Stanford Universitystanford.edu/~jgrimmer/tc4.pdf · Where We’ve Been, Where We’re Going-Class...
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Political Science 452: Text as Data Justin Grimmer Assistant Professor Department of Political Science Stanford University April 27th, 2011 Justin Grimmer (Stanford University) Text as Data April 27th, 2011 1 / 29
Transcript of Stanford Universitystanford.edu/~jgrimmer/tc4.pdf · Where We’ve Been, Where We’re Going-Class...
Political Science 452: Text as Data
Justin Grimmer
Assistant ProfessorDepartment of Political Science
Stanford University
April 27th, 2011
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 1 / 29
Where We’ve Been, Where We’re Going
- Class 1: Finding Text Data
- Class 2: Representing Texts Quantitatively
- Class 3: Dictionary Methods for Classification
- Class 4: Comparing Language Across Groups
- Class 5: Texts in Space
- Class 6: Clustering
- Class 7: Topic models
- Class 8: Supervised methods for classification
- Class 9: Ensemble methods for classification
- Class 10: Scaling Speech
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 2 / 29
Question (from email received 1 hour ago):I’m curious if you have ever used mechanical turk for
coding of data (e.g., from text). Any experience with
that? Thoughts?
How is Homework Going? Class? What Can I do to help you?
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 3 / 29
Question (from email received 1 hour ago):I’m curious if you have ever used mechanical turk for
coding of data (e.g., from text). Any experience with
that? Thoughts?
How is Homework Going? Class? What Can I do to help you?
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 3 / 29
More About R Code
How to write to a file in R
Many method, easiest: sink
> sink(’Test.txt’)
> print(’This is a great tool’)
> sink()
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 4 / 29
Congressional Language Across Sources
Congressional Press Releases and Floor Speeches
- Collected 64,033 press releases
- Problem: are they distinct from floor statements (approx. 52,000during same time)?
- Yes: press releases have different purposes, targets, and need not relateto official business
- No: press releases are just reactive to floor activity, will follow floorstatements
- Deeper question: what does it mean for two text collections to bedifferent?
- One Answer: texts used for different purposes
- Partial answer: identify words that distinguish press releases and floorspeeches
Today’s Lecture: How to identify those words?
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 5 / 29
Congressional Language Across Sources
Congressional Press Releases and Floor Speeches
- Collected 64,033 press releases
- Problem: are they distinct from floor statements (approx. 52,000during same time)?
- Yes: press releases have different purposes, targets, and need not relateto official business
- No: press releases are just reactive to floor activity, will follow floorstatements
- Deeper question: what does it mean for two text collections to bedifferent?
- One Answer: texts used for different purposes
- Partial answer: identify words that distinguish press releases and floorspeeches
Today’s Lecture: How to identify those words?
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 5 / 29
Congressional Language Across Sources
Congressional Press Releases and Floor Speeches
- Collected 64,033 press releases
- Problem: are they distinct from floor statements (approx. 52,000during same time)?
- Yes: press releases have different purposes, targets, and need not relateto official business
- No: press releases are just reactive to floor activity, will follow floorstatements
- Deeper question: what does it mean for two text collections to bedifferent?
- One Answer: texts used for different purposes
- Partial answer: identify words that distinguish press releases and floorspeeches
Today’s Lecture: How to identify those words?
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 5 / 29
Congressional Language Across Sources
Congressional Press Releases and Floor Speeches
- Collected 64,033 press releases
- Problem: are they distinct from floor statements (approx. 52,000during same time)?
- Yes: press releases have different purposes, targets, and need not relateto official business
- No: press releases are just reactive to floor activity, will follow floorstatements
- Deeper question: what does it mean for two text collections to bedifferent?
- One Answer: texts used for different purposes
- Partial answer: identify words that distinguish press releases and floorspeeches
Today’s Lecture: How to identify those words?
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 5 / 29
Congressional Language Across Sources
Congressional Press Releases and Floor Speeches
- Collected 64,033 press releases
- Problem: are they distinct from floor statements (approx. 52,000during same time)?
- Yes: press releases have different purposes, targets, and need not relateto official business
- No: press releases are just reactive to floor activity, will follow floorstatements
- Deeper question: what does it mean for two text collections to bedifferent?
- One Answer: texts used for different purposes
- Partial answer: identify words that distinguish press releases and floorspeeches
Today’s Lecture: How to identify those words?
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 5 / 29
Congressional Language Across Sources
Congressional Press Releases and Floor Speeches
- Collected 64,033 press releases
- Problem: are they distinct from floor statements (approx. 52,000during same time)?
- Yes: press releases have different purposes, targets, and need not relateto official business
- No: press releases are just reactive to floor activity, will follow floorstatements
- Deeper question: what does it mean for two text collections to bedifferent?
- One Answer: texts used for different purposes
- Partial answer: identify words that distinguish press releases and floorspeeches
Today’s Lecture: How to identify those words?
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 5 / 29
Congressional Language Across Sources
Congressional Press Releases and Floor Speeches
- Collected 64,033 press releases
- Problem: are they distinct from floor statements (approx. 52,000during same time)?
- Yes: press releases have different purposes, targets, and need not relateto official business
- No: press releases are just reactive to floor activity, will follow floorstatements
- Deeper question: what does it mean for two text collections to bedifferent?
- One Answer: texts used for different purposes
- Partial answer: identify words that distinguish press releases and floorspeeches
Today’s Lecture: How to identify those words?
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 5 / 29
Congressional Language Across Sources
Congressional Press Releases and Floor Speeches
- Collected 64,033 press releases
- Problem: are they distinct from floor statements (approx. 52,000during same time)?
- Yes: press releases have different purposes, targets, and need not relateto official business
- No: press releases are just reactive to floor activity, will follow floorstatements
- Deeper question: what does it mean for two text collections to bedifferent?
- One Answer: texts used for different purposes
- Partial answer: identify words that distinguish press releases and floorspeeches
Today’s Lecture: How to identify those words?
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 5 / 29
Congressional Language Across Sources
Congressional Press Releases and Floor Speeches
- Collected 64,033 press releases
- Problem: are they distinct from floor statements (approx. 52,000during same time)?
- Yes: press releases have different purposes, targets, and need not relateto official business
- No: press releases are just reactive to floor activity, will follow floorstatements
- Deeper question: what does it mean for two text collections to bedifferent?
- One Answer: texts used for different purposes
- Partial answer: identify words that distinguish press releases and floorspeeches
Today’s Lecture: How to identify those words?
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 5 / 29
Congressional Language Across Sources
Congressional Press Releases and Floor Speeches
- Collected 64,033 press releases
- Problem: are they distinct from floor statements (approx. 52,000during same time)?
- Yes: press releases have different purposes, targets, and need not relateto official business
- No: press releases are just reactive to floor activity, will follow floorstatements
- Deeper question: what does it mean for two text collections to bedifferent?
- One Answer: texts used for different purposes
- Partial answer: identify words that distinguish press releases and floorspeeches
Today’s Lecture: How to identify those words?
