Equitable Valuation of Data
Amirata Ghorbani

A Simple Example
AI4H Company
Detecting Melanoma

60% melanoma prediction
accuracy2

A Simple Example
Hospital

AI4H Company
Detecting Melanoma

60% melanoma prediction
accuracy3

A Simple Example
Hospital

AI4H Company
Detecting Melanoma

80% melanoma prediction
accuracy

4

A Simple Example
Hospital

AI4H Company
Detecting Melanoma$$$???

80% melanoma prediction
accuracy5

If data is fuel, then we need to measure itsvalue

Data valuation

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If data is fuel, then we need to measure itsvalueAnalyst/ML Engineer

Data vendor

Data valuation
Individual or data producer
7

If data is fuel, then we need to measure its
value
Analyst/ML Engineer
Heterogeneous data sources.
What’s the quality? What more?

Data vendor

Data valuation
Individual or data producer
8If data is fuel, then we need to measure its
value
Analyst/ML Engineer
Heterogeneous data sources.
What’s the quality? What more?

Data vendor
Buying and selling data.
What price?

Data valuation
Individual or data producer
9If data is fuel, then we need to measure itsvalue
Analyst/ML Engineer
Heterogeneous data sources.
What’s the quality? What more?

Data vendor
Buying and selling data.
What price?

Data valuation
Individual or data producer
Credit/compensation?
10Ingredients of ML and Data Value

Train Data

Learning Algorithm Performance Evaluation

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Ingredients of ML and Data Value

Train Data

Learning Algorithm Performance Evaluation

Value

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Ingredients of ML and Data Value

Train Data

Learning Algorithm Performance Evaluation

Value depends
on the learner,evaluation anddataset.

Value

There are manyways to “value”
data.
Is there oneright way?

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Leave One Out Score (LOO)
Example: value ()=?

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Leave One Out Score (LOO)
Example: value () = 0.80 – 0.77 = 0.03

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Leave One Out Score (LOO)
Example: value () = 0.80 – 0.77 = 0.03

Reasonable???

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Desirable Properties of Valuation

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Desirable Properties of Valuation
1. Null Element: If adding to any subset of train data neverchanges the learned model’s performance:
value( ) = 018

Desirable Properties of Valuation
1. Null Element: If adding to any subset of train data neverchanges the learned model’s performance:
value( ) = 0
2. Symmetry: If adding or
to any subset of train data
always results in the same change in performance:
value ( ) = value ( )19Desirable Properties of Valuation
1. Null Element: If adding to any subset of train data neverchanges the learned model’s performance:
value( ) = 0
2. Symmetry: If adding or
to any subset of train data
always results in the same change in performance:
value ( ) = value ( )3- Linearity: In ML, performance metric can be the sum ofperformance on individual tasks (e.g. individual test points)

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Desirable Properties of Valuation
1. Null Element: If adding to any subset of train data neverchanges the learned model’s performance:
value( ) = 0
2. Symmetry: If adding or
to any subset of train data
always results in the same change in performance:
value ( ) = value ( )3- Linearity: In ML, performance metric can be the sum ofperformance on individual tasks (e.g. individual test points)
Add/remove one taks,… should correspond to add/remove
value ( ) for that task.
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Data Shapley Value
Setting: A data point z in a dataset B containing n data points.

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Data Shapley Value
Setting: A data point z in a dataset B containing n data points.

Theorem (Ghorbani and Zou 19) The only data value that satisfies these 3 properties is23

Data Shapley Value
Setting: A data point z in a dataset B containing n data points.

Theorem (Ghorbani and Zou 19) The only data value that satisfies these 3 properties ismarginal contribution (LOO score with respect to S)

Data Shapley Value
Setting: A data point z in a dataset B containing n data points.

Theorem (Ghorbani and Zou 19) The only data value that satisfies these 3 properties ismarginal contribution (LOO score with respect to S)

Normalized by number of size |S| subsets

Data Shapley Value
Setting: A data point z in a dataset B containing n data points.

Theorem (Ghorbani and Zou 19) The only data value that satisfies these 3 properties ismarginal contribution (LOO score with respect to S)

Normalized by number of size |S| subsets

Data Shapley Value
Setting: A data point z in a dataset B containing n data points.

Theorem (Ghorbani and Zou 19) The only data value that satisfies these 3 properties ismarginal contribution (LOO score with respect to S)

Normalized by number of size |S| subsets

Expected LLO scores with respect to all possible sizes of data

Data Shapley Value
Example: value ()=?

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Data Shapley Value
Example: value (One size two subset)=?

|S| = 229

Data Shapley Value
One size two subset

Example: value (Two size one subset)=?
|S| = 1

|S| = 2+

|S| = 1+30

Data Shapley Value
Example: value (One size zero subset) = 0.05
|S| = 1|S| = 2+|S| = 0|S| = 1++31

Data Shapley Value
Example: value () = 0.05
|S| = 1|S| = 2+

|S| = 0|S| = 1++

We developed efficient algorithms to estimate data Shapley for complex models.

