title: Directing Generative Networks with Weighted Maximum Mean Discrepancy
abstract: The maximum mean discrepancy (MMD) between two probability measures P
  and Q is a metric that is zero if and only if all moments of the two measures
  are equal, making it an appealing statistic for two-sample tests. Given i.i.d. samples
  from P and Q, Gretton et al. (2012) show that we can construct an unbiased
  estimator for the square of the MMD between the two distributions. If P is a
  distribution of interest and Q is the distribution implied by a generative neural
  network with stochastic inputs, we can use this estimator to train our neural