Text as Data

Justin Grimmer

Associate ProfessorDepartment of Political Science

Stanford University

October 7th, 2014

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 1 / 30

Estimating Word Discrimination

1) Task

a) Classification learn word weights for dictionariesb) Fictitious prediction problem Identify features that discriminate

between groups to learn features that are indicative of some group

2) Objective function

f (θ,X ) = f (θ,X ,Y )

where:

Y = Document LabelsX = Document Featuresθ = Parameters that measure words discrimination between categories

3) Optimization method specific

4) Validation depends on task

i) Classification Accuracy, Precision, Recallii) Fictitious prediction Face, convergent, discriminatory, and confound

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 2 / 30

Stylometry Who Wrote Disputed Federalist Papers?Federalist papers Mosteller and Wallace (1963)

- Persuade citizens of New York State to adopt constitution

- Canonical texts in study of American politics

- 77 essays

- Published from 1787-1788 in Newspapers- And under the name Publius, anonymously

Who Wrote the Federalist papers?

- Jay wrote essays 2, 3, 4,5, and 64

- Hamilton: wrote 43 papers

- Madison: wrote 12 papers

Disputed: Hamilton or Madison?

- Essays: 49-58, 62, and 63

- Joint Essays: 18-20

Task: identify authors of the disputed papers.Task: Classify papers as Hamilton or Madison using dictionary methodsJustin Grimmer (Stanford University) Text as Data October 7th, 2014 3 / 30

Setting up the Analysis

Training papers Hamilton, Madison are known to have authoredTest unlabeled papersPreprocessing:

- Hamilton/Madison both discuss similar issues

- Differ in extent they use stop words

- Focus analysis on the stop words

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 4 / 30

Setting up the Analysis

- Y = (Y1,Y2, . . . ,YN) = (Hamilton,Hamilton,Madison, ...,Hamilton)N × 1 matrix with author labels

- Define the number of words in federalist paper i as numi

X =

1

num1

2num1

0num1

. . . 3num1

0num2

1num2

0num2

. . . 0num2

......

.... . .

...0

numN

0numN

1numN

. . . 0numN

N × J counting stop word usage rate

- θ = (θ1, θ2, . . . , θJ)Word weights.

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 5 / 30

Objective FunctionHeuristically: find θ∗ = (θ∗1, θ

∗2, . . . , θ

∗J) used to create score

pi =J∑

j=1

θ∗j Xij

that maximally discriminates between categories

−30 −20 −10 0 10 20 30

−4

−2

02

4

Word1

Wor

d2

●

●

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 6 / 30

Objective Function

Define:

µMadison =1

NMadison

N∑i=1

I (Yi = Madison)X i

µHamilton =1

NHamilton

N∑i=1

I (Yi = Hamilton)X i

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 7 / 30

Objective Function

We can then define functions that describe the “projected” mean and variance foreach author

g(θ,X ,Y ,Madison) =1

NMadison

N∑i=1

I (Yi = Madison)θ′X i = θ

′µMadison

g(θ,X ,Y ,Hamilton) =1

NHamilton

N∑i=1

I (Yi = Hamilton)θ′X i = θ

′µHamilton

s(θ,X ,Y ,Madison) =N∑i=1

I (Yi = Madison)(θ′X i − θ

′µMadison)2

s(θ,X ,Y ,Hamilton) =N∑i=1

I (Yi = Hamilton)(θ′X i − θ

′µHamilton)2

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 8 / 30

Objective Function Optimization

f (θ,X ,Y ) =(g(θ,X ,Y ,Hamilton)− g(θ,X ,Y ,Madison))2

s(θ,X ,Y ,Hamilton) + s(θ,X ,Y ,Madison)

=

(θ

′(µHamilton − µMadison)

)2ScatterHamilton + ScatterMadison

Optimization find θ∗ to maximize f (θ,X ,Y ), assuming independenceacross dimensions.(Fisher’s) Linear Discriminant Analysis

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 9 / 30

Optimization Word Weights

For each word j , construct weight θ∗j ,

µj,Hamilton =

∑Ni=1 I (Yi = Hamilton)Xij∑J

j=1

∑Ni=1 I (Yi = Hamilton)Xij

µj,Madison =

∑Ni=1 I (Yi = Madison)Xij∑J

j=1

∑Ni=1 I (Yi = Madison)Xij

σ2j,Hamilton = Var(Xi,j |Hamilton)

σ2j,Madison = Var(Xi,j |Madison)

We can then generate weight θ∗j as

θ∗j =µj ,Hamilton − µj ,Madison

σ2j ,Hamilton + σ2j ,Madison

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 10 / 30

Optimization Trimming the Dictionary

- Trimming weights: Focus on discriminating words (very simpleregularization)

- Cut off: For all |θ∗j | < 0.025 set θ∗j = 0.

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 11 / 30

Classification Determining Authorship

For each disputed document i , compute discrimination statistic

pi =J∑

j=1

θ∗j Xij

pi classification (linear discriminator)

- Above midpoint in training set → Hamilton text

- Below midpoint in training set → Madison text

Findings: Madison is the author of the disputed federalist papers.

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 12 / 30

Inferring Separating WordsClassification Custom Dictionaries

- Stylometry Classify Authors

- Dictionary based classification Gentzkow and Shapiro (2010) andmeasures of media slant

- Dictionary based classification Customized to particular setting

Fictitious Prediction Problem Infer words that are indicative of someclass/group

- Difference in Republican, Democratic language Partisan words

- Difference in Liberal, Conservative language Ideological Language

- Difference in Secret/Not Secret Language Secretive Language (Gilland Spirling 2014)

- Difference in Toy advertising

- Difference in Language across groups Labeling output fromClustering/Topic Models

Vague and Difficult to derive before hand

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 13 / 30

Inferring Separating WordsClassification Custom Dictionaries

- Stylometry Classify Authors

- Dictionary based classification Gentzkow and Shapiro (2010) andmeasures of media slant

