CSE514 – Solved

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Q1 (6pts): A friend informs you that a casino is using loaded dice, such that:

1112 ๐‘–๐‘“ ๐‘˜ โˆˆ {1, 2, 3}
๐‘™๐‘œ๐‘Ž๐‘‘๐‘’๐‘‘! = ๐‘๐‘Ÿ๐‘œ๐‘ ๐‘–๐‘“ ๐‘˜ โˆˆ {4, 5, 6}
0 ๐‘œ๐‘กโ„Ž๐‘’๐‘Ÿ๐‘ค๐‘–๐‘ ๐‘’

Q1a: What is the entropy of a roll at this casino? Please use log base 2

Q1b: Imagine your friend is right, but you choose to give the casino the benefit of the doubt and assume fair dice. Whatโ€™s the KL divergence of fair dice (Q) from the true
distribution (P)? i.e. calculate ๐ท”#(๐‘™๐‘œ๐‘Ž๐‘‘๐‘’๐‘‘ ๐‘‘๐‘–๐‘๐‘’||๐‘“๐‘Ž๐‘–๐‘Ÿ ๐‘‘๐‘–๐‘๐‘’)
Please use log base 2

Q1c: Imagine you choose to believe your friend, but it turned out the casino has since switched back to fair dice. Whatโ€™s the KL divergence of the loaded dice (Q) from the true distribution (P)? i.e. calculate ๐ท”#(๐‘“๐‘Ž๐‘–๐‘Ÿ ๐‘‘๐‘–๐‘๐‘’||๐‘™๐‘œ๐‘Ž๐‘‘๐‘’๐‘‘ ๐‘‘๐‘–๐‘๐‘’)
Please use log base 2

Q2 (5pts): Given this ANN structure:

And the following parameter/function definitions:

W = [-15, -3, -2, 4, 1, 10] B = [4, 1, -0.5]

๐‘“$(๐‘ฅ) = ๐‘“%(๐‘ฅ) = max (0.1๐‘ฅ, ๐‘ฅ) ๐‘“&(๐‘ฅ) = ๐‘ฅ%

What are the intermediate and/or output values for the following data points?

Q2a: Data point: a = 0.5, c = 0.5

๐‘Žโ€ฒ$ value: ๐‘Žโ€ฒ% value:

๐‘โ€ฒ$ value:

Q2b: Data point: a = 1, c = 0

๐‘โ€ฒ% value: ๐‘“$ value:

๐‘“% value:

Q2c: Data point: a = 0, c = 1

๐‘ฅโ€ฒ$ value: ๐‘ฅโ€ฒ% value:

๐‘“& value:

Q3 (4pts): Given a test data point:
Height = 200
Weight = 200

And the training dataset in the table below, use kNN classification with k=1, k=3, and k=5 to label the test data point. Break ties by increasing k by 1.
Show your work by filling in the table and writing in the modelโ€™s class label predictions.

Class Height Weight Manhattan Distance from test sample
1 105 114
1 92 169
1 87 140
2 111 109
2 79 44
2 92 55
3 265 331
3 330 284
3 185 309

Model predictions for:

k = 1 _________ k = 3 _________ k = 5 _________

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