Learning Mahalanobis Distance Metrics from Data

Patent metadata

Field	Value
Publication number	US-2022405529-A1
Application number	US-202117345730-A
Country	US
Kind code	A1
Filing date	Jun 11, 2021
Priority date	Jun 11, 2021
Publication date	Dec 22, 2022
Grant date	—

Abstract

The present invention provides techniques for learning Mahalanobis distance similarity metrics from data for individually fair machine learning models. In one aspect, a method for learning a fair Mahalanobis distance similarity metric includes: obtaining data with similarity annotations; selecting, based on the data obtained, a model for learning a Mahalanobis covariance matrix Σ; and learning the Mahalanobis covariance matrix Σ from the data using the model selected, wherein the Mahalanobis covariance matrix Σ fully defines the fair Mahalanobis distance similarity metric.

First claim

What is claimed is:

1 . A method for learning a fair Mahalanobis distance similarity metric, the method comprising:
obtaining data with similarity annotations; selecting, based on the data obtained, a model for learning a Mahalanobis covariance matrix Σ; and learning the Mahalanobis covariance matrix Σ from the data using the model selected, wherein the Mahalanobis covariance matrix Σ fully defines the fair Mahalanobis distance similarity metric.

2 . The method of claim 1 , wherein the fair Mahalanobis distance similarity metric is of a form:
d x ( x 1 ,x 2 ) (φ( x 1 )−φ)( x 2 )Σ(φ( x 1 )−φ( x 2 ))),
wherein φ(x):X→R d is an embedding map and Σ∈S + d .

3 . The method of claim 1 , wherein the data obtained comprises groups of comparable samples.

4 . The method of claim 3 , wherein the model selected comprises a factor model.

5 . The method of claim 4 , wherein the factor model comprises:
φ i =A * u i +B * υ i +∈ i ,

wherein φ i ∈R d is a learned representation of x i , u i ∈R K is a sensitive attribute of x i for a task at hand, υ i ∈R L is a relevant attribute of x i for the task at hand, and ∈ i is an error term.

6 . The method of claim 5 , further comprising:
choosing an orthogonal complement of ran (A * ) for the Mahalanobis covariance matrix Σ, wherein ran (A * ) is a column space of A * ; and solving for ran (A * ).

7 . The method of claim 1 , wherein the data obtained comprises pairs of samples that are comparable, incomparable, or combinations thereof.

8 . The method of claim 7 , wherein the model selected comprises a binary response model.

9 . The method of claim 8 , wherein the data comprises human user feedback in a form of triplets {(x i1 , x i2 , y i )} i=1 n , where y i ∈{0,1} indicates whether a human user considers x i1 and x i2 comparable, wherein (x i1 , x i2 , y i ) satisfies the binary response model:

y
i

❘

x

i
⁢
1

,

x

i
⁢
2

∼

Ber
⁢

(

2
⁢

σ
⁡
(

-

d
i

)

)

,

d
i

=
Δ



φ

i
⁢
1

-

φ

i
⁢
2



Σ
0

2

⁢

=

(

φ

i
⁢
1

-

φ

i
⁢
2

)

T

⁢

Σ
0

(

φ

i
⁢
1

-

φ

i
⁢
2

)

⁢

=

〈

(

φ

i
⁢
1

-

φ

i
⁢
2

)

⁢

(

φ

i
⁢
1

-

φ

i

Assignees

• IBM
• Univ Michigan

Inventors

• Yurochkin Mikhail
• Mukherjee Debarghya
• Banerjee Moulinath
• Sun Yuekai
• Upadhyay Sohini

Classifications

• G06F18/285 Primary

  Selection of pattern recognition techniques, e.g. of classifiers in a multi-classifier system · CPC title

• G06F18/214

  Generating training patterns; Bootstrap methods, e.g. bagging or boosting · CPC title

• G06F18/40

  Software arrangements specially adapted for pattern recognition, e.g. user interfaces or toolboxes therefor · CPC title

• G06F18/22 Primary

  Matching criteria, e.g. proximity measures · CPC title

• G06N3/08

  Learning methods · CPC title