- Dictionary based classification Customized to particular setting

Fictitious Prediction Problem Infer words that are indicative of someclass/group

- Difference in Republican, Democratic language Partisan words

- Difference in Liberal, Conservative language Ideological Language

- Difference in Secret/Not Secret Language Secretive Language (Gilland Spirling 2014)

- Difference in Toy advertising

- Difference in Language across groups Labeling output fromClustering/Topic Models

Vague and Difficult to derive before hand

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 13 / 30

Inferring Separating WordsClassification Custom Dictionaries

- Stylometry Classify Authors

- Dictionary based classification Gentzkow and Shapiro (2010) andmeasures of media slant

- Dictionary based classification Customized to particular setting

Fictitious Prediction Problem Infer words that are indicative of someclass/group

- Difference in Republican, Democratic language Partisan words

- Difference in Liberal, Conservative language Ideological Language

- Difference in Secret/Not Secret Language Secretive Language (Gilland Spirling 2014)

- Difference in Toy advertising

- Difference in Language across groups Labeling output fromClustering/Topic Models

Vague and Difficult to derive before hand

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 13 / 30

Inferring Separating WordsClassification Custom Dictionaries

- Stylometry Classify Authors

- Dictionary based classification Gentzkow and Shapiro (2010) andmeasures of media slant

- Dictionary based classification Customized to particular setting

Fictitious Prediction Problem Infer words that are indicative of someclass/group

- Difference in Republican, Democratic language Partisan words

- Difference in Liberal, Conservative language Ideological Language

- Difference in Secret/Not Secret Language Secretive Language (Gilland Spirling 2014)

- Difference in Toy advertising

- Difference in Language across groups Labeling output fromClustering/Topic Models

Vague and Difficult to derive before hand

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 13 / 30

Inferring Separating WordsClassification Custom Dictionaries

- Stylometry Classify Authors

- Dictionary based classification Gentzkow and Shapiro (2010) andmeasures of media slant

- Dictionary based classification Customized to particular setting

Fictitious Prediction Problem Infer words that are indicative of someclass/group

- Difference in Republican, Democratic language Partisan words

- Difference in Liberal, Conservative language Ideological Language

- Difference in Secret/Not Secret Language Secretive Language (Gilland Spirling 2014)

- Difference in Toy advertising

- Difference in Language across groups Labeling output fromClustering/Topic Models

Vague and Difficult to derive before hand

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 13 / 30

Inferring Separating WordsClassification Custom Dictionaries

- Stylometry Classify Authors

- Dictionary based classification Gentzkow and Shapiro (2010) andmeasures of media slant

- Dictionary based classification Customized to particular setting

Fictitious Prediction Problem Infer words that are indicative of someclass/group

- Difference in Republican, Democratic language Partisan words

- Difference in Liberal, Conservative language Ideological Language

- Difference in Secret/Not Secret Language Secretive Language (Gilland Spirling 2014)

- Difference in Toy advertising

- Difference in Language across groups Labeling output fromClustering/Topic Models

Vague and Difficult to derive before hand

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 13 / 30

Inferring Separating WordsClassification Custom Dictionaries

- Stylometry Classify Authors

- Dictionary based classification Gentzkow and Shapiro (2010) andmeasures of media slant

- Dictionary based classification Customized to particular setting

Fictitious Prediction Problem Infer words that are indicative of someclass/group

- Difference in Republican, Democratic language Partisan words

- Difference in Liberal, Conservative language Ideological Language

- Difference in Secret/Not Secret Language Secretive Language (Gilland Spirling 2014)

- Difference in Toy advertising

- Difference in Language across groups Labeling output fromClustering/Topic Models

Vague and Difficult to derive before hand

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 13 / 30

Inferring Separating WordsClassification Custom Dictionaries

- Stylometry Classify Authors

- Dictionary based classification Gentzkow and Shapiro (2010) andmeasures of media slant

- Dictionary based classification Customized to particular setting

Fictitious Prediction Problem Infer words that are indicative of someclass/group

- Difference in Republican, Democratic language Partisan words

- Difference in Liberal, Conservative language Ideological Language

- Difference in Secret/Not Secret Language Secretive Language (Gilland Spirling 2014)

- Difference in Toy advertising

- Difference in Language across groups Labeling output fromClustering/Topic Models

Vague and Difficult to derive before hand

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 13 / 30

Inferring Separating WordsClassification Custom Dictionaries

- Stylometry Classify Authors

- Dictionary based classification Gentzkow and Shapiro (2010) andmeasures of media slant

- Dictionary based classification Customized to particular setting

Fictitious Prediction Problem Infer words that are indicative of someclass/group

- Difference in Republican, Democratic language Partisan words

- Difference in Liberal, Conservative language Ideological Language

- Difference in Secret/Not Secret Language Secretive Language (Gilland Spirling 2014)

- Difference in Toy advertising

- Difference in Language across groups Labeling output fromClustering/Topic Models

Vague and Difficult to derive before hand

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 13 / 30

Inferring Separating Words

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 13 / 30

Inferring Separating WordsClassification Custom Dictionaries

- Stylometry Classify Authors

- Dictionary based classification Gentzkow and Shapiro (2010) andmeasures of media slant

- Dictionary based classification Customized to particular setting

Fictitious Prediction Problem Infer words that are indicative of someclass/group

- Difference in Republican, Democratic language Partisan words

- Difference in Liberal, Conservative language Ideological Language

- Difference in Secret/Not Secret Language Secretive Language (Gilland Spirling 2014)

- Difference in Toy advertising

- Difference in Language across groups Labeling output fromClustering/Topic Models

Vague and Difficult to derive before hand

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 13 / 30

Inferring Separating WordsClassification Custom Dictionaries

- Stylometry Classify Authors

- Dictionary based classification Gentzkow and Shapiro (2010) andmeasures of media slant

- Dictionary based classification Customized to particular setting

Fictitious Prediction Problem Infer words that are indicative of someclass/group

- Difference in Republican, Democratic language Partisan words

- Difference in Liberal, Conservative language Ideological Language

- Difference in Secret/Not Secret Language Secretive Language (Gilland Spirling 2014)

- Difference in Toy advertising

- Difference in Language across groups Labeling output fromClustering/Topic Models

