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📗 (Fall 2016 Final Q18, Fall 2011 Midterm Q20) Consider a classification problem with \(n\) = classes \(y \in \left\{1, 2, ..., n\right\}\), and two binary features \(x_{1}, x_{2} \in \left\{0, 1\right\}\). Suppose \(\mathbb{P}\left\{Y = y\right\}\) = , \(\mathbb{P}\left\{x_{1} = 1 | Y = y\right\}\) = , \(\mathbb{P}\left\{x_{2} = 1 | Y = y\right\}\) = . Which class will naive Bayes classifier produce on a test item with \(x_{1}\) = and \(x_{2}\) = .
📗 Hint: make sure you read and understand Fall 2016 Final Q18.
📗 (Fall 2019 Final Q22, Fall 2019 Final Q23, Fall 2014 Final Q9) Consider the following directed graphical model over binary variables: \(A \to B \leftarrow C\). Given the CPTs:
Variable
Probability
Variable
Probability
\(\mathbb{P}\left\{A = 1\right\}\)
\(\mathbb{P}\left\{C = 1\right\}\)
\(\mathbb{P}\left\{B = 1 | A = C = 1\right\}\)
\(\mathbb{P}\left\{B = 1 | A = 0, C = 1\right\}\)
\(\mathbb{P}\left\{B = 1 | A = 1, C = 0\right\}\)
\(\mathbb{P}\left\{B = 1 | A = C = 0\right\}\)
What is the probability that \(\mathbb{P}\left\{A = a, B = b, C = c\right\}\), \(a, b, c\) = ?
📗 (Fall 2019 Final Q22, Fall 2019 Final Q23, Fall 2014 Final Q9) Consider the following directed graphical model over binary variables: \(A \to B \to C\). Given the CPTs:
Variable
Probability
Variable
Probability
\(\mathbb{P}\left\{A = 1\right\}\)
\(\mathbb{P}\left\{B = 1 | A = 1\right\}\)
\(\mathbb{P}\left\{B = 1 | A = 0\right\}\)
\(\mathbb{P}\left\{C = 1 | B = 1\right\}\)
\(\mathbb{P}\left\{C = 1 | B = 0\right\}\)
What is the probability that \(\mathbb{P}\left\{A = a | C = c\right\}\), \(a, c\) = ?
📗 (Fall 2019 Final Q22, Fall 2019 Final Q23, Fall 2014 Final Q9) Consider the following directed graphical model over binary variables: \(A \leftarrow B \to C\). Given the CPTs:
Variable
Probability
Variable
Probability
\(\mathbb{P}\left\{B = 1\right\}\)
\(\mathbb{P}\left\{C = 1 | B = 1\right\}\)
\(\mathbb{P}\left\{C = 1 | B = 0\right\}\)
\(\mathbb{P}\left\{A = 1 | B = 1\right\}\)
\(\mathbb{P}\left\{A = 1 | B = 0\right\}\)
What is the probability that \(\mathbb{P}\left\{A = a | C = c\right\}\), \(a, c\) = ?
📗 (Fall 2011 Midterm Q15) Given the following network \(A \to B \to C\) where A can take on values, B can take on values, C can take on values. Write down the minimum number of conditional probabilities that define the CPTs.
📗 (Spring 2018 Final Q21, Fall 2011 Midterm Q16) You roll a 6-sided die times and observe the following counts: . Use Laplace smoothing (i.e. add-1 smoothing), estimate the probability of each side.
📗 (Fall 2011 Midterm Q18) An n-gram language model computes the probability \(\mathbb{P}\left\{w_{n} | w_{1}, w_{2}, ..., w_{n-1}\right\}\). How many parameters need to be estimated for a -gram language model given a vocabulary size of ?
📗 (Fall 2010 Final Q19) We have a biased coin with probability of producing Heads. We create a predictor as follows: generate a random number uniformly distributed in (0, 1). If the random number is less than we predict Heads, otherwise, we predict Tails. What is this predictor's accuracy in predicting the coin's outcome?
📗 Use the Transformer: Link to generate some interesting (funny, nonsensical, etc) stories and share one on Piazza: Link. You should start with a sentence instead of a word or a phrase.
📗 Note: We did not talk about attention mechanisms and the Transformers during the RNN lecture, but you can read about it on the "Talk to Transformer" website.
📗 The initial sentence is: and I have participated in the discussion on Piazza.
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