52‘50"{9“ @,‘ \ 2| +(3- ""‘ 5,5, =10 -4 1s- L34l +(F-0] = | ¢ s 3 Y o U - S‘SS} Geve b;v~§(q'/ §23&, hasbe &Od"siukm l 1 oM | o Seutenws S, B Sy Qe oSt Su lar \dwsw/i_: ¢ 85 Tdme«z-_szzgq] ‘f?fim _ PaT . - n degrang bW Mfiufi’(ﬂm; .\ra\je Satens 4 IL\:("V(“); Qhfi?‘“\ if‘:q»QL a$ ;’t‘ 5:;}/ whors ;g e o 55, V(’.Wmihfi Page v Qwfihdgqm [ fi%‘%\’cf distente P S(fis;/.\ﬂ u(\\(.e Ta Ohe dus\eyat{\_; ¢

Question 4 - Naive Bayes - 10 points Naive Bayes is a machine learning algorithm that relies heavily on probabilistic modeling. The Bayes rule indicate the following, where X is a Bernoulli, categorical, or Gaussian random variable, and Y is Bernoulli or categorical random variable). P(YIX) = PXV)p(Y) _ p(XIY)p(Y) p(X) 2, p(X1y) p(y) Suppose that the following data was collected from a police report of stolen cars or cars erroneously reported a3 stolen. The table provides color, type and origin of the car for each record. ExampleNo | Color Type Origin | Stolen? Red Sports Domestic | Yes Red Sports Domestic | No Red Sports Domestic | Yes Yellow Sports Domestic | No Yellow Sports Imported | Yes Yellow SUV Imported | No Yellow SUV Imported | Yes Yellow SUV Domestic | No Red SUV Imported | No Red Sports Imported | Yes SO0ONAGE w8 Answer the following questions based on the table data.To receive full credit, briefly justify each answer 1. (1.5 pts) What is the probability of a car being stolen? %o = l,\i theve ave (o e, aroJm'ok 5 weye stolen 2. (2.5 pts) What is the probability that a YELLOW car being stolen? \ € Stolen | yellow§ " ~ 'F( (ow | S n\(h s ( ) = 2l 4 a Plsden | yelloo)= J.fiﬂ—j—“——\jl—m“cw(o ) === 3. (6 pts) Determine if a car with the properties RED, SUV, dnd DOMESTIC is more likely to be stolen or not stolen. Show all work to receive full credit. (Hint: you need to compute both probabilities (Stolen or not-Stolen) using Bayes rules to see which is more likely. You do not need to use the denominator as it will be the same for both. It is not necessary to simplify the fractions) T(Slen | FED, OV, DOMETHC) = PCRED, SUV, POMESTIC [ Sielen) » eckolen) - Nst STOLEN ‘rsmhkelg SAE NEEE N A el gk e 55, (o Srolen | 2,50V Jonedsd) = o (pep, Sov, Pomesic) ) \ l oyl \“S(’D\P.‘ 2% 5 .r.f{\;ko\u bo-uct ke Sple, Page vi rage 1v i

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Question 5 - Linear Regression - 10 points (a) (4 pts) Consider the following data plots (in blue) of high temp vs peak demand and linear regression models (in green) that might fit the data " ot " s Discuss the suitability of models A, B and C using bias (high, ok,low), variance(high, ok,low), regularization (yes—no). i A% biag-high, variance - Wiqh, vegplavizabion - no i.B bias -0, Yariana - oK, veoplari 2ekion - po ii. ¢ oty ~low, Naviana g ‘ow, Vend«wi 2<tion -8 (b) (3 pts) Given below is a plot of a data set (x,y) points. ).(,2_{) | /° s R Copy ) We would like to find a linear model that fits the above data well. The following linear model (in 6) was considered (note the scaling of the axes). Estimate values of 6, 0; , 0 that will likely give a good fit to the data. i ho(z) =6 +01z — \I\WO( “-‘- ~2o42X =0 6= > e S égﬂfifi—-")——v b e s | 2Byt e xres ¥2oy Y e Xy’ *oa-Fou-0 -G L Aloptepees 2oy ) 76 '4;;)) 2 \Z'OV%;'_‘O =3 (c) (3 pts) Consider the following regularized loss function I(d): where first term is the regularized term and second term is the loss term. Find the value of § that minimizes the value of /(f). You must show all work to receive credit. 00) = N0 —4)* + % Zn:(n -0y i=1 J‘L_(L(e)\: aXk(o-Y) {—*’,;I ‘:=|u -9) =o 9 = )4‘{/\ dh(e-u) 4 '% 5'::((/(\ -0 4 =lA = x)—Own R“““%e% S J\7\(%” J X r A X He) S Pugevii g} fpn = A E