Vague and Difficult to derive before hand

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 13 / 30

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

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 14 / 30

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

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 14 / 30

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

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 14 / 30

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

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 14 / 30

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

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 14 / 30

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

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 14 / 30

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

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 14 / 30

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

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 14 / 30

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

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 14 / 30

A Method for Identifying Distinguishing Words

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 (Xj) (conditional entropy)

- Condition on presence of word Xj

- 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(Xj): uncertainty - conditional uncertainty (Xj)

- Maximum: Uncertainty → Xj is perfect predictor- Minimum: 0 → Xj fails to separate speeches and floor statements

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 15 / 30

A Method for Identifying Distinguishing Words

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 (Xj) (conditional entropy)

- Condition on presence of word Xj

- 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(Xj): uncertainty - conditional uncertainty (Xj)

- Maximum: Uncertainty → Xj is perfect predictor- Minimum: 0 → Xj fails to separate speeches and floor statements

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 15 / 30

A Method for Identifying Distinguishing Words

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 (Xj) (conditional entropy)

- Condition on presence of word Xj

- 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(Xj): uncertainty - conditional uncertainty (Xj)

- Maximum: Uncertainty → Xj is perfect predictor- Minimum: 0 → Xj fails to separate speeches and floor statements

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 15 / 30

A Method for Identifying Distinguishing Words

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 (Xj) (conditional entropy)

- Condition on presence of word Xj

- 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(Xj): uncertainty - conditional uncertainty (Xj)

- Maximum: Uncertainty → Xj is perfect predictor- Minimum: 0 → Xj fails to separate speeches and floor statements

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 15 / 30

A Method for Identifying Distinguishing Words

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 (Xj) (conditional entropy)

- Condition on presence of word Xj

- 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(Xj): uncertainty - conditional uncertainty (Xj)

- Maximum: Uncertainty → Xj is perfect predictor- Minimum: 0 → Xj fails to separate speeches and floor statements

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 15 / 30

A Method for Identifying Distinguishing Words

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 (Xj) (conditional entropy)

- Condition on presence of word Xj

- 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(Xj): uncertainty - conditional uncertainty (Xj)

- Maximum: Uncertainty → Xj is perfect predictor- Minimum: 0 → Xj fails to separate speeches and floor statements

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 15 / 30

A Method for Identifying Distinguishing Words

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 (Xj) (conditional entropy)

- Condition on presence of word Xj

- 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(Xj): uncertainty - conditional uncertainty (Xj)

- Maximum: Uncertainty → Xj is perfect predictor- Minimum: 0 → Xj fails to separate speeches and floor statements

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 15 / 30

A Method for Identifying Distinguishing Words

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 (Xj) (conditional entropy)

- Condition on presence of word Xj

- 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(Xj): uncertainty - conditional uncertainty (Xj)

- Maximum: Uncertainty → Xj is perfect predictor- Minimum: 0 → Xj fails to separate speeches and floor statements

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 15 / 30

A Method for Identifying Distinguishing Words

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 (Xj) (conditional entropy)

- Condition on presence of word Xj

- 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(Xj): uncertainty - conditional uncertainty (Xj)

- Maximum: Uncertainty → Xj is perfect predictor- Minimum: 0 → Xj fails to separate speeches and floor statements

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 15 / 30

A Method for Identifying Distinguishing Words

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 (Xj) (conditional entropy)

- Condition on presence of word Xj

- 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(Xj): uncertainty - conditional uncertainty (Xj)

- Maximum: Uncertainty → Xj is perfect predictor- Minimum: 0 → Xj fails to separate speeches and floor statements

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 15 / 30

A Method for Identifying Distinguishing Words

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 (Xj) (conditional entropy)

- Condition on presence of word Xj

- 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(Xj): uncertainty - conditional uncertainty (Xj)

- Maximum: Uncertainty → Xj is perfect predictor- Minimum: 0 → Xj fails to separate speeches and floor statements

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 15 / 30

A Method for Identifying Distinguishing Words

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 (Xj) (conditional entropy)

- Condition on presence of word Xj

- 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(Xj): uncertainty - conditional uncertainty (Xj)

- Maximum: Uncertainty → Xj is perfect predictor- Minimum: 0 → Xj fails to separate speeches and floor statements

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 15 / 30

A Method for Identifying Distinguishing Words

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 (Xj) (conditional entropy)

- Condition on presence of word Xj

- 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(Xj): uncertainty - conditional uncertainty (Xj)

- Maximum: Uncertainty → Xj is perfect predictor- Minimum: 0 → Xj fails to separate speeches and floor statements

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 15 / 30

A Method for Identifying Distinguishing Words

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 (Xj) (conditional entropy)

- Condition on presence of word Xj

- 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(Xj): uncertainty - conditional uncertainty (Xj)

- Maximum: Uncertainty → Xj is perfect predictor- Minimum: 0 → Xj fails to separate speeches and floor statements

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 15 / 30

A Method for Identifying Distinguishing Words

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 (Xj) (conditional entropy)

- Condition on presence of word Xj

- 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(Xj): uncertainty - conditional uncertainty (Xj)

- Maximum: Uncertainty → Xj is perfect predictor- Minimum: 0 → Xj fails to separate speeches and floor statements

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 15 / 30

A Method for Identifying Distinguishing Words

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 (Xj) (conditional entropy)

- Condition on presence of word Xj

- 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(Xj): uncertainty - conditional uncertainty (Xj)

- Maximum: Uncertainty → Xj is perfect predictor- Minimum: 0 → Xj fails to separate speeches and floor statements

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 15 / 30

A Method for Identifying Distinguishing Words

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 (Xj) (conditional entropy)

- Condition on presence of word Xj

- 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(Xj): uncertainty - conditional uncertainty (Xj)

- Maximum: Uncertainty → Xj is perfect predictor

- Minimum: 0 → Xj fails to separate speeches and floor statements

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 15 / 30

A Method for Identifying Distinguishing Words

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 (Xj) (conditional entropy)

- Condition on presence of word Xj

- 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(Xj): uncertainty - conditional uncertainty (Xj)