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 5 / 29
A Method for Identifying Distinguishing Words
Method 1: Mutual Information
- Unconditional uncertainty (entropy):
- Randomly sample a press release- Guess press release/floor statement- Uncertainty about guess
- Maximum: No. press releases = No. floor statements- Minimum : All documents in one category
- Conditional uncertainty (w) (conditional entropy)
- Condition on presence of word w- Randomly sample a press release- Guess press release/floor statement- Word presence reduces uncertainty
- Unrelated: Conditional uncertainty = uncertainty- Perfect predictor: Conditional uncertainty = 0
- Mutual information(w): uncertainty - conditional uncertainty (w)
- Maximum: Uncertainty → w is perfect predictor- Minimum: 0 → w fails to separate speeches and floor statements
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 6 / 29
A Method for Identifying Distinguishing Words
Method 1: Mutual Information
- Unconditional uncertainty (entropy):
- Randomly sample a press release- Guess press release/floor statement- Uncertainty about guess
- Maximum: No. press releases = No. floor statements- Minimum : All documents in one category
- Conditional uncertainty (w) (conditional entropy)
- Condition on presence of word w- Randomly sample a press release- Guess press release/floor statement- Word presence reduces uncertainty
- Unrelated: Conditional uncertainty = uncertainty- Perfect predictor: Conditional uncertainty = 0
- Mutual information(w): uncertainty - conditional uncertainty (w)
- Maximum: Uncertainty → w is perfect predictor- Minimum: 0 → w fails to separate speeches and floor statements
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 6 / 29
A Method for Identifying Distinguishing Words
Method 1: Mutual Information
- Unconditional uncertainty (entropy):
- Randomly sample a press release- Guess press release/floor statement- Uncertainty about guess
- Maximum: No. press releases = No. floor statements- Minimum : All documents in one category
- Conditional uncertainty (w) (conditional entropy)
- Condition on presence of word w- Randomly sample a press release- Guess press release/floor statement- Word presence reduces uncertainty
- Unrelated: Conditional uncertainty = uncertainty- Perfect predictor: Conditional uncertainty = 0
- Mutual information(w): uncertainty - conditional uncertainty (w)
- Maximum: Uncertainty → w is perfect predictor- Minimum: 0 → w fails to separate speeches and floor statements
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 6 / 29
A Method for Identifying Distinguishing Words
Method 1: Mutual Information
- Unconditional uncertainty (entropy):
- Randomly sample a press release
- Guess press release/floor statement- Uncertainty about guess
- Maximum: No. press releases = No. floor statements- Minimum : All documents in one category
- Conditional uncertainty (w) (conditional entropy)
- Condition on presence of word w- Randomly sample a press release- Guess press release/floor statement- Word presence reduces uncertainty
- Unrelated: Conditional uncertainty = uncertainty- Perfect predictor: Conditional uncertainty = 0
- Mutual information(w): uncertainty - conditional uncertainty (w)
- Maximum: Uncertainty → w is perfect predictor- Minimum: 0 → w fails to separate speeches and floor statements
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 6 / 29
A Method for Identifying Distinguishing Words
Method 1: Mutual Information
- Unconditional uncertainty (entropy):
- Randomly sample a press release- Guess press release/floor statement
- Uncertainty about guess
- Maximum: No. press releases = No. floor statements- Minimum : All documents in one category
- Conditional uncertainty (w) (conditional entropy)
- Condition on presence of word w- Randomly sample a press release- Guess press release/floor statement- Word presence reduces uncertainty
- Unrelated: Conditional uncertainty = uncertainty- Perfect predictor: Conditional uncertainty = 0
- Mutual information(w): uncertainty - conditional uncertainty (w)
- Maximum: Uncertainty → w is perfect predictor- Minimum: 0 → w fails to separate speeches and floor statements
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 6 / 29
A Method for Identifying Distinguishing Words
Method 1: Mutual Information
- Unconditional uncertainty (entropy):
- Randomly sample a press release- Guess press release/floor statement- Uncertainty about guess
- Maximum: No. press releases = No. floor statements- Minimum : All documents in one category
- Conditional uncertainty (w) (conditional entropy)
- Condition on presence of word w- Randomly sample a press release- Guess press release/floor statement- Word presence reduces uncertainty
- Unrelated: Conditional uncertainty = uncertainty- Perfect predictor: Conditional uncertainty = 0
- Mutual information(w): uncertainty - conditional uncertainty (w)
- Maximum: Uncertainty → w is perfect predictor- Minimum: 0 → w fails to separate speeches and floor statements
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 6 / 29
A Method for Identifying Distinguishing Words
Method 1: Mutual Information
- Unconditional uncertainty (entropy):
- Randomly sample a press release- Guess press release/floor statement- Uncertainty about guess
- Maximum: No. press releases = No. floor statements
- Minimum : All documents in one category
- Conditional uncertainty (w) (conditional entropy)
- Condition on presence of word w- Randomly sample a press release- Guess press release/floor statement- Word presence reduces uncertainty
- Unrelated: Conditional uncertainty = uncertainty- Perfect predictor: Conditional uncertainty = 0
- Mutual information(w): uncertainty - conditional uncertainty (w)
- Maximum: Uncertainty → w is perfect predictor- Minimum: 0 → w fails to separate speeches and floor statements
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 6 / 29
A Method for Identifying Distinguishing Words
Method 1: Mutual Information
- Unconditional uncertainty (entropy):
- Randomly sample a press release- Guess press release/floor statement- Uncertainty about guess
- Maximum: No. press releases = No. floor statements- Minimum : All documents in one category
- Conditional uncertainty (w) (conditional entropy)
- Condition on presence of word w- Randomly sample a press release- Guess press release/floor statement- Word presence reduces uncertainty
- Unrelated: Conditional uncertainty = uncertainty- Perfect predictor: Conditional uncertainty = 0
- Mutual information(w): uncertainty - conditional uncertainty (w)
- Maximum: Uncertainty → w is perfect predictor- Minimum: 0 → w fails to separate speeches and floor statements
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 6 / 29
A Method for Identifying Distinguishing Words
Method 1: Mutual Information
- Unconditional uncertainty (entropy):
- Randomly sample a press release- Guess press release/floor statement- Uncertainty about guess
- Maximum: No. press releases = No. floor statements- Minimum : All documents in one category
- Conditional uncertainty (w) (conditional entropy)
- Condition on presence of word w- Randomly sample a press release- Guess press release/floor statement- Word presence reduces uncertainty
- Unrelated: Conditional uncertainty = uncertainty- Perfect predictor: Conditional uncertainty = 0
- Mutual information(w): uncertainty - conditional uncertainty (w)
- Maximum: Uncertainty → w is perfect predictor- Minimum: 0 → w fails to separate speeches and floor statements
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 6 / 29
