maximum mean discrepancy – Optimization Online

Variable Selection for Kernel Two-Sample Tests

Published: 2023/02/15

(Mixed) Integer Nonlinear Programming, Optimization in Data Science maximum mean discrepancy, mixed-integer programming, Two-sample test

We consider the variable selection problem for two-sample tests, aiming to select the most informative features to best distinguish samples from two groups. We propose a kernel maximum mean discrepancy (MMD) framework to solve this problem and further derive its equivalent mixed-integer programming formulations for linear, quadratic, and Gaussian types of kernel functions. Our proposed … Read more

Metrizing Fairness

Published: 2022/05/30

Yves Rychener

Bahar Tașkesen

Daniel Kuhn

Statistics, Stochastic Programming, Unconstrained Optimization fairness, Kolmogorov distance, maximum mean discrepancy, statistical parity, stochastic gradient descent algorithms, unbiased estimator

We study supervised learning problems for predicting properties of individuals who belong to one of two demographic groups, and we seek predictors that are fair according to statistical parity. This means that the distributions of the predictions within the two groups should be close with respect to the Kolmogorov distance, and fairness is achieved by … Read more