- Maximum: Uncertainty → Xj is perfect predictor- Minimum: 0 → Xj fails to separate speeches and floor statements

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 15 / 30

A Method for Identifying Distinguishing Words

- Pr(Press) ≡ Probability selected document press release

- Pr(Speech) ≡ Probability selected document speech

- Define entropy H(Doc)

H(Doc) = −∑

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 October 7th, 2014 16 / 30

A Method for Identifying Distinguishing Words

- Pr(Press) ≡ Probability selected document press release

- Pr(Speech) ≡ Probability selected document speech

- Define entropy H(Doc)

H(Doc) = −∑

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 October 7th, 2014 16 / 30

A Method for Identifying Distinguishing Words

- Pr(Press) ≡ Probability selected document press release

- Pr(Speech) ≡ Probability selected document speech

- Define entropy H(Doc)

H(Doc) = −∑

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 October 7th, 2014 16 / 30

A Method for Identifying Distinguishing Words

- Pr(Press) ≡ Probability selected document press release

- Pr(Speech) ≡ Probability selected document speech

- Define entropy H(Doc)

H(Doc) = −∑

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 October 7th, 2014 16 / 30

A Method for Identifying Distinguishing Words

- Pr(Press) ≡ Probability selected document press release

- Pr(Speech) ≡ Probability selected document speech

- Define entropy H(Doc)

H(Doc) = −∑

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 October 7th, 2014 16 / 30

A Method for Identifying Distinguishing Words

- Pr(Press) ≡ Probability selected document press release

- Pr(Speech) ≡ Probability selected document speech

- Define entropy H(Doc)

H(Doc) = −∑

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 October 7th, 2014 16 / 30

A Method for Identifying Distinguishing Words

- Pr(Press) ≡ Probability selected document press release

- Pr(Speech) ≡ Probability selected document speech

- Define entropy H(Doc)

H(Doc) = −∑

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 October 7th, 2014 16 / 30

A Method for Identifying Distinguishing Words

- Pr(Press) ≡ Probability selected document press release

- Pr(Speech) ≡ Probability selected document speech

- Define entropy H(Doc)

H(Doc) = −∑

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 October 7th, 2014 16 / 30

A Method for Identifying Distinguishing Words

- Consider presence/absence of word Xj

- Define conditional entropy H(Doc|Xj)

H(Doc|Xj) = −1∑

s=0

∑t∈{Pre,Spe}

Pr(t,Xj = s) log2 Pr(t|Xj = s)

- Maximum: Xj unrelated to Press Releases/Floor Speeches

- Minimum: Xj is a perfect predictor of press release/floor speech

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 17 / 30

A Method for Identifying Distinguishing Words

- Consider presence/absence of word Xj

- Define conditional entropy H(Doc|Xj)

H(Doc|Xj) = −1∑

s=0

∑t∈{Pre,Spe}

Pr(t,Xj = s) log2 Pr(t|Xj = s)

- Maximum: Xj unrelated to Press Releases/Floor Speeches

- Minimum: Xj is a perfect predictor of press release/floor speech

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 17 / 30

A Method for Identifying Distinguishing Words

- Consider presence/absence of word Xj

- Define conditional entropy H(Doc|Xj)

H(Doc|Xj) = −1∑

s=0

∑t∈{Pre,Spe}

Pr(t,Xj = s) log2 Pr(t|Xj = s)

- Maximum: Xj unrelated to Press Releases/Floor Speeches

- Minimum: Xj is a perfect predictor of press release/floor speech

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 17 / 30

A Method for Identifying Distinguishing Words

- Consider presence/absence of word Xj

- Define conditional entropy H(Doc|Xj)

H(Doc|Xj) = −1∑

s=0

∑t∈{Pre,Spe}

Pr(t,Xj = s) log2 Pr(t|Xj = s)

- Maximum: Xj unrelated to Press Releases/Floor Speeches

- Minimum: Xj is a perfect predictor of press release/floor speech

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 17 / 30

A Method for Identifying Distinguishing Words

- Consider presence/absence of word Xj

- Define conditional entropy H(Doc|Xj)

H(Doc|Xj) = −1∑

s=0

∑t∈{Pre,Spe}

Pr(t,Xj = s) log2 Pr(t|Xj = s)

- Maximum: Xj unrelated to Press Releases/Floor Speeches

- Minimum: Xj is a perfect predictor of press release/floor speech

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 17 / 30

A Method for Identifying Distinguishing Words

- Consider presence/absence of word Xj

- Define conditional entropy H(Doc|Xj)

H(Doc|Xj) = −1∑

s=0

∑t∈{Pre,Spe}

Pr(t,Xj = s) log2 Pr(t|Xj = s)

- Maximum: Xj unrelated to Press Releases/Floor Speeches

- Minimum: Xj is a perfect predictor of press release/floor speech

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 17 / 30

A Method for Identifying Distinguishing Words

- Define Mutual Information(Xj) as

Mutual Information(Xj) = H(Doc)− H(Doc|Xj)

- Maximum: entropy ⇒ H(Doc|Xj) = 0

- Minimum: 0 ⇒ H(Doc|Xj) = H(Doc).

Bigger mutual information ⇒ better discrimination

Objective function and optimization estimate probabilities that wethen place in mutual information

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 18 / 30

A Method for Identifying Distinguishing Words

- Define Mutual Information(Xj) as

Mutual Information(Xj) = H(Doc)− H(Doc|Xj)

- Maximum: entropy ⇒ H(Doc|Xj) = 0

- Minimum: 0 ⇒ H(Doc|Xj) = H(Doc).

Bigger mutual information ⇒ better discrimination

Objective function and optimization estimate probabilities that wethen place in mutual information

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 18 / 30

A Method for Identifying Distinguishing Words

- Define Mutual Information(Xj) as

Mutual Information(Xj) = H(Doc)− H(Doc|Xj)

- Maximum: entropy ⇒ H(Doc|Xj) = 0

- Minimum: 0 ⇒ H(Doc|Xj) = H(Doc).

