Filter Out Unwanted Informtion in Data
Wenjie Zheng
29 September 2022
@Oxford
| Name | Var1 | Var2 |
|---|---|---|
| Bruce Wayne | AAA | BBB |
| Peter Parker | CCC | DDD |
| Wenjie Zheng | EEE | FFF |
| ... | ... | ... |
| Name | Var1 | Var2 |
|---|---|---|
| Batman | AAA | BBB |
| Spider-Man | CCC | DDD |
| ... | ... | ... |
| Name | Var1 | Var2 |
|---|---|---|
| Poker | EEE | FFF |
| ... | ... | ... |
Census
Villain
Justice League
Scenario 1
| Income | Expense | Debt | Score |
|---|---|---|---|
| XXXX | 1234.5 | 0 | ? |
| XXXXX | 9876 | 333 | ? |
Private
Scenario 2
| Gender | Smoking | Insurance Premium |
|---|---|---|
| Male | No | ? |
| Female | Yes | ? |
Unfair
Scenario 3
Individual
Private
Unfair
Non-distributional
Distributional
Differential Privacy
Privacy Funnel
A Flawed Method
| Income | Expense | Debt |
|---|---|---|
| XXXX | 1234.5 | 0 |
| XXXXX | 9876 | 333 |
| Gender | Smoking |
|---|---|
| Male | No |
| Female | Yes |
| Income | Expense | Debt |
|---|---|---|
| XXXX | 1234.5 | 0 |
| XXXXX | 9876 | 333 |
S
X
I(S; Y) = 0
Y
\max_Y I(X; Y)
\max_Y I(X; Y) - \beta I(S;Y)
\max_Y I(X; Y) - \beta I(S;Y)
- Discrete: submodular optimization
- Gaussian: semi-definite programming
- Continuous: variational method
\((S, X)\) : Gaussian...
Y := X - \text{proj}_S(X)
Y := X - S S^+ X
I(S; Y) = 0
\max_Y I(X; Y)
I(S;Y|Z) = 0
Y := X - S S^+ X
I(S; Y) = 0
Y:= ?