A Method for Identifying Distinguishing Words
Method 1: Mutual Information
- Unconditional uncertainty (entropy):
- Randomly sample a press release- Guess press release/floor statement- Uncertainty about guess
- Maximum: No. press releases = No. floor statements- Minimum : All documents in one category
- Conditional uncertainty (w) (conditional entropy)
- Condition on presence of word w
- Randomly sample a press release- Guess press release/floor statement- Word presence reduces uncertainty
- Unrelated: Conditional uncertainty = uncertainty- Perfect predictor: Conditional uncertainty = 0
- Mutual information(w): uncertainty - conditional uncertainty (w)
- Maximum: Uncertainty → w is perfect predictor- Minimum: 0 → w fails to separate speeches and floor statements
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 6 / 29
A Method for Identifying Distinguishing Words
Method 1: Mutual Information
- Unconditional uncertainty (entropy):
- Randomly sample a press release- Guess press release/floor statement- Uncertainty about guess
- Maximum: No. press releases = No. floor statements- Minimum : All documents in one category
- Conditional uncertainty (w) (conditional entropy)
- Condition on presence of word w- Randomly sample a press release
- Guess press release/floor statement- Word presence reduces uncertainty
- Unrelated: Conditional uncertainty = uncertainty- Perfect predictor: Conditional uncertainty = 0
- Mutual information(w): uncertainty - conditional uncertainty (w)
- Maximum: Uncertainty → w is perfect predictor- Minimum: 0 → w fails to separate speeches and floor statements
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 6 / 29
A Method for Identifying Distinguishing Words
Method 1: Mutual Information
- Unconditional uncertainty (entropy):
- Randomly sample a press release- Guess press release/floor statement- Uncertainty about guess
- Maximum: No. press releases = No. floor statements- Minimum : All documents in one category
- Conditional uncertainty (w) (conditional entropy)
- Condition on presence of word w- Randomly sample a press release- Guess press release/floor statement
- Word presence reduces uncertainty
- Unrelated: Conditional uncertainty = uncertainty- Perfect predictor: Conditional uncertainty = 0
- Mutual information(w): uncertainty - conditional uncertainty (w)
- Maximum: Uncertainty → w is perfect predictor- Minimum: 0 → w fails to separate speeches and floor statements
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 6 / 29
A Method for Identifying Distinguishing Words
Method 1: Mutual Information
- Unconditional uncertainty (entropy):
- Randomly sample a press release- Guess press release/floor statement- Uncertainty about guess
- Maximum: No. press releases = No. floor statements- Minimum : All documents in one category
- Conditional uncertainty (w) (conditional entropy)
- Condition on presence of word w- Randomly sample a press release- Guess press release/floor statement- Word presence reduces uncertainty
- Unrelated: Conditional uncertainty = uncertainty- Perfect predictor: Conditional uncertainty = 0
- Mutual information(w): uncertainty - conditional uncertainty (w)
- Maximum: Uncertainty → w is perfect predictor- Minimum: 0 → w fails to separate speeches and floor statements
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 6 / 29
A Method for Identifying Distinguishing Words
Method 1: Mutual Information
- Unconditional uncertainty (entropy):
- Randomly sample a press release- Guess press release/floor statement- Uncertainty about guess
- Maximum: No. press releases = No. floor statements- Minimum : All documents in one category
- Conditional uncertainty (w) (conditional entropy)
- Condition on presence of word w- Randomly sample a press release- Guess press release/floor statement- Word presence reduces uncertainty
- Unrelated: Conditional uncertainty = uncertainty
- Perfect predictor: Conditional uncertainty = 0
- Mutual information(w): uncertainty - conditional uncertainty (w)
- Maximum: Uncertainty → w is perfect predictor- Minimum: 0 → w fails to separate speeches and floor statements
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 6 / 29
A Method for Identifying Distinguishing Words
Method 1: Mutual Information
- Unconditional uncertainty (entropy):
- Randomly sample a press release- Guess press release/floor statement- Uncertainty about guess
- Maximum: No. press releases = No. floor statements- Minimum : All documents in one category
- Conditional uncertainty (w) (conditional entropy)
- Condition on presence of word w- Randomly sample a press release- Guess press release/floor statement- Word presence reduces uncertainty
- Unrelated: Conditional uncertainty = uncertainty- Perfect predictor: Conditional uncertainty = 0
- Mutual information(w): uncertainty - conditional uncertainty (w)
- Maximum: Uncertainty → w is perfect predictor- Minimum: 0 → w fails to separate speeches and floor statements
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 6 / 29
A Method for Identifying Distinguishing Words
Method 1: Mutual Information
- Unconditional uncertainty (entropy):
- Randomly sample a press release- Guess press release/floor statement- Uncertainty about guess
- Maximum: No. press releases = No. floor statements- Minimum : All documents in one category
- Conditional uncertainty (w) (conditional entropy)
- Condition on presence of word w- Randomly sample a press release- Guess press release/floor statement- Word presence reduces uncertainty
- Unrelated: Conditional uncertainty = uncertainty- Perfect predictor: Conditional uncertainty = 0
- Mutual information(w): uncertainty - conditional uncertainty (w)
- Maximum: Uncertainty → w is perfect predictor- Minimum: 0 → w fails to separate speeches and floor statements
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 6 / 29
A Method for Identifying Distinguishing Words
Method 1: Mutual Information
- Unconditional uncertainty (entropy):
- Randomly sample a press release- Guess press release/floor statement- Uncertainty about guess
- Maximum: No. press releases = No. floor statements- Minimum : All documents in one category
- Conditional uncertainty (w) (conditional entropy)
- Condition on presence of word w- Randomly sample a press release- Guess press release/floor statement- Word presence reduces uncertainty
- Unrelated: Conditional uncertainty = uncertainty- Perfect predictor: Conditional uncertainty = 0
- Mutual information(w): uncertainty - conditional uncertainty (w)
- Maximum: Uncertainty → w is perfect predictor
- Minimum: 0 → w fails to separate speeches and floor statements
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 6 / 29
A Method for Identifying Distinguishing Words
Method 1: Mutual Information
- Unconditional uncertainty (entropy):
- Randomly sample a press release- Guess press release/floor statement- Uncertainty about guess
- Maximum: No. press releases = No. floor statements- Minimum : All documents in one category
- Conditional uncertainty (w) (conditional entropy)
- Condition on presence of word w- Randomly sample a press release- Guess press release/floor statement- Word presence reduces uncertainty
- Unrelated: Conditional uncertainty = uncertainty- Perfect predictor: Conditional uncertainty = 0
- Mutual information(w): uncertainty - conditional uncertainty (w)
- Maximum: Uncertainty → w is perfect predictor- Minimum: 0 → w fails to separate speeches and floor statements
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 6 / 29
A Method for Identifying Distinguishing Words
- Pr(Press) ≡ Probability selected document press release