Bigger mutual information ⇒ better discrimination

Objective function and optimization estimate probabilities that wethen place in mutual information

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 18 / 30

A Method for Identifying Distinguishing Words

- Define Mutual Information(Xj) as

Mutual Information(Xj) = H(Doc)− H(Doc|Xj)

- Maximum: entropy ⇒ H(Doc|Xj) = 0

- Minimum: 0 ⇒ H(Doc|Xj) = H(Doc).

Bigger mutual information ⇒ better discrimination

Objective function and optimization estimate probabilities that wethen place in mutual information

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 18 / 30

A Method for Identifying Distinguishing Words

- Define Mutual Information(Xj) as

Mutual Information(Xj) = H(Doc)− H(Doc|Xj)

- Maximum: entropy ⇒ H(Doc|Xj) = 0

- Minimum: 0 ⇒ H(Doc|Xj) = H(Doc).

Bigger mutual information ⇒ better discrimination

Objective function and optimization estimate probabilities that wethen place in mutual information

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 18 / 30

A Method for Identifying Distinguishing Words

- Define Mutual Information(Xj) as

Mutual Information(Xj) = H(Doc)− H(Doc|Xj)

- Maximum: entropy ⇒ H(Doc|Xj) = 0

- Minimum: 0 ⇒ H(Doc|Xj) = H(Doc).

Bigger mutual information ⇒ better discrimination

Objective function and optimization estimate probabilities that wethen place in mutual information

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 18 / 30

A Method for Identifying Distinguishing Words

- Define Mutual Information(Xj) as

Mutual Information(Xj) = H(Doc)− H(Doc|Xj)

- Maximum: entropy ⇒ H(Doc|Xj) = 0

- Minimum: 0 ⇒ H(Doc|Xj) = H(Doc).

Bigger mutual information ⇒ better discrimination

Objective function and optimization estimate probabilities that wethen place in mutual information

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 18 / 30

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

Xi ,j (No. docs Xj appears )

n−j = No. docs Xj does not appear

nj ,p = No. press and Xj

nj ,s = No. speech and Xj

n−j ,p = No. press and not Xj

n−j ,s = No. speech and not Xj

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 19 / 30

A Method for Identifying Distinguishing Words

Formula for Mutual Information

MI(Xj) =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.

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 20 / 30

What’s Different About Press Releases

−20000 −10000 0 10000

0.00

0.02

0.04

0.06

0.08

0.10

No. Times Speech − No. Times Press

Mut

ual I

nfor

mat

ion

What’s Different?

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 21 / 30

What’s Different About Press Releases

−20000 −10000 0 10000

0.00

0.02

0.04

0.06

0.08

0.10

No. Times Speech − No. Times Press

Mut

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What’s Different?

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 21 / 30

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What’s Different?

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 21 / 30

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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 October 7th, 2014 21 / 30

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 October 7th, 2014 21 / 30

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 October 7th, 2014 21 / 30

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 October 7th, 2014 21 / 30

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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 October 7th, 2014 21 / 30

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 October 7th, 2014 21 / 30

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 October 7th, 2014 21 / 30

What’s Different About Press Releases

Difference

−0.04 −0.02 0 0.02 0.04

Press Attention − Speech Attention

fund000

departmillionbusi

waterprogramguardviolencfarm

disastsecur

veteranenergiland

schoolclimatdrughistor

healthbeef

studentnucleardrugtrade

securcellhonor

childrensocial

publictax

oilbordervotewariraq

bankruptcibracimmigr

judgbudgetacademi

serv

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 October 7th, 2014 21 / 30

Fightin’ Words An Introduction to Regularization

Monroe, Colaresi, and Quinn (2009) what makes a word partisan?

Argue for using Log Odds Ratio, weighted by varianceRecall: For some event E and F

P(E ) = 1− P(E c)

Odds(E ) =P(E )

1− P(E )

Odds Ratio(E ,F ) =

P(E))(1−P(E))

P(F )1−P(F )

Log Odds Ratio(E ,F ) = log

(P(E )

1− P(E )

)− log

(P(F )

1− P(F )

)Strategy Construct objective function on proportions (and thencalculate log-odds)

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 22 / 30

Fightin’ Words An Introduction to Regularization

Monroe, Colaresi, and Quinn (2009) what makes a word partisan?Argue for using Log Odds Ratio, weighted by variance

Recall: For some event E and F

P(E ) = 1− P(E c)

Odds(E ) =P(E )

1− P(E )

Odds Ratio(E ,F ) =

P(E))(1−P(E))

P(F )1−P(F )

Log Odds Ratio(E ,F ) = log

(P(E )

1− P(E )

)− log

(P(F )

1− P(F )

)Strategy Construct objective function on proportions (and thencalculate log-odds)

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 22 / 30

Fightin’ Words An Introduction to Regularization

Monroe, Colaresi, and Quinn (2009) what makes a word partisan?Argue for using Log Odds Ratio, weighted by varianceRecall: For some event E and F

P(E ) = 1− P(E c)

Odds(E ) =P(E )

1− P(E )

Odds Ratio(E ,F ) =

P(E))(1−P(E))

P(F )1−P(F )

Log Odds Ratio(E ,F ) = log

(P(E )

1− P(E )

)− log

(P(F )

1− P(F )

)Strategy Construct objective function on proportions (and thencalculate log-odds)

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 22 / 30

Fightin’ Words An Introduction to Regularization

Monroe, Colaresi, and Quinn (2009) what makes a word partisan?Argue for using Log Odds Ratio, weighted by varianceRecall: For some event E and F

P(E ) = 1− P(E c)

Odds(E ) =P(E )

1− P(E )

Odds Ratio(E ,F ) =

P(E))(1−P(E))

P(F )1−P(F )

Log Odds Ratio(E ,F ) = log

(P(E )

1− P(E )

)− log

(P(F )

1− P(F )

)Strategy Construct objective function on proportions (and thencalculate log-odds)

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 22 / 30

Fightin’ Words An Introduction to Regularization

Monroe, Colaresi, and Quinn (2009) what makes a word partisan?Argue for using Log Odds Ratio, weighted by varianceRecall: For some event E and F

P(E ) = 1− P(E c)

