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Multi-Criteria Dimensionality Reduction with Applications to Fairness UTHAIPON (TAO) TANTIPONGPIPAT (GRADUATING) PHD STUDENT, INDUSTRY JOB MARKET GEORGIA INSTITUTE OF TECHNOLOGY JOINT WORK WITH JAMIE MORGERNSTERN, SAMIRA SAMADI, MOHIT SINGH,

  1. Multi-Criteria Dimensionality Reduction with Applications to Fairness UTHAIPON (TAO) TANTIPONGPIPAT (GRADUATING) PHD STUDENT, INDUSTRY JOB MARKET GEORGIA INSTITUTE OF TECHNOLOGY JOINT WORK WITH JAMIE MORGERNSTERN, SAMIRA SAMADI, MOHIT SINGH, AND SANTOSH VEMPALA

  2. PCA can be unfair! Standard PCA on face data LFW of male and female

  3. PCA can be unfair! Standard PCA on face data LFW of Equalizing male and female male and female weight before PCA

  4. Contribution 1: Problem Formulation Multi-criteria dimensionality reduction (MCDR) : projection 𝑄 𝑕 𝑔 max 1 𝑄 , 𝑔 2 𝑄 , … , 𝑔 𝑙 𝑄 Utility criterion 𝑔 𝑗 ’s and social welfare 𝑕

  5. Contribution 1: Problem Formulation Multi-criteria dimensionality reduction (MCDR) : projection 𝑄 𝑕 𝑔 max 1 𝑄 , 𝑔 2 𝑄 , … , 𝑔 𝑙 𝑄 Utility criterion 𝑔 𝑗 ’s and social welfare 𝑕 2 βˆ’ 𝐡 𝑗 𝑄 𝐺 2 β€’ Mar-Loss : min π‘—βˆˆ{1,…,𝑙} max max 𝐡 𝑗 𝑅 𝐺 𝑄 𝑅 𝑙 2 β€’ NSW : max Ο‚ 𝑗=1 𝐡 𝑗 𝑄 𝐺 𝑄

  6. Contribution 2: Algorithms and Guarantees 𝑗 in 𝑄𝑄 T and concave 𝑕 : On linear 𝑔 β€’ Polynomial-time algorithm for MCDR with optimal utility and small rank violation 𝑑 = 2𝑙 + 1/4 βˆ’ 3/2 β€’ Approximation ratio 1 βˆ’ 𝑑/𝑒 on utility when no rank violation

  7. Contribution 2: Algorithms and Guarantees 𝑗 in 𝑄𝑄 T and concave 𝑕 : On linear 𝑔 β€’ Polynomial-time algorithm for MCDR with optimal utility and small rank violation 𝑑 = 2𝑙 + 1/4 βˆ’ 3/2 β€’ Approximation ratio 1 βˆ’ 𝑑/𝑒 on utility when no rank violation β€’ Semi-definite Program (SDP) β†’ Multiplicative Weight (MW) method β€’ scalable up to β‰ˆ 1000 dimensions

  8. Contribution 2: Algorithms and Guarantees β€’ Mar-Loss : 2 βˆ’ 𝐡 𝑗 𝑄 𝐺 2 min π‘—βˆˆ{1,…,𝑙} max max 𝐡 𝑗 𝑅 𝐺 𝑄 𝑅 β€’ NSW : 𝑙 2 Ο‚ 𝑗=1 max 𝐡 𝑗 𝑄 𝐺 𝑄

  9. Contribution 3: Optimization Theory β€’ Every extreme point of the semi-definite program relaxation of MCDR has low rank β€’ Generalize work on low-rank property in semi-definite program by Barvinok’95, Pataki’98 β€’ Optimization result + ML application

  10. Contribution 4: Complexity of MCDR β€’ NP-hard for general 𝑙 β€’ Reduction to MAX-CUT β€’ Polynomial-time for fixed 𝑙 β€’ Algorithmic theory of quadratic maps.

  11. More details β€’ Poster: Thursday Dec 12 th at 10:45 AM -- 12:45 PM, East Exhibition Hall B + C #80 β€’ Happy to chat! β€’ Code: github.com/uthaipon/multi-criteria-dimensionality-reduction β€’ Web: sites.google.com/site/ssamadi/fair-pca-homepage (searchable links at NeurIPS website or my website Uthaipon Tantipongpipat)

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