- Pr(Speech) ≡ Probability selected document speech
- Define entropy H(k)
H(k) = −∑
t∈{Pre,Spe}
Pr(t) log2 Pr(t)
- log2? Encodes bits
- Maximum: Pr(Press) = Pr(Speech) = 0.5
- Minimum: Pr(Press) → 0 (or Pr(Press) → 1)
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 7 / 29
A Method for Identifying Distinguishing Words
- Pr(Press) ≡ Probability selected document press release
- Pr(Speech) ≡ Probability selected document speech
- Define entropy H(k)
H(k) = −∑
t∈{Pre,Spe}
Pr(t) log2 Pr(t)
- log2? Encodes bits
- Maximum: Pr(Press) = Pr(Speech) = 0.5
- Minimum: Pr(Press) → 0 (or Pr(Press) → 1)
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 7 / 29
A Method for Identifying Distinguishing Words
- Pr(Press) ≡ Probability selected document press release
- Pr(Speech) ≡ Probability selected document speech
- Define entropy H(k)
H(k) = −∑
t∈{Pre,Spe}
Pr(t) log2 Pr(t)
- log2? Encodes bits
- Maximum: Pr(Press) = Pr(Speech) = 0.5
- Minimum: Pr(Press) → 0 (or Pr(Press) → 1)
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 7 / 29
A Method for Identifying Distinguishing Words
- Pr(Press) ≡ Probability selected document press release
- Pr(Speech) ≡ Probability selected document speech
- Define entropy H(k)
H(k) = −∑
t∈{Pre,Spe}
Pr(t) log2 Pr(t)
- log2? Encodes bits
- Maximum: Pr(Press) = Pr(Speech) = 0.5
- Minimum: Pr(Press) → 0 (or Pr(Press) → 1)
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 7 / 29
A Method for Identifying Distinguishing Words
- Pr(Press) ≡ Probability selected document press release
- Pr(Speech) ≡ Probability selected document speech
- Define entropy H(k)
H(k) = −∑
t∈{Pre,Spe}
Pr(t) log2 Pr(t)
- log2? Encodes bits
- Maximum: Pr(Press) = Pr(Speech) = 0.5
- Minimum: Pr(Press) → 0 (or Pr(Press) → 1)
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 7 / 29
A Method for Identifying Distinguishing Words
- Pr(Press) ≡ Probability selected document press release
- Pr(Speech) ≡ Probability selected document speech
- Define entropy H(k)
H(k) = −∑
t∈{Pre,Spe}
Pr(t) log2 Pr(t)
- log2? Encodes bits
- Maximum: Pr(Press) = Pr(Speech) = 0.5
- Minimum: Pr(Press) → 0 (or Pr(Press) → 1)
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 7 / 29
A Method for Identifying Distinguishing Words
- Pr(Press) ≡ Probability selected document press release
- Pr(Speech) ≡ Probability selected document speech
- Define entropy H(k)
H(k) = −∑
t∈{Pre,Spe}
Pr(t) log2 Pr(t)
- log2? Encodes bits
- Maximum: Pr(Press) = Pr(Speech) = 0.5
- Minimum: Pr(Press) → 0 (or Pr(Press) → 1)
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 7 / 29
A Method for Identifying Distinguishing Words
- Pr(Press) ≡ Probability selected document press release
- Pr(Speech) ≡ Probability selected document speech
- Define entropy H(k)
H(k) = −∑
t∈{Pre,Spe}
Pr(t) log2 Pr(t)
- log2? Encodes bits
- Maximum: Pr(Press) = Pr(Speech) = 0.5
- Minimum: Pr(Press) → 0 (or Pr(Press) → 1)
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 7 / 29
A Method for Identifying Distinguishing Words
- Consider presence/absence of word wj
- Define conditional entropy H(k |wj)
H(k |wj) = −1∑
s=0
∑t∈{Pre,Spe}
Pr(t,wj = s) log2 Pr(t|wj = s)
- Maximum: wj unrelated to Press Releases/Floor Speeches
- Minimum: wj is a perfect predictor of press release/floor speech
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 8 / 29
A Method for Identifying Distinguishing Words
- Consider presence/absence of word wj
- Define conditional entropy H(k |wj)
H(k |wj) = −1∑
s=0
∑t∈{Pre,Spe}
Pr(t,wj = s) log2 Pr(t|wj = s)
- Maximum: wj unrelated to Press Releases/Floor Speeches
- Minimum: wj is a perfect predictor of press release/floor speech
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 8 / 29
A Method for Identifying Distinguishing Words
- Consider presence/absence of word wj
- Define conditional entropy H(k |wj)
H(k |wj) = −1∑
s=0
∑t∈{Pre,Spe}
Pr(t,wj = s) log2 Pr(t|wj = s)
- Maximum: wj unrelated to Press Releases/Floor Speeches
- Minimum: wj is a perfect predictor of press release/floor speech
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 8 / 29
A Method for Identifying Distinguishing Words
- Consider presence/absence of word wj
- Define conditional entropy H(k |wj)
H(k |wj) = −1∑
s=0
∑t∈{Pre,Spe}
Pr(t,wj = s) log2 Pr(t|wj = s)
- Maximum: wj unrelated to Press Releases/Floor Speeches
- Minimum: wj is a perfect predictor of press release/floor speech
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 8 / 29
A Method for Identifying Distinguishing Words
- Consider presence/absence of word wj
- Define conditional entropy H(k |wj)
H(k |wj) = −1∑
s=0
∑t∈{Pre,Spe}
Pr(t,wj = s) log2 Pr(t|wj = s)
- Maximum: wj unrelated to Press Releases/Floor Speeches
- Minimum: wj is a perfect predictor of press release/floor speech
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 8 / 29
A Method for Identifying Distinguishing Words
- Consider presence/absence of word wj
- Define conditional entropy H(k |wj)
H(k |wj) = −1∑
s=0
∑t∈{Pre,Spe}
Pr(t,wj = s) log2 Pr(t|wj = s)
- Maximum: wj unrelated to Press Releases/Floor Speeches
- Minimum: wj is a perfect predictor of press release/floor speech
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 8 / 29
A Method for Identifying Distinguishing Words
- Define Mutual Information(wj) as
Mutual Information(wj) = H(k)− H(k|wj)
- Maximum: entropy ⇒ H(k |wj) = 0
- Minimum: 0 ⇒ H(k |wj) = H(k).
Bigger mutual information ⇒ better discrimination
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 9 / 29
A Method for Identifying Distinguishing Words
- Define Mutual Information(wj) as
Mutual Information(wj) = H(k)− H(k|wj)
- Maximum: entropy ⇒ H(k |wj) = 0
- Minimum: 0 ⇒ H(k |wj) = H(k).
Bigger mutual information ⇒ better discrimination
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 9 / 29
A Method for Identifying Distinguishing Words
- Define Mutual Information(wj) as
Mutual Information(wj) = H(k)− H(k|wj)
- Maximum: entropy ⇒ H(k |wj) = 0
- Minimum: 0 ⇒ H(k |wj) = H(k).
Bigger mutual information ⇒ better discrimination
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 9 / 29
A Method for Identifying Distinguishing Words
- Define Mutual Information(wj) as
Mutual Information(wj) = H(k)− H(k|wj)
- Maximum: entropy ⇒ H(k |wj) = 0
- Minimum: 0 ⇒ H(k |wj) = H(k).
Bigger mutual information ⇒ better discrimination
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 9 / 29
A Method for Identifying Distinguishing Words
- Define Mutual Information(wj) as
Mutual Information(wj) = H(k)− H(k|wj)
- Maximum: entropy ⇒ H(k |wj) = 0
- Minimum: 0 ⇒ H(k |wj) = H(k).
Bigger mutual information ⇒ better discrimination
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 9 / 29
A Method for Identifying Distinguishing Words
- Define Mutual Information(wj) as
Mutual Information(wj) = H(k)− H(k|wj)
- Maximum: entropy ⇒ H(k |wj) = 0
- Minimum: 0 ⇒ H(k |wj) = H(k).
Bigger mutual information ⇒ better discrimination
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 9 / 29
A Method for Identifying Distinguishing Words
Formula for mutual information(based on ML estimates of probabilities)
np = Number Press Releases
ns = Number of Speeches
D = np + ns
nj =D∑i=1
wi ,j (No. docs wj appears )
n−j = No. docs wj does not appear
nj ,p = No. press and wj
nj ,s = No. speech and wj
n−j ,p = No. press and not wj
n−j ,s = No. speech and not wj
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 10 / 29
A Method for Identifying Distinguishing Words
Formula for Mutual Information
MI(wj) =nj ,pD
log2nj ,pD
njnp+
nj ,sD
log2nj ,sD
njns
+n−j ,pD
log2n−j ,pD
n−jnp+
n−j ,sD
log2n−j ,sD
n−jns.
