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courses:rg:2014:crf [2014/10/28 14:16]
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courses:rg:2014:crf [2014/10/28 14:22] (current)
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| ====== Conditional Random Fields - Questions ====== | ===== Conditional Random Fields - Questions ===== |
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| (1) Definition of CRF in Section 3 contains a formula with a shortcut notation: <latex>P(Y_v | X, Y_w, w \neq v) = P(Y_v | X, Y_w, w \sim v)</latex>. | 1. Definition of CRF in Section 3 contains a formula with a shortcut notation: <latex>P(Y_v | X, Y_w, w \neq v) = P(Y_v | X, Y_w, w \sim v)</latex>. |
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| a) Try to rewrite this general formula using some more clear notation (or explain it in your words). | a) Try to rewrite this general formula using some more clear notation (or explain it in your words). |
| **Hint:** If you don't understand the shortcut notation, just ignore it and use your intuition (vertices connected by edges are not independent). | **Hint:** If you don't understand the shortcut notation, just ignore it and use your intuition (vertices connected by edges are not independent). |
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| (2) MEMMs suffer from Label Bias Problem. What about HMMs? Why? | 2. MEMMs suffer from Label Bias Problem. What about HMMs? Why? |
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| (3) Which of the following features are meaningful? Why? | 3. Which of the following features are meaningful? Why? |
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| a) <latex>X_i</latex> == can | a) <latex>X_i</latex> == "can" |
| b) <latex>X_i</latex> == can && <latex>Y_i</latex> == N | b) <latex>X_i</latex> == "can" && <latex>Y_i</latex> == N |
| c) <latex>X_i</latex> == can && <latex>Y_{i-1}</latex> == N | c) <latex>X_i</latex> == "can" && <latex>Y_{i-1}</latex> == N |
| d) <latex>X_{i-1}</latex>== can && <latex>Y_i</latex> == N && <latex>Y_{i-1}</latex> == V | d) <latex>X_{i-1}</latex>== "can" && <latex>Y_i</latex> == N && <latex>Y_{i-1}</latex> == V |
| e) <latex>X_{i-1}</latex> == can && <latex>Y_i</latex> == N && <latex>Y_{i+1}</latex> == V | e) <latex>X_{i-1}</latex> == "can" && <latex>Y_i</latex> == N && <latex>Y_{i+1}</latex> == V |
| f) <latex>X_{i-2}</latex> == can && <latex>Y_i</latex> == V && <latex>Y_{i-1}</latex> == N | f) <latex>X_{i-2}</latex> == "can" && <latex>Y_i</latex> == V && <latex>Y_{i-1}</latex> == N |
| g) <latex>X_{i+3}</latex> == can && <latex>Y_i</latex> == N && <latex>Y_{i-2}</latex> == V | g) <latex>X_{i+3}</latex> == "can" && <latex>Y_i</latex> == N && <latex>Y_{i-2}</latex> == V |
| h) <latex>X_1</latex> == The && <latex>Y_{i-1}</latex> == N && <latex>Y_i</latex> == N | h) <latex>X_1</latex> == "The" && <latex>Y_{i-1}</latex> == N && <latex>Y_i</latex> == N |
| i) <latex>X_i</latex> has more letters than <latex>X_{i-1}</latex> && <latex>Y_i</latex> == N | i) <latex>X_i</latex> has more letters than <latex>X_{i-1}</latex> && <latex>Y_i</latex> == N |
| j) <latex> X</latex> contains word "dog" && (<latex>Y_i</latex> == N || <latex>Y_i</latex> == V) | j) <latex> X</latex> contains word "dog" && (<latex>Y_i</latex> == N || <latex>Y_i</latex> == V) |
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| (4) Let's suppose, that we have a CRF for the data "he/N can/V can/V a/N can/N" and these features: | 4. Let's suppose, that we have a CRF for the data "he/N can/V can/V a/N can/N" and these features: |
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| <latex>f_1</latex>: <latex>X_i</latex> == can && <latex>Y_i</latex> == V && (<latex>Y_{i-1}</latex> == N || <latex>Y_{i-1}</latex> == V) | <latex>f_1</latex>: <latex>X_i</latex> == can && <latex>Y_i</latex> == V && (<latex>Y_{i-1}</latex> == N || <latex>Y_{i-1}</latex> == V) |
| **Hint2:** The vertical bar in <latex>y|_v</latex> does not mean conditional probability, see its definition under Formula 1. | **Hint2:** The vertical bar in <latex>y|_v</latex> does not mean conditional probability, see its definition under Formula 1. |
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| d) Let's suppose, that | d) (optional) Let's suppose, that |
| <latex>\lambda_1</latex> = 1 | <latex>\lambda_1</latex> = 1 |
| <latex>\lambda_2</latex> = 1 | <latex>\lambda_2</latex> = 1 |
| <latex>\mu_1</latex> = 1 | <latex>\mu_1</latex> = 1 |
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| Show, that exp(...) expression in Formula 1 (page 3) and <latex>\prod_{i=1}^{n+1} M_i(y_{i-1}, y_i | x))</latex> in formula on page 4 | Show, that exp(...) expression in Formula 1 (page 3) and <latex>\prod_{i=1}^{n+1} M_i(y_{i-1}, y_i | x))</latex> in formula on page 4 |
| give the same result. | give the same result. |