Odds(E ) =P(E )

1− P(E )

Odds Ratio(E ,F ) =

P(E))(1−P(E))

P(F )1−P(F )

Log Odds Ratio(E ,F ) = log

(P(E )

1− P(E )

)− log

(P(F )

1− P(F )

)Strategy Construct objective function on proportions (and thencalculate log-odds)

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 22 / 30

Fightin’ Words An Introduction to Regularization

Monroe, Colaresi, and Quinn (2009) what makes a word partisan?Argue for using Log Odds Ratio, weighted by varianceRecall: For some event E and F

P(E ) = 1− P(E c)

Odds(E ) =P(E )

1− P(E )

Odds Ratio(E ,F ) =

P(E))(1−P(E))

P(F )1−P(F )

Log Odds Ratio(E ,F ) = log

(P(E )

1− P(E )

)− log

(P(F )

1− P(F )

)Strategy Construct objective function on proportions (and thencalculate log-odds)

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 22 / 30

Fightin’ Words An Introduction to Regularization

Monroe, Colaresi, and Quinn (2009) what makes a word partisan?Argue for using Log Odds Ratio, weighted by varianceRecall: For some event E and F

P(E ) = 1− P(E c)

Odds(E ) =P(E )

1− P(E )

Odds Ratio(E ,F ) =

P(E))(1−P(E))

P(F )1−P(F )

Log Odds Ratio(E ,F ) = log

(P(E )

1− P(E )

)− log

(P(F )

1− P(F )

)

Strategy Construct objective function on proportions (and thencalculate log-odds)

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 22 / 30

Fightin’ Words An Introduction to Regularization

Monroe, Colaresi, and Quinn (2009) what makes a word partisan?Argue for using Log Odds Ratio, weighted by varianceRecall: For some event E and F

P(E ) = 1− P(E c)

Odds(E ) =P(E )

1− P(E )

Odds Ratio(E ,F ) =

P(E))(1−P(E))

P(F )1−P(F )

Log Odds Ratio(E ,F ) = log

(P(E )

1− P(E )

)− log

(P(F )

1− P(F )

)Strategy Construct objective function on proportions (and thencalculate log-odds)

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 22 / 30

Fightin’ Words An Introduction to Regularization

Monroe, Colaresi, and Quinn (2009) what makes a word partisan?Argue for using Log Odds Ratio, weighted by varianceRecall: For some event E and F

P(E ) = 1− P(E c)

Odds(E ) =P(E )

1− P(E )

Odds Ratio(E ,F ) =

P(E))(1−P(E))

P(F )1−P(F )

Log Odds Ratio(E ,F ) = log

(P(E )

1− P(E )

)− log

(P(F )

1− P(F )

)Strategy Construct objective function on proportions (and thencalculate log-odds)

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 22 / 30

Objective Function

Suppose we’re interested in how a word separates partisan speech.Y = (Republican,Republican,Democrat, . . . ,Republican)X = Unnormalized matrix of word counts N × JDefine

xRepublican = (N∑i=1

I (Yi = Republican)Xi1,

N∑i=1

I (Yi = Republican)Xi2,

. . . ,

N∑i=1

I (Yi = Republican)XiJ)

with NRepublican = Total number of Republican words

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 23 / 30

Objective Function

πRepublican ∼ Dirichlet(α)

xRepublican|πRepublican ∼ Multinomial(NRepublican,πRepublican)

This implies an objective function on π,

p(π|α,X ,Y ) ∝ p(π|α)p(xRepublican|πα,Y )

∝Γ(∑J

j=1 αj)∏j Γ(αj)

J∏j=1

παj−1j π

xRepublican,jj

p(π|α,X ,Y ) is a Dirichlet distribution:

π∗Republican,j =xRepublican,j + αj

NRepublican +∑J

j=1 αj

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 24 / 30

Objective Function

πRepublican ∼ Dirichlet(α)

xRepublican|πRepublican ∼ Multinomial(NRepublican,πRepublican)

This implies an objective function on π,

p(π|α,X ,Y ) ∝ p(π|α)p(xRepublican|πα,Y )

∝Γ(∑J

j=1 αj)∏j Γ(αj)

J∏j=1

παj−1j π

xRepublican,jj

p(π|α,X ,Y ) is a Dirichlet distribution:

π∗Republican,j =xRepublican,j + αj

NRepublican +∑J

j=1 αj

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 24 / 30

Objective Function

πRepublican ∼ Dirichlet(α)

xRepublican|πRepublican ∼ Multinomial(NRepublican,πRepublican)

This implies an objective function on π,

p(π|α,X ,Y ) ∝ p(π|α)p(xRepublican|πα,Y )

∝Γ(∑J

j=1 αj)∏j Γ(αj)

J∏j=1

παj−1j π

xRepublican,jj

p(π|α,X ,Y ) is a Dirichlet distribution:

π∗Republican,j =xRepublican,j + αj

NRepublican +∑J

j=1 αj

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 24 / 30

Objective Function

πRepublican ∼ Dirichlet(α)

xRepublican|πRepublican ∼ Multinomial(NRepublican,πRepublican)

This implies an objective function on π,

p(π|α,X ,Y ) ∝ p(π|α)p(xRepublican|πα,Y )

∝Γ(∑J

j=1 αj)∏j Γ(αj)

J∏j=1

παj−1j π

xRepublican,jj

p(π|α,X ,Y ) is a Dirichlet distribution:

π∗Republican,j =xRepublican,j + αj

NRepublican +∑J

j=1 αj

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 24 / 30

Objective Function

πRepublican ∼ Dirichlet(α)

xRepublican|πRepublican ∼ Multinomial(NRepublican,πRepublican)

This implies an objective function on π,

p(π|α,X ,Y ) ∝ p(π|α)p(xRepublican|πα,Y )

∝Γ(∑J

j=1 αj)∏j Γ(αj)

J∏j=1

παj−1j π

xRepublican,jj

p(π|α,X ,Y ) is a Dirichlet distribution:

π∗Republican,j =xRepublican,j + αj

NRepublican +∑J

j=1 αj

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 24 / 30

Objective Function

πRepublican ∼ Dirichlet(α)

xRepublican|πRepublican ∼ Multinomial(NRepublican,πRepublican)

This implies an objective function on π,

p(π|α,X ,Y ) ∝ p(π|α)p(xRepublican|πα,Y )

∝Γ(∑J

j=1 αj)∏j Γ(αj)

J∏j=1

παj−1j π

xRepublican,jj

p(π|α,X ,Y ) is a Dirichlet distribution:

π∗Republican,j =xRepublican,j + αj

NRepublican +∑J

j=1 αj

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 24 / 30

Objective Function

πRepublican ∼ Dirichlet(α)

xRepublican|πRepublican ∼ Multinomial(NRepublican,πRepublican)

This implies an objective function on π,

p(π|α,X ,Y ) ∝ p(π|α)p(xRepublican|πα,Y )

∝Γ(∑J

j=1 αj)∏j Γ(αj)

J∏j=1

παj−1j π

xRepublican,jj

p(π|α,X ,Y ) is a Dirichlet distribution:

π∗Republican,j =xRepublican,j + αj

NRepublican +∑J

j=1 αj

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 24 / 30

Objective Function

πRepublican ∼ Dirichlet(α)

xRepublican|πRepublican ∼ Multinomial(NRepublican,πRepublican)

This implies an objective function on π,

p(π|α,X ,Y ) ∝ p(π|α)p(xRepublican|πα,Y )

∝Γ(∑J

j=1 αj)∏j Γ(αj)

J∏j=1

παj−1j π

xRepublican,jj

p(π|α,X ,Y ) is a Dirichlet distribution:

π∗Republican,j =xRepublican,j + αj

NRepublican +∑J

j=1 αj

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 24 / 30

Objective Function

πRepublican ∼ Dirichlet(α)

xRepublican|πRepublican ∼ Multinomial(NRepublican,πRepublican)

This implies an objective function on π,

p(π|α,X ,Y ) ∝ p(π|α)p(xRepublican|πα,Y )

∝Γ(∑J

j=1 αj)∏j Γ(αj)

J∏j=1

παj−1j π

xRepublican,jj

p(π|α,X ,Y ) is a Dirichlet distribution:

π∗Republican,j =xRepublican,j + αj

NRepublican +∑J

j=1 αj

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 24 / 30

Calculating Log Odds Ratio

Define log Odds Ratioj as

log Odds Ratioj = log

(πRepublican,j

1− πRepublican,j

)− log

(πDemocratic,j

1− πDemocratic,j

)

Var(log Odds Ratioj) ≈1

xjD + αj+

1

xjR + αj

Std. Log Oddsj =log Odds Ratioj√

Var(log Odds Ratioj)

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 25 / 30

Applying the Model

How do Republicans and Democrats differ in debate?Condition on topic and examine word usage

- Press Releases (64,033)

- Topic Coded (Structural Topic Model)

- Given press release is about topic, what are the features thatdistinguish Republican and Democratic language?

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 26 / 30

Mutual Information, Standardized Log Odds

−1.5 −1.0 −0.5 0.0 0.5 1.0

0.00

00.

002

0.00

40.

006

0.00

80.

010

0.01

2

Iraq War, Partisan Words

Log Odds

Mut

ual I

nfor

mat

ion

want

travel

wrong

extend

extens

assurunionemploy

suffici

roleintend

300

address

enhancsponsor

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world

leadership

conclud

creat

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past

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depart

morn

compani

learn

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budget

real

implement

acknowledg

land

train

processoveralarea

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consequ

safe

nomin

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awarhandrequest

test

costprepar

occureconomiproductapprov

replac

america

importdamag

death

start

month

base

ask

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close

threatengrant

000

institutsimilar

congression

urgwon

scienc

welcompartiloss

lost

necessari

lose

home

northgain

highestvoic

men

met

confidpromismarin

troop

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servicsavedeal

dear

resourcextremvisitgroup

polici

continu

200improv

ultim

400assistfirefight

hous

remainkatrinaexpressdebatexperitaskwithdraw

cutagriculturaccess

honor

later

paymentreformequalpartner

like

successjusticschool

direct

considlevel

critic

vital

practic

joint

informindividu

turnposit

sure

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failur

listversion

sourcstori

kind

destructwrotedemandburden

long

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determinlocatlocal

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largestdifficultmilitarirelatletterrespond

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recommend

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enablcontainequip

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Justin Grimmer (Stanford University) Text as Data October 7th, 2014 27 / 30

Mutual Information, Standardized Log Odds

−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5

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sustain

expand

clearcleanparticip

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control

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Justin Grimmer (Stanford University) Text as Data October 7th, 2014 27 / 30

Multinomial Inverse Regression

- In classification we’re generally interested in:

E [Y |X ] = g(X1,X2, . . . ,XJ)

- Problem: J might be very, very big.

- Potential solution invert regression

E [X |Y ] = g(Y )

- Inversion is particularly useful for feature selection

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 28 / 30

Multinomial Inverse Regression: Objective Function(Taddy 2014)

As before, xRepublican to be the Republican count vector.

xRepublican ∼ Multinomial(NRepublican,πRepublican)

πRepublican,j =exp[αj + I (Republican)φj ]∑Jl=1 exp[αl + I (Republican)φl ]

φj ∼ Laplace(λj)

λj ∼ Gamma(s, r)

Laplace priors regularize or shrink estimates toward zeroLaplace priors Equivalent to L1 or lasso penalizationGamma-Lasso priorOptimization Coordinate descent (paper is great!) textir package

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 29 / 30

Multinomial Inverse Regression: Objective Function(Taddy 2014)

As before, xRepublican to be the Republican count vector.

xRepublican ∼ Multinomial(NRepublican,πRepublican)

πRepublican,j =exp[αj + I (Republican)φj ]∑Jl=1 exp[αl + I (Republican)φl ]

φj ∼ Laplace(λj)

λj ∼ Gamma(s, r)

Laplace priors regularize or shrink estimates toward zeroLaplace priors Equivalent to L1 or lasso penalizationGamma-Lasso priorOptimization Coordinate descent (paper is great!) textir package