(Page 258, 259 of this documenthttp://stanford.edu/~jgrimmer/RepStyle.pdf for more information)
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 11 / 29
What’s Different About Press Releases
−20000 −10000 0 10000
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No. Times Speech − No. Times Press
Mut
ual I
nfor
mat
ion
What’s Different?
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 12 / 29
What’s Different About Press Releases
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What’s Different?
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 12 / 29
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- Press Releases: Credit Claiming
- Floor Speeches: Procedural Words
- Validate: Manual Classification
- Sample 500 Press Releases, 500 Floor Speeches
- Credit Claiming: 36% Press Releases, 4% Floor Speeches
- Procedural: 0% Press Releases, 44% Floor Speeches
- Validate: Topic Classification
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 12 / 29
What’s Different About Press Releases
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- Press Releases: Credit Claiming
- Floor Speeches: Procedural Words
- Validate: Manual Classification
- Sample 500 Press Releases, 500 Floor Speeches
- Credit Claiming: 36% Press Releases, 4% Floor Speeches
- Procedural: 0% Press Releases, 44% Floor Speeches
- Validate: Topic Classification
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 12 / 29
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- Press Releases: Credit Claiming
- Floor Speeches: Procedural Words
- Validate: Manual Classification
- Sample 500 Press Releases, 500 Floor Speeches
- Credit Claiming: 36% Press Releases, 4% Floor Speeches
- Procedural: 0% Press Releases, 44% Floor Speeches
- Validate: Topic Classification
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 12 / 29
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- Press Releases: Credit Claiming
- Floor Speeches: Procedural Words
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- Sample 500 Press Releases, 500 Floor Speeches
- Credit Claiming: 36% Press Releases, 4% Floor Speeches
- Procedural: 0% Press Releases, 44% Floor Speeches
- Validate: Topic Classification
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What’s Different?
- Press Releases: Credit Claiming
- Floor Speeches: Procedural Words
- Validate: Manual Classification
- Sample 500 Press Releases, 500 Floor Speeches
- Credit Claiming: 36% Press Releases, 4% Floor Speeches
- Procedural: 0% Press Releases, 44% Floor Speeches
- Validate: Topic Classification
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 12 / 29
What’s Different About Press Releases
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What’s Different?
- Press Releases: Credit Claiming
- Floor Speeches: Procedural Words
- Validate: Manual Classification
- Sample 500 Press Releases, 500 Floor Speeches
- Credit Claiming: 36% Press Releases, 4% Floor Speeches
- Procedural: 0% Press Releases, 44% Floor Speeches
- Validate: Topic Classification
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 12 / 29
What’s Different About Press Releases
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What’s Different?
- Press Releases: Credit Claiming
- Floor Speeches: Procedural Words
- Validate: Manual Classification
- Sample 500 Press Releases, 500 Floor Speeches
- Credit Claiming: 36% Press Releases, 4% Floor Speeches
- Procedural: 0% Press Releases, 44% Floor Speeches
- Validate: Topic Classification
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 12 / 29
What’s Different About Press Releases
Difference
−0.04 −0.02 0 0.02 0.04
Press Attention − Speech Attention
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What’s Different?
- Press Releases: Credit Claiming- Floor Speeches: Procedural Words- Validate: Manual Classification- Sample 500 Press Releases, 500 Floor Speeches- Credit Claiming: 36% Press Releases, 4% Floor Speeches- Procedural: 0% Press Releases, 44% Floor Speeches- Validate: Topic Classification
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 12 / 29
General Idea
- What we know: document labels
- Certain- Complete
- Inference: discriminating words
- Words that separate classes
- All methods presented today:
- Know labels- Infer words
- All methods last week:
- Know words- Infer labels
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 13 / 29
General Idea
- What we know: document labels
- Certain- Complete
- Inference: discriminating words
- Words that separate classes
- All methods presented today:
- Know labels- Infer words
- All methods last week:
- Know words- Infer labels
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 13 / 29
General Idea
- What we know: document labels
- Certain- Complete
- Inference: discriminating words
- Words that separate classes
- All methods presented today:
- Know labels- Infer words
- All methods last week:
- Know words- Infer labels
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 13 / 29
General Idea
- What we know: document labels
- Certain- Complete
- Inference: discriminating words
- Words that separate classes
- All methods presented today:
- Know labels- Infer words
- All methods last week:
- Know words- Infer labels
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 13 / 29
General Idea
- What we know: document labels
- Certain- Complete
- Inference: discriminating words
- Words that separate classes
- All methods presented today:
- Know labels- Infer words
- All methods last week:
- Know words- Infer labels
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 13 / 29
General Idea
- What we know: document labels
- Certain- Complete
- Inference: discriminating words
- Words that separate classes
- All methods presented today:
- Know labels- Infer words
- All methods last week:
- Know words- Infer labels
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 13 / 29
General Idea
- What we know: document labels
- Certain- Complete
- Inference: discriminating words
- Words that separate classes
- All methods presented today:
- Know labels
- Infer words
- All methods last week:
- Know words- Infer labels
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 13 / 29
General Idea
- What we know: document labels
- Certain- Complete
- Inference: discriminating words
- Words that separate classes
- All methods presented today:
- Know labels- Infer words
- All methods last week:
- Know words- Infer labels
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 13 / 29
General Idea
- What we know: document labels
- Certain- Complete
- Inference: discriminating words
- Words that separate classes
- All methods presented today:
- Know labels- Infer words
- All methods last week:
- Know words- Infer labels
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 13 / 29
General Idea
- What we know: document labels
- Certain- Complete
- Inference: discriminating words
- Words that separate classes
- All methods presented today:
- Know labels- Infer words
- All methods last week:
- Know words
- Infer labels
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 13 / 29
General Idea
- What we know: document labels
- Certain- Complete
- Inference: discriminating words
- Words that separate classes
- All methods presented today:
- Know labels- Infer words
- All methods last week:
- Know words- Infer labels
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 13 / 29
Why Infer Separating Words?
Why do we care?
Social Science Inference:
- Differences in Republican, Democrat Language
- Differences in Liberal, Conservative Language
- Differences in Campaign Agendas
- Different Advice to Muslim and Christian Kings
- Recommendation Letters for Men and Women?
- Toy Advertising for Boys and Girls?
- Beginning of Inference
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 14 / 29
Why Infer Separating Words?
Why do we care?Social Science Inference:
- Differences in Republican, Democrat Language
- Differences in Liberal, Conservative Language
- Differences in Campaign Agendas
- Different Advice to Muslim and Christian Kings
- Recommendation Letters for Men and Women?
- Toy Advertising for Boys and Girls?
- Beginning of Inference
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 14 / 29
Why Infer Separating Words?
Why do we care?Social Science Inference:
- Differences in Republican, Democrat Language
- Differences in Liberal, Conservative Language
- Differences in Campaign Agendas
- Different Advice to Muslim and Christian Kings
- Recommendation Letters for Men and Women?
- Toy Advertising for Boys and Girls?
- Beginning of Inference
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 14 / 29
Why Infer Separating Words?
Why do we care?Social Science Inference:
- Differences in Republican, Democrat Language
- Differences in Liberal, Conservative Language
- Differences in Campaign Agendas
- Different Advice to Muslim and Christian Kings
- Recommendation Letters for Men and Women?