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Data Shapley Value
Lloyd Shapley

2012 Nobel Prizein Economics

Cooperative game

data
data

data33

Applications

Data point value = expected contribution to performance34

Applications

Data point value = expected contribution to performanceHigh value dataAdds significant information

35

Applications

Data point value = expected contribution to performanceHigh value data
Adds significant information
e.g. in-distribution clean
data

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Applications

Data point value = expected contribution to performanceHigh value data

Low value data

Adds significant information
e.g. in-distribution clean
data

Adds low or harmful
information

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Applications

Data point value = expected contribution to performanceHigh value data

Low value data

Adds significant information
e.g. in-distribution clean
data

Adds low or harmful
information
e.g. noisy data, outliers,
mislabeled data38

Applications

Identify low quality
dataData valuation

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Applications: Idnetifying mislabeled data
Spam Classification Naïve Bayes Classifier
20% mislabeled

random40

Applications: Idnetifying mislabeled data
Spam Classification Naïve Bayes Classifier
20% mislabeled

Data Shapley

randomleave-one-out

41Applications

Identify low quality
data

Identify most importantdata

Data valuation

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Applications: Identifying essential data
• UK Biobank Data set• 500,000 individual in UK• Phenotype, Genotype• Gathered from 22 centers in UK

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Applications: Identifying essential data
• UK Biobank Data set• 500,000 individual in UK• Phenotype, Genotype• Gathered from 22 centers in UK = 22 data sources• We create binary-balanced disease prediction datasets• Let’s look at each center as source of data...

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Applications: Identifying essential data
# of patients

Breast Cancer

Colon Cancer

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Applications: Identifying essential data
# of patients46

Applications: Identifying essential data
# of patients

Breast Cancer

Most predictive feature: Age

Colon Cancer

🡺 Colon Cancer(p=1.5e-6)47

Applications: Identifying essential data
# of patients

Breast Cancer

Colon Cancer

Most predictive feature: Age 🡺 Colon Cancer (p=1.5e-6)Center-15: cancer unrelated to age (p=0.14)
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Applications: Identifying essential data
• UK Biobank Data set• 500,000 individual in UK• Phenotype, Genotype• Gathered from 22 centers in UK = 22 data sources• We create binary-balanced disease prediction datasets• Let’s look at individual data points as sources of data...

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Applications: Identifying essential data

Breast Cancer

50Applications: Identifying essential data

Breast Cancer

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Applications: Identifying bad data

Breast Cancer

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Applications: Identifying bad data

Applications: Identifying bad data

Applications: Identifying bad dataIf data is fuel, then we need to measure itsvalue
Identify low quality
data

Identify most importantdata

Data valuation
Domainadaptation

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Domain adaptation: face recognition

Training data

Test data

Trained model

Performance Valution

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Domain adaptation: face recognition
Are there train data points that areharmful/helpful for adaptation?
Training data
Trained model

Different in quality,distribution, classbalance, etc.

Test data
Performance Valution

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Domain adaptation: face recognition
1-Remove data with negative value

Training data
Trained model

Different in quality,distribution, classbalance, etc.

Test data
Performance Valution

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Domain adaptation: face recognition
1-Remove data with negative value
II-Reweight rest of the data with relative weight
Training data
Trained model

Different in quality,
distribution, classbalance, etc.

Test data
Performance Valution

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Skin lesion classification
Train data
google image search

Target data
Clinical examples

accuracy61

Skin lesion classification≈ 25%

Domain adaptation: gender detection
Train Data: LFW+A

Test Data: PPBaccuracy
esp. for minorities

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Domain adaptation: gender detection≈ 7%64

Neuron Shapley: Similar idea

Neuron Shapley: Important ImageNet filters

Neuron Shapley: Removing unfair filters

Distributional Shapley Value

Train Data
Distribution

Learning Algorithm Performance Evaluation
Distributional value () = ???

A distributional framework tailored to ML applications
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Distributional Shapley Value
Setting: A data point z with respect to a data distribution D

Definition (GKZ20)
For a data point z, its distributional shapley value for size m datasets coming from
distribution D:86Distributional Shapley Value
Definition (GKZ20)
For a data point z, its distributional shapley value for size m datasets coming from
distribution D:

A random variable87

Distributional Shapley Value
Definition (GKZ20)
For a data point z, its distributional shapley value for size m datasets coming from
distribution D:

A random variable

Problem solved:
No dependance on a specific dataset!
88Distributional Shapley Value
Definition (GKZ20)
For a data point z, its distributional shapley value for size m datasets coming from
distribution D:

Expectation over leave-one-out scores89

Distributional Shapley Value
Definition (GKZ20)
For a data point z, its distributional shapley value for size m datasets coming from
distribution D:

Expectation over leave-one-out scores
Good news:
It satisfies (statistical variant of) Shapley axioms

90Distributional Shapley Value
Definition (GKZ20)
For a data point z, its distributional shapley value for size m datasets coming from
distribution D:

Expectation over leave-one-out scores
Good news:
It satisfies (statistical variant of) Shapley axioms
Efficient monte-carlo approximation
91

Distributional Shapley Value
Definition (GKZ20)
For a data point z, its distributional shapley value for size m datasets coming from
distribution D:

Expectation over leave-one-out scores
Good news:
It satisfies (statistical variant of) Shapley axioms
Efficient monte-carlo approximation
Value is not dependent on a particular dataset ⇒ Intrinsic92

Distributional Shapley Value
Definition (GKZ20)
For a data point z, its distributional shapley value for size m datasets coming from
distribution D:

Expectation over leave-one-out scores
Good news:
It satisfies (statistical variant of) Shapley axioms
Efficient monte-carlo approximationValue is not dependent on a particular dataset ⇒ Intrinsic
We can apply existing ML knowledge to value93

Thank you!