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 29 / 30

Multinomial Inverse Regression: Objective Function(Taddy 2014)

As before, xRepublican to be the Republican count vector.

xRepublican ∼ Multinomial(NRepublican,πRepublican)

πRepublican,j =exp[αj + I (Republican)φj ]∑Jl=1 exp[αl + I (Republican)φl ]

φj ∼ Laplace(λj)

λj ∼ Gamma(s, r)

Laplace priors regularize or shrink estimates toward zeroLaplace priors Equivalent to L1 or lasso penalizationGamma-Lasso priorOptimization Coordinate descent (paper is great!) textir package

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 29 / 30

Multinomial Inverse Regression: Objective Function(Taddy 2014)

As before, xRepublican to be the Republican count vector.

xRepublican ∼ Multinomial(NRepublican,πRepublican)

πRepublican,j =exp[αj + I (Republican)φj ]∑Jl=1 exp[αl + I (Republican)φl ]

φj ∼ Laplace(λj)

λj ∼ Gamma(s, r)

Laplace priors regularize or shrink estimates toward zeroLaplace priors Equivalent to L1 or lasso penalizationGamma-Lasso priorOptimization Coordinate descent (paper is great!) textir package

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 29 / 30

Multinomial Inverse Regression: Objective Function(Taddy 2014)

As before, xRepublican to be the Republican count vector.

xRepublican ∼ Multinomial(NRepublican,πRepublican)

πRepublican,j =exp[αj + I (Republican)φj ]∑Jl=1 exp[αl + I (Republican)φl ]

φj ∼ Laplace(λj)

λj ∼ Gamma(s, r)

Laplace priors regularize or shrink estimates toward zeroLaplace priors Equivalent to L1 or lasso penalizationGamma-Lasso priorOptimization Coordinate descent (paper is great!) textir package

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 29 / 30

Multinomial Inverse Regression: Objective Function(Taddy 2014)

As before, xRepublican to be the Republican count vector.

xRepublican ∼ Multinomial(NRepublican,πRepublican)

πRepublican,j =exp[αj + I (Republican)φj ]∑Jl=1 exp[αl + I (Republican)φl ]

φj ∼ Laplace(λj)

λj ∼ Gamma(s, r)

Laplace priors regularize or shrink estimates toward zero

Laplace priors Equivalent to L1 or lasso penalizationGamma-Lasso priorOptimization Coordinate descent (paper is great!) textir package

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 29 / 30

Multinomial Inverse Regression: Objective Function(Taddy 2014)

As before, xRepublican to be the Republican count vector.

xRepublican ∼ Multinomial(NRepublican,πRepublican)

πRepublican,j =exp[αj + I (Republican)φj ]∑Jl=1 exp[αl + I (Republican)φl ]

φj ∼ Laplace(λj)

λj ∼ Gamma(s, r)

Laplace priors regularize or shrink estimates toward zeroLaplace priors Equivalent to L1 or lasso penalization

Gamma-Lasso priorOptimization Coordinate descent (paper is great!) textir package

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 29 / 30

Multinomial Inverse Regression: Objective Function(Taddy 2014)

As before, xRepublican to be the Republican count vector.

xRepublican ∼ Multinomial(NRepublican,πRepublican)

πRepublican,j =exp[αj + I (Republican)φj ]∑Jl=1 exp[αl + I (Republican)φl ]

φj ∼ Laplace(λj)

λj ∼ Gamma(s, r)

Laplace priors regularize or shrink estimates toward zeroLaplace priors Equivalent to L1 or lasso penalizationGamma-Lasso prior

Optimization Coordinate descent (paper is great!) textir package

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 29 / 30

Multinomial Inverse Regression: Objective Function(Taddy 2014)

As before, xRepublican to be the Republican count vector.

xRepublican ∼ Multinomial(NRepublican,πRepublican)

πRepublican,j =exp[αj + I (Republican)φj ]∑Jl=1 exp[αl + I (Republican)φl ]

φj ∼ Laplace(λj)

λj ∼ Gamma(s, r)

Laplace priors regularize or shrink estimates toward zeroLaplace priors Equivalent to L1 or lasso penalizationGamma-Lasso priorOptimization Coordinate descent (paper is great!) textir package

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 29 / 30

Applying Multinomial Inverse Regression: ObjectiveFunction

Taddy (2014) considers speeches made on Congressional floor in 2005“Most” Republican words

un.official,term.care.insurance, weapons.grade.plutonium

million.illegal.immigrant, grand ole opry, ...,

personal.injury.lawyer

“Most” Democratic Wordswild.bird, dealth.penalty.system, record.budget.deficit

security.private.account, able.buy.gun

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 30 / 30

Applying Multinomial Inverse Regression: ObjectiveFunction

Taddy (2014) considers speeches made on Congressional floor in 2005“Most” Republican wordsun.official,term.care.insurance, weapons.grade.plutonium

million.illegal.immigrant, grand ole opry, ...,

personal.injury.lawyer

“Most” Democratic Wordswild.bird, dealth.penalty.system, record.budget.deficit

security.private.account, able.buy.gun

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 30 / 30

Applying Multinomial Inverse Regression: ObjectiveFunction

Taddy (2014) considers speeches made on Congressional floor in 2005“Most” Republican wordsun.official,term.care.insurance, weapons.grade.plutonium

million.illegal.immigrant, grand ole opry, ...,

personal.injury.lawyer

“Most” Democratic Words

wild.bird, dealth.penalty.system, record.budget.deficit

security.private.account, able.buy.gun

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 30 / 30

Applying Multinomial Inverse Regression: ObjectiveFunction

Taddy (2014) considers speeches made on Congressional floor in 2005“Most” Republican wordsun.official,term.care.insurance, weapons.grade.plutonium

million.illegal.immigrant, grand ole opry, ...,

personal.injury.lawyer

“Most” Democratic Wordswild.bird, dealth.penalty.system, record.budget.deficit

security.private.account, able.buy.gun

Justin Grimmer (Stanford University) Text as Data October 7th, 2014 30 / 30