- Toy Advertising for Boys and Girls?
- Beginning of Inference
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 14 / 29
Why Infer Separating Words?
Why do we care?Social Science Inference:
- Differences in Republican, Democrat Language
- Differences in Liberal, Conservative Language
- Differences in Campaign Agendas
- Different Advice to Muslim and Christian Kings
- Recommendation Letters for Men and Women?
- Toy Advertising for Boys and Girls?
- Beginning of Inference
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 14 / 29
Why Infer Separating Words?
Why do we care?Social Science Inference:
- Differences in Republican, Democrat Language
- Differences in Liberal, Conservative Language
- Differences in Campaign Agendas
- Different Advice to Muslim and Christian Kings
- Recommendation Letters for Men and Women?
- Toy Advertising for Boys and Girls?
- Beginning of Inference
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 14 / 29
Why Infer Separating Words?
Why do we care?Social Science Inference:
- Differences in Republican, Democrat Language
- Differences in Liberal, Conservative Language
- Differences in Campaign Agendas
- Different Advice to Muslim and Christian Kings
- Recommendation Letters for Men and Women?
- Toy Advertising for Boys and Girls?
- Beginning of Inference
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 14 / 29
Why Infer Separating Words?
Why do we care?Social Science Inference:
- Differences in Republican, Democrat Language
- Differences in Liberal, Conservative Language
- Differences in Campaign Agendas
- Different Advice to Muslim and Christian Kings
- Recommendation Letters for Men and Women?
- Toy Advertising for Boys and Girls?
- Beginning of Inference
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 14 / 29
Why Infer Separating Words?
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 14 / 29
Why Infer Separating Words?
Why do we care?Social Science Inference:
- Differences in Republican, Democrat Language
- Differences in Liberal, Conservative Language
- Differences in Campaign Agendas
- Different Advice to Muslim and Christian Kings
- Recommendation Letters for Men and Women?
- Toy Advertising for Boys and Girls?
- Beginning of Inference
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 14 / 29
Why Infer Separating Words?
Labeling
- Methods to estimate classes (Week 6 and 7)
- Label classes: why grouped together?
Dictionary Creation
- Training Set: use documents to identify separating words
- Test Set: Validate separating words
Improve Supervised Learning Classification (Weeks 8, 9)
- Usually: more information, better
- Reality: rare words can cause over fitting
- Feature selection: one method to mitigate over fitting
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 15 / 29
Why Infer Separating Words?
Labeling
- Methods to estimate classes (Week 6 and 7)
- Label classes: why grouped together?
Dictionary Creation
- Training Set: use documents to identify separating words
- Test Set: Validate separating words
Improve Supervised Learning Classification (Weeks 8, 9)
- Usually: more information, better
- Reality: rare words can cause over fitting
- Feature selection: one method to mitigate over fitting
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 15 / 29
Why Infer Separating Words?
Labeling
- Methods to estimate classes (Week 6 and 7)
- Label classes: why grouped together?
Dictionary Creation
- Training Set: use documents to identify separating words
- Test Set: Validate separating words
Improve Supervised Learning Classification (Weeks 8, 9)
- Usually: more information, better
- Reality: rare words can cause over fitting
- Feature selection: one method to mitigate over fitting
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 15 / 29
Why Infer Separating Words?
Labeling
- Methods to estimate classes (Week 6 and 7)
- Label classes: why grouped together?
Dictionary Creation
- Training Set: use documents to identify separating words
- Test Set: Validate separating words
Improve Supervised Learning Classification (Weeks 8, 9)
- Usually: more information, better
- Reality: rare words can cause over fitting
- Feature selection: one method to mitigate over fitting
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 15 / 29
Why Infer Separating Words?
Labeling
- Methods to estimate classes (Week 6 and 7)
- Label classes: why grouped together?
Dictionary Creation
- Training Set: use documents to identify separating words
- Test Set: Validate separating words
Improve Supervised Learning Classification (Weeks 8, 9)
- Usually: more information, better
- Reality: rare words can cause over fitting
- Feature selection: one method to mitigate over fitting
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 15 / 29
Why Infer Separating Words?
Labeling
- Methods to estimate classes (Week 6 and 7)
- Label classes: why grouped together?
Dictionary Creation
- Training Set: use documents to identify separating words
- Test Set: Validate separating words
Improve Supervised Learning Classification (Weeks 8, 9)
- Usually: more information, better
- Reality: rare words can cause over fitting
- Feature selection: one method to mitigate over fitting
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 15 / 29
Why Infer Separating Words?
Labeling
- Methods to estimate classes (Week 6 and 7)
- Label classes: why grouped together?
Dictionary Creation
- Training Set: use documents to identify separating words
- Test Set: Validate separating words
Improve Supervised Learning Classification (Weeks 8, 9)
- Usually: more information, better
- Reality: rare words can cause over fitting
- Feature selection: one method to mitigate over fitting
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 15 / 29
Why Infer Separating Words?
Labeling
- Methods to estimate classes (Week 6 and 7)
- Label classes: why grouped together?
Dictionary Creation
- Training Set: use documents to identify separating words
- Test Set: Validate separating words
Improve Supervised Learning Classification (Weeks 8, 9)
- Usually: more information, better
- Reality: rare words can cause over fitting
- Feature selection: one method to mitigate over fitting
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 15 / 29
Why Infer Separating Words?
Labeling
- Methods to estimate classes (Week 6 and 7)
- Label classes: why grouped together?
Dictionary Creation
- Training Set: use documents to identify separating words
- Test Set: Validate separating words
Improve Supervised Learning Classification (Weeks 8, 9)
- Usually: more information, better
- Reality: rare words can cause over fitting
- Feature selection: one method to mitigate over fitting
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 15 / 29
Why Infer Separating Words?
Labeling
- Methods to estimate classes (Week 6 and 7)
- Label classes: why grouped together?
Dictionary Creation
- Training Set: use documents to identify separating words
- Test Set: Validate separating words
Improve Supervised Learning Classification (Weeks 8, 9)
- Usually: more information, better
- Reality: rare words can cause over fitting
- Feature selection: one method to mitigate over fitting
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 15 / 29
Why Infer Separating Words?
Labeling
- Methods to estimate classes (Week 6 and 7)
- Label classes: why grouped together?
Dictionary Creation
- Training Set: use documents to identify separating words
- Test Set: Validate separating words
Improve Supervised Learning Classification (Weeks 8, 9)
- Usually: more information, better
- Reality: rare words can cause over fitting
- Feature selection: one method to mitigate over fitting
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 15 / 29
Methods for Inference/Labeling
Task 1: Well defined
- Identifying maximally discriminating words
- Objective function for discrimination
- Identify each word’s discrimination
We can derive optimal method, given objectiveTake 2: Vague
- Generate intuition about differences
- Use this intuition then to investigate claims
- Intuition very hard to formalize
Very difficult (impossible) to derive optimal method a priori
Be skeptical!
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 16 / 29
Methods for Inference/Labeling
Task 1: Well defined
- Identifying maximally discriminating words
- Objective function for discrimination
- Identify each word’s discrimination
We can derive optimal method, given objectiveTake 2: Vague
- Generate intuition about differences
- Use this intuition then to investigate claims
- Intuition very hard to formalize
Very difficult (impossible) to derive optimal method a priori
Be skeptical!