Question 6 - Unsupervised Learning - 20 points algorithm getting stuck (a) (1 pt) In k-means clustering, how do we select cluster centers initially to avoid the in a local minima? Explain clearly. m we Pk the fupial chster KD Gaudommly (o n po s (b) (4 pts) Given the 2D points (0,0), (1,0), (0,1), (1,1), (2,3) find the two cluste algorithm (k=2). Start with the first center (1,1) and find the next center usin, belong to each cluster. Use Manhattan distance. Show work to receive full credit. r centers using k-means++ g k++. Identify the points (LA~ Co,o)"‘>7-—/ AT |, (0,0 1, (2,2)> 3 'j(@fi‘} 'S fwthest, & toakCs e naw clster@dor 2 (4, L) (0,00, LlieY el (2,3 2 ro poins (c) (1 pt) If we increase the number of clusters, does the overall/sum error (error is how far a point from its assigned center) increase or decrease? Why? The ovearall Lapgeror will Lueast as b & ro'mk i emain bR ((A~g4—w o R hfiagfiqw« Lecarye Ahe degtangs 15 Swaller, % Hena, Ft O e grear, s (each of dim n) into k clusters using t iterations, write down the (complexity) of the k-means+-+ algorithm using m, k, t and n. Do arly identifying each component as cost of initializing, (d) (4 pts) If we are clustering m point; approximate number of operations not simplify the terms. Justify your answer by cle determining new centers, identifying which point belongs to which center etc.. i. initializing P . GG il et number 94 U‘:evqhws: (s L i : Sint yoa o through alh porafx ii. Determining new centers Grd CGlCaLcJK ey & O M, Gina dhawe ave W -f«‘b\'f(v\(‘g,s T 1(,1,(‘1 4 e waub +he fiw«fl«m—ou, iii. Identifying new cluster centers for each point tnr We hkowe to c‘daal\ajé o Aé&l’fin& each poind o W imen) op alk Kr-d‘\((”firh A Qw'-m-l*’\j(’“‘i Page viii

((1(?135511"‘1C8ti0n) Consider the following figures (A), (B), (C) and (D) of different shapes plotted in & two imensional feature space (21, 7,). Suppose we are interested in classifying the type of shape A iy *:z te v v + v/ v ¢ o L N {' viv LA v v (A) (8) (a) (2 pt) Which figure best illustrate the substantial class imbalance? Briefly explain your answer as V"“)"’\*'jer T(M Po,/\ﬂ ave heads B « Lowg peveentesl o R (b) (2 pt) Which figure is linearly separable? That is, can you draw a straight line to separate the categories? Briefly explain your answer. @\S (Me«« Jemu@ e S S(..,Y(e, \j ek Vae “scpevateg by 2 cotegoics. (c) (2 pt) Which figure corresponds to a multi-class classification problem? Briefly explain your answer. Fquwe ) as thae aw moe Thon 2 cé)«ezbw;e S (d) (4 pts) Suppose we apply the following feature transformation ¢(z) = [z1 < 0,22 >0, 1] where (z1 <0 and z > 0) is a boolean expression where if the expression is true, we use value 1 and if the expression is false, we use the value 0. Which of the above plots is linearly separable and why? s oy e Y are T The quedvand e Hh velugy ore X <0 % X2 Page ix

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Question 7 - Recommendation Systems - 15 points ; e the le and if a 1. (3 pts) For each of the following statements, briefly describe if you think it is a benefit or obstacle benefit, why you think so and in the case of obstacles, how we may overcome them. (a) Using someone else’s taste to recommend something to you beueli+, because e cargee g %H\L of-bur pessok wse hdo yredich mistn v ey (b) Excessive amount of information on the web . 5 ?W ; : W exzessivo e fovmadix b e cavge the is o bt %—L’\QS w . sv\c')l_,e,c% wst pic(s = s,v(,&f; thok we are (~fereshed G, (4 (c) Lack of data on user participation! O“’Sf‘“(lt, it Can DWWy Come L’n L«Kve} e —item Oﬂ\waf/ti, « th—e S S:A-'\‘(C\l/'g 2. In collaborative filtering, the missing rating ngfor user i and item j is given by g Zk:x“*owjk (X — y) Zk;x“,;;o Wik Where w;j; is the weight coefficient between item j and item k. The missing ratings in the table (user-item matrix) can be calculated using user-user or item-item weights. 2 1 1 1 2| ? ? 3| ? 4 2 4 5 - wlm EORRYTN ? 5 @ 4 ? (IR [ C R (a) (4 pts) Find the missing entry X3 using item-item collaborative filtering (use Manhatian distance). Show work. {2-S\ & ; 2 "o.0%y "‘h'lkj VM‘WQ\% ‘. 635.%) % “3!1 (s-4) b) (2 pts) Describe the circumstances under which you would use item-item and circumstances under which you would you go with user-user. Briefly explain. e would WW@W“‘*”%““‘*L‘MW&&W e [ Co . %»Zt b v?«}(’hT},J Gty hovicy e 7”%:“@“*%3 Wd predik poilLe o [emg ovwl fer- the V&hﬂaig@ Q«)\"&s (N”"L'd{‘- D o outd af en-itun Mﬂoum over heg veded gHun~ povdes P‘E}Z"I :C‘j d"H“k ""‘3*\% g e et

3. Consider a content-based recommender system where products are rated by consumers. Suppose we consider a product rating table where each product is defined by 3 features. Features X Xz % | \ Joe Bl Cindy ‘Andy Refabilty | Pice | - nolse l oven 2 4 1 7 le04 ] [0 \ dishwasher 5 5 7 01 02 | 08 | ‘ Cloth dryer 5 2 08 0z | 05 | l Refrigerator 4 5 05 02 04 l microwave 1 4 02 08 T (2) (2 pts) Explain briefly the differences between collaborative filtering and content-based recommender systems f&\(fib«ah’w? (feving RS fthe wmr-item MNanifiM wvfif‘ o n K velon mumdo N9, ey~ &A vt Syoens ayd ke th,(zs fo wake ¢ Covmmtindaions n haay veqression WW«“. (b) (2 pt) Write the full feature vector for appliance Dishwasher? (c) (2 pts) Suppose parameters 0) for Joe is learned as [0.1 0.7 0.2 -0.2], what is the rating estimate for a new product with feature values reliability=0.9 , price = 0.1 and noise = 0.2 7 Co.\ 03 0.2 ‘o.'Z.j ["l‘c\ oo~.(?— 0-(x( 4 0FX0.q + p-2Xo.|l 4 —0-2X0.2 n - o\ 4+ 06 F¥00T , -0y = i@o?’\l Page xi

Question 8 - Deep Learning - 15 points i, Consider the following deep learning architecture, Hidden | A. (2 pts) Assuming no bias in the network, how many ¢ parameters need to be learned? Justify | your answer. : XUt LK 4 —_@, €ah awoes s & pavamober B. (2 pts) If you increase the number of hidden layers in the network would the model has high bias or high variance? Explain. (ujk-bfas, becanse the iddgn "’*‘d"ff lecon Qea,d'wu % So Vavicends wood dcorals ii. Consider the following network. The network output at each layer is a binary value 9(h(6, 7)) (using Sigmoid function). Recall that the Sigmoid function g(z) is 1 if 2 >= 0 and 0 if z < 0. T ) — output [ A. (3 pts) Given hy(z1,x3) = 0 + 0121 + Oa2, determine a set of values of 0y, 0y,60; so that the network outputs 1 if and only if both z; and z; are 0 and otherwise returns 0. The boolean variables z; and 25 can only take binary (0/1) values. If no such values exists, state so. Need to show work to receive credit. 0= \Q 0,= 0 = k o3>0 = —$ > Lo €.t ox oG =-5 - -0 ©s%° ip Yo b0 thon ge®d 29, s (LMISO W& L Page xii

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B. (3 pts) Determine values of 0y, 0y, 0, so that the function g(hg(z)) returns 1 if both 21 and z, are 0 or both are 1. Otherwise returns 0. The boolean variables #1 and &, can only take binary (0/1) values. If no such values exists, state so. Need to show work to verify that your values of 0 provides the correct output. W N/A- Via a3 CondeHonse =2 91=? 0y = % U, 10,1 €.7%0\ (Nosack Volue exists b ol )\ asS Stoked o £ ekt dont-overlap, - 3 [§ ( ®p20 Do 010,820 38, 70 5, T S 0 Tsl < |Consider the following extended network with a hidden layer. The inputs z; and Ig are binary fO/ 1) <0 as well as hidden layer values y; and yz. The sigmoid function is applied at each level to convert © (4] 02 inear model to non-linear. N 0(\(90“’ ) 799*617/07 ) ‘31, Q(e o) S 8,+t8:>0 ~s (»I«,u A. (2 pts) If 21 = 1 and 22 = 0, what values of theta’s will give the output y1 =1 and y2 = 1?7 6= 1 6= 1 0= 4 3= 1 i= © 05 =0 / 'L B. (3 pts) Find the 6 values determined in above network to build a neural network for computing XNOR function. The XNOR function is defined as (A AND B) OR (A AND B). b= (O 0= "IS 0, Page xiii

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F22 - CS 439 - Final Exam - V1

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