PrivacyPreserving Approximation Center for Computational Mathematics Seminar UCSD

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Privacy-Preserving Approximation Center for Computational Mathematics Seminar UCSD January 24, 2012 Olvi Mangasarian UW

Privacy-Preserving Approximation Center for Computational Mathematics Seminar UCSD January 24, 2012 Olvi Mangasarian UW Madison & UCSD La Jolla Glenn Fung Siemens Medical Solutions, Malvern, PA

Problem Statement • Entities with related data points wish to obtain a function approximation

Problem Statement • Entities with related data points wish to obtain a function approximation based on all the data points • The entities are unwilling to reveal their data to each other • Each entity holds a different set of data points for all variables. Thus, the data is said to be horizontally partitioned • Our approach: privacy-preserving approximation (PPA) using random matrix transformations • PPA provides exact solution based on the total data • PPA does not reveal any private information

Outline • Horizontally partitioned approximation problem • Secure transformation via a random matrix •

Outline • Horizontally partitioned approximation problem • Secure transformation via a random matrix • Method of solution: Privacy-preserving linear programming • Computational results • Summary

Horizontally Partitioned Example EPA wishes to compute total green house emission from three industries

Horizontally Partitioned Example EPA wishes to compute total green house emission from three industries without revealing the data of each industry A 1 A 2 A 3

Horizontally Partitioned Data Matrix Variables 1 2. . …………. n 1 2. . Data

Horizontally Partitioned Data Matrix Variables 1 2. . …………. n 1 2. . Data Points. . . m A 1 A 2 A A 3

Secure Linear Approximation

Secure Linear Approximation

Why Linear Approximation is Secure?

Why Linear Approximation is Secure?

Linear Equation Representation

Linear Equation Representation

Linear Privacy Preserving Approximation Algorithm

Linear Privacy Preserving Approximation Algorithm

Linear Privacy Preserving Approximation Algorithm (Continued)

Linear Privacy Preserving Approximation Algorithm (Continued)

Privacy Preserving Nonlinear Kernel Approximation

Privacy Preserving Nonlinear Kernel Approximation

Nonlinear Privacy Preserving Approximation Algorithm

Nonlinear Privacy Preserving Approximation Algorithm

Nonlinear Privacy Preserving Approximation Algorithm (Continued)

Nonlinear Privacy Preserving Approximation Algorithm (Continued)

Computatinal Results

Computatinal Results

Entities’ Regions

Entities’ Regions

The Exact Sinc Function

The Exact Sinc Function

Entity 1 Alone: Approximation to the sinc function

Entity 1 Alone: Approximation to the sinc function

Entity 2 Alone: Approximation to the sinc function

Entity 2 Alone: Approximation to the sinc function

Entities 1 & 2: Secure Approximation to the sinc function

Entities 1 & 2: Secure Approximation to the sinc function

Summary & Outlook Privacy preserving approximation of functions using privately held data: – Based

Summary & Outlook Privacy preserving approximation of functions using privately held data: – Based on a transformation using a random matrix B – Get essentially exact approximation to the original function without revealing privately held data Possible extensions to problems with privately held constraints

References ftp: //ftp. cs. wisc. edu/pub/dmi/tech-reports/11 -04. pdf ftp: //ftp. cs. wisc. edu/pub/dmi/tech-reports/07 -03.

References ftp: //ftp. cs. wisc. edu/pub/dmi/tech-reports/11 -04. pdf ftp: //ftp. cs. wisc. edu/pub/dmi/tech-reports/07 -03. pdf

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