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 16 / 29
Methods for Inference/Labeling
Task 1: Well defined
- Identifying maximally discriminating words
- Objective function for discrimination
- Identify each word’s discrimination
We can derive optimal method, given objectiveTake 2: Vague
- Generate intuition about differences
- Use this intuition then to investigate claims
- Intuition very hard to formalize
Very difficult (impossible) to derive optimal method a priori
Be skeptical!
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 16 / 29
Methods for Inference/Labeling
Task 1: Well defined
- Identifying maximally discriminating words
- Objective function for discrimination
- Identify each word’s discrimination
We can derive optimal method, given objectiveTake 2: Vague
- Generate intuition about differences
- Use this intuition then to investigate claims
- Intuition very hard to formalize
Very difficult (impossible) to derive optimal method a priori
Be skeptical!
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 16 / 29
Methods for Inference/Labeling
Task 1: Well defined
- Identifying maximally discriminating words
- Objective function for discrimination
- Identify each word’s discrimination
We can derive optimal method, given objectiveTake 2: Vague
- Generate intuition about differences
- Use this intuition then to investigate claims
- Intuition very hard to formalize
Very difficult (impossible) to derive optimal method a priori
Be skeptical!
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 16 / 29
Methods for Inference/Labeling
Task 1: Well defined
- Identifying maximally discriminating words
- Objective function for discrimination
- Identify each word’s discrimination
We can derive optimal method, given objective
Take 2: Vague
- Generate intuition about differences
- Use this intuition then to investigate claims
- Intuition very hard to formalize
Very difficult (impossible) to derive optimal method a priori
Be skeptical!
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 16 / 29
Methods for Inference/Labeling
Task 1: Well defined
- Identifying maximally discriminating words
- Objective function for discrimination
- Identify each word’s discrimination
We can derive optimal method, given objectiveTake 2: Vague
- Generate intuition about differences
- Use this intuition then to investigate claims
- Intuition very hard to formalize
Very difficult (impossible) to derive optimal method a priori
Be skeptical!
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 16 / 29
Methods for Inference/Labeling
Task 1: Well defined
- Identifying maximally discriminating words
- Objective function for discrimination
- Identify each word’s discrimination
We can derive optimal method, given objectiveTake 2: Vague
- Generate intuition about differences
- Use this intuition then to investigate claims
- Intuition very hard to formalize
Very difficult (impossible) to derive optimal method a priori
Be skeptical!
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 16 / 29
Methods for Inference/Labeling
Task 1: Well defined
- Identifying maximally discriminating words
- Objective function for discrimination
- Identify each word’s discrimination
We can derive optimal method, given objectiveTake 2: Vague
- Generate intuition about differences
- Use this intuition then to investigate claims
- Intuition very hard to formalize
Very difficult (impossible) to derive optimal method a priori
Be skeptical!
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 16 / 29
Methods for Inference/Labeling
Task 1: Well defined
- Identifying maximally discriminating words
- Objective function for discrimination
- Identify each word’s discrimination
We can derive optimal method, given objectiveTake 2: Vague
- Generate intuition about differences
- Use this intuition then to investigate claims
- Intuition very hard to formalize
Very difficult (impossible) to derive optimal method a priori
Be skeptical!
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 16 / 29
Methods for Inference/Labeling
Task 1: Well defined
- Identifying maximally discriminating words
- Objective function for discrimination
- Identify each word’s discrimination
We can derive optimal method, given objectiveTake 2: Vague
- Generate intuition about differences
- Use this intuition then to investigate claims
- Intuition very hard to formalize
Very difficult (impossible) to derive optimal method a priori
Be skeptical!
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 16 / 29
Methods for Inference/Labeling
Task 1: Well defined
- Identifying maximally discriminating words
- Objective function for discrimination
- Identify each word’s discrimination
We can derive optimal method, given objectiveTake 2: Vague
- Generate intuition about differences
- Use this intuition then to investigate claims
- Intuition very hard to formalize
Very difficult (impossible) to derive optimal method a priori
Be skeptical!
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 16 / 29
Running Example
How Do Democrat and Republican Arguments About the Iraq War Differ?
- Assume: Identified set of documents (press releases) about Iraq War
- Speaker labels: know who (Democrat, Republican) issued pressrelease
- Inferential Goal: framing–considerations Democrats and Republicansuse when discussing war
Present simple methods, show similarity.The example already has stop words and some names removed.
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 17 / 29
Methods for Identifying Words
(Following steps are from Fightin’ Words )Difference in word frequency:For each word j compute
njD = No. times used in Dem Documents
njR = No. times used in Rep Documents
Difference = njD − njR
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 18 / 29
Methods for Identifying Words(Following steps are from Fightin’ Words )Difference = njD − njR
Dem
Fre
quen
cy −
Rep
Fre
quen
cy
dialogu
refug
china
deterior
controversi
golden
music
want
travel
wrong
fit
fix
accommod
adapt
masterspectrum
dozen
tech
restaur
rich
rice
extend
extens
extent
unemploy
southeastern
assur
assum
union
regul
davi
employ
refin
endur
shadow
attorney
creativfabric
suffici
safeguard
role
roll
intend
devot
intens
intent
chain
chair
substitut
oversight
hardwork
300
boost
modif
address
instal
enhanc
ideolog
civilian
clotur
quarterreceipt
sponsor
internet
modestneglect
spoken
allevi
transact
vision
televis
unconscion
taxpay
west
resolut
convinc
statewid
exercis
unveil
world
obstruct
notabl
leadership
basin
conclud
pull
triplruss
creat
cheney
midwest
roadway
colleagu
sand
small
past
deleg
inher
prior
depart
morn
door
uncov
compani
learn
huge
simplpaper
bypass
procedur
research
packag
shortchang
sell
self
barrel
jurisdict
remedi
compass
sunni
tanker
exacerb
thrive
irrespons
infect
budgetreal
vow
read
implement
mandatbureaucrat
simplifi
acknowledg
sampl
caucu
span
land
train
broaderharbor
videoevacu
survey
maker
babi
process
lockhoustoninsightperfect
prosper
overal
model
area
length
unman
tonight
placement
jay
tape
ohio
nuclear
lawsuit
obstacl
purchas
reclam
diversifi
audio
web
piec
incent
passion
congresswoman
problem
filibust
deadli
repeat
repeal
worth
consequ
longstand
supervis
redeploy
110th
era
impair
chines
diagnos
safe
barrier
renew
nomin
wastewat
subsid
grave
roundtabl
secretari
septemb
awar
away
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hand
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client
leagu
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percentag
born
underserv
peer
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maximum
request
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test
outdat
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supplement
diplomaci
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cost
defici
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regardless
extra
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prepar
chip
occuroccup
multipl
economi
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drastic
loophol
approv
brain dynam
wealthiintroduct
drop
replac
nonprofit
blind
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satellit
importantli
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steadi
import
exploit
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waterway
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start
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140
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200
208
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minimumexplor
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withdraw
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detain
342
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hide
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exclud
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545
discoveri
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wrote
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sole
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oversea
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sweep
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collabor
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emphasi
long
ralli
meaning
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breach
folk
compar
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chose
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larger
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attend
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villag
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651
diminish
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fear
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confere
scrutini
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largest
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incred
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charter
miller
militari
spoke
relat
hurt
household
wing
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vari
enrich
township
silver
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navig
wast
wash
instruct
175
listen
wisdom
specifi
letter
drought
professor
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advisori
respond
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fairli
preserv
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tell
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Justin Grimmer (Stanford University) Text as Data April 27th, 2011 18 / 29
Methods for Identifying Words
Differences in Word Proportions:For each word j compute
pjD =njDnD
= Proportion of Dem words that are j
pjR =njRnR
= Proportion of Rep words that are j
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Justin Grimmer (Stanford University) Text as Data April 27th, 2011 19 / 29
Methods for Identifying WordsDifference = pjD − pjR
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Justin Grimmer (Stanford University) Text as Data April 27th, 2011 20 / 29
Methods for Identifying Words
Problem: What to Do With Dem (GOP) Only Words?If Only Dems Use Words:
pjR =0
nR
OddsjR =0
1log OddsjR = log 0− log 1
What should we do?
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 21 / 29
Methods for Identifying WordsSolution: “add” a little, but in a principled way
We need a model!: Intro to Bayes in 10 minutesNotation:
pR = (p1R , p2R , . . . , pNR)
pD = (p1D , p2D , . . . , pND)
yD ∼ Multinomial(nD ,pD)
Prior
pR ∼ Dirichlet(α)
pD ∼ Dirichlet(α)
α = (α1, α2, . . . , αN)
Before showing why this “adds” a little.Let me teach you how to Dirichlet
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 22 / 29
Methods for Identifying WordsSolution: “add” a little, but in a principled wayWe need a model!: Intro to Bayes in 10 minutes
Notation:
pR = (p1R , p2R , . . . , pNR)
pD = (p1D , p2D , . . . , pND)
yD ∼ Multinomial(nD ,pD)
Prior
pR ∼ Dirichlet(α)
pD ∼ Dirichlet(α)
α = (α1, α2, . . . , αN)
Before showing why this “adds” a little.Let me teach you how to Dirichlet
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 22 / 29
Methods for Identifying WordsSolution: “add” a little, but in a principled wayWe need a model!: Intro to Bayes in 10 minutesNotation:
pR = (p1R , p2R , . . . , pNR)
pD = (p1D , p2D , . . . , pND)
yD ∼ Multinomial(nD ,pD)
Prior
pR ∼ Dirichlet(α)
pD ∼ Dirichlet(α)
α = (α1, α2, . . . , αN)
Before showing why this “adds” a little.Let me teach you how to Dirichlet
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 22 / 29
Methods for Identifying WordsSolution: “add” a little, but in a principled wayWe need a model!: Intro to Bayes in 10 minutesNotation:
pR = (p1R , p2R , . . . , pNR)
pD = (p1D , p2D , . . . , pND)
yD ∼ Multinomial(nD ,pD)
Prior
pR ∼ Dirichlet(α)
pD ∼ Dirichlet(α)
α = (α1, α2, . . . , αN)
Before showing why this “adds” a little.Let me teach you how to Dirichlet
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 22 / 29
Methods for Identifying WordsSolution: “add” a little, but in a principled wayWe need a model!: Intro to Bayes in 10 minutesNotation:
pR = (p1R , p2R , . . . , pNR)
pD = (p1D , p2D , . . . , pND)
yD ∼ Multinomial(nD ,pD)
Prior
pR ∼ Dirichlet(α)
pD ∼ Dirichlet(α)
α = (α1, α2, . . . , αN)
Before showing why this “adds” a little.Let me teach you how to Dirichlet
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 22 / 29
Methods for Identifying WordsSolution: “add” a little, but in a principled wayWe need a model!: Intro to Bayes in 10 minutesNotation:
pR = (p1R , p2R , . . . , pNR)
pD = (p1D , p2D , . . . , pND)
yD ∼ Multinomial(nD ,pD)
Prior
pR ∼ Dirichlet(α)
pD ∼ Dirichlet(α)
α = (α1, α2, . . . , αN)
Before showing why this “adds” a little.Let me teach you how to Dirichlet
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 22 / 29
Methods for Identifying WordsSolution: “add” a little, but in a principled wayWe need a model!: Intro to Bayes in 10 minutesNotation:
pR = (p1R , p2R , . . . , pNR)
pD = (p1D , p2D , . . . , pND)
yD ∼ Multinomial(nD ,pD)
Prior
pR ∼ Dirichlet(α)
pD ∼ Dirichlet(α)
α = (α1, α2, . . . , αN)
Before showing why this “adds” a little.
Let me teach you how to Dirichlet
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 22 / 29
Methods for Identifying WordsSolution: “add” a little, but in a principled wayWe need a model!: Intro to Bayes in 10 minutesNotation:
pR = (p1R , p2R , . . . , pNR)
pD = (p1D , p2D , . . . , pND)
yD ∼ Multinomial(nD ,pD)
Prior
pR ∼ Dirichlet(α)
pD ∼ Dirichlet(α)
α = (α1, α2, . . . , αN)
Before showing why this “adds” a little.Let me teach you how to DirichletJustin Grimmer (Stanford University) Text as Data April 27th, 2011 22 / 29
Dirichlet Distribution
Distribution over proportions.
π ∼ Dirichlet(α)
p(π|α) =Γ(∑
j αj∏j Γαj
N∏j=1
παj−1j
Facts:
E [πj ] =αj∑N
k=1 αk
Variance[πj ] =E [πj ](1− E [πj ])∑N
k=1(αk) + 1
Conjugate to Multinomial : easily apply to the model
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 23 / 29
Methods for Identifying Separating Words
pD |α ∼ Dirichlet(α)
yD |pD ∼ Multinomial(nD ,pD)
Conjugacy implies
pD |yD ,α ∼ Dirichlet(α′)
α′j = yjD + αj
E [pj ,D ] =yjD + α
′j
nD +∑N
k=1 α′k
Smoothing (borrowing information): easy to understand in Bayesianframework, take Simon’s class
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 24 / 29
Methods for Identifying Separating Words
Now, we can compute all log-odds.But same problem: rare words dominateSolution: include estimate of variance
Var(log Odds Ratioj) ≈1
yjD + αj+
1
yjR + αj
Std. Log Oddsj =log Odds Ratioj√
Var(log Odds Ratioj)
Analogues from Contingency TablesKey Idea:Systematic or Random Difference
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 25 / 29
Methods For Identifying Words
−60 −40 −20 0 20 40
−2
−1
01
23
Std. Log Odds Ratio
Log
Odd
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Justin Grimmer (Stanford University) Text as Data April 27th, 2011 27 / 29
Mutual Information, Standardized Log Odds
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Justin Grimmer (Stanford University) Text as Data April 27th, 2011 27 / 29
Methods for Identifying Words
There are many other similar methods
- Difference in standardized proportions
- χ2 statistics
- Pointwise Mutual Information
- ...
Characteristics:
- Definition of separation
- Word by word test of separation
- Providing rank ordering of words
- Best Method: depends on context, intuition provided
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 28 / 29
Moving Forward
- Considered word by word methods solely
- During supervised classification, we will consider joint separability
- Conditional on other words, how much more information does this wordprovide
Next Week:
- Geometry of texts
- Foundation for clustering
- topic modeling
- supervised classification
Justin Grimmer (Stanford University) Text as Data April 27th, 2011 29 / 29
