cs420_old_assignment

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Singapore Management *

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103

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Computer Science

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May 8, 2024

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SMU Classification: Restricted Assignment 1 — Introduction to AI Note: Your solution for this assignment should have two parts— a pdf document and code files . 1. Have a single pdf document that shows your solution for different questions (show either numerical values if the question asks for it, and/or theoretical justification as required). Include in this pdf, the code you wrote for the solution for the respective question (if coding is required). 2. Upload your real code files that you used to solve the particular question. Make sure your code is neatly organized per question, runs correctly, and has comments that highlight the part you implemented so that I can easily understand it 3. Combine your solution pdf and code files in a single zip folder and upload it on the eLearn assignment folder 4. Solution should be typeset using a professional software (word, keynote, latex etc). Figures should also be made using software such as power point. No handwritten solutions are allowed and will not be graded.

SMU Classification: Restricted Question 1 [10 points]: Consider the following Bayesian network: Write True/False for the following conditional independence statements. Justify clearly your answer. For example, show the active/blocked trails as necessary and the reason for them to be active or blocked (e.g., use rules such as cascade, common cause or v-structure). [No coding required for this question. Each sub- part has 2.5 points ] 1. A ⟂ E |{C} 2. A ⟂ E | {C, G} 3. F ⟂ E | {C} 4. B ⟂ E | {A, D}

SMU Classification: Restricted Question 2 [10 points] A box contains three dices. Each dice has three faces, numbered from 1 to 3. We also know the following about the three dices: - Dice 1 (say D1) is a fair dice with each face equally likely to come. - Dice 2 (say D2) is a biased dice with outcome 1 likely with probability 0.2. The rest of the outcomes have equal probability (i.e., P(D2=2) = P(D2=3) ). - Dice 3 (say D3) is also a biased dice with outcome 2 likely with probability 0.5. The rest of the outcomes have equal probability of coming up. We pick a dice from the box. The probability of: • Picking Dice D1 is 0.4, • Picking Dice D2 is 0.2 • Picking Dice D3 is 0.4 Once the dice is picked from the box as per the distribution above, then that dice is rolled three times to generate outcomes X1, X2 and X3. (i) Draw the Bayes net corresponding to this setup. Explain what each random variable of this Bayes represents, and show the domain of each random variable [3 points] Hint: There should be 4 random variables. Variable Name Domain (Set of Values) Interpretation (intuitive explanation of what the variable represents) Draw Bayesian Net Below

SMU Classification: Restricted (ii) Write conditional probabilities (numerical values) associated with each node of this Bayes net. As there are 4 variables, please specify one conditional probability table (CPT) for each variable [3 points] (iii) Assume that the observed outcome was X1=2, X2=1, X3=2. Calculate which dice (D1 or D2 or D3) was most likely to have been picked from the box. Show numerical calculations (based on conditional probabilities) to justify your answer (do not use pgmpy to just write the final answer). [4 points] CPT for variable 1 CPT for variable 2 CPT for variable 3 CPT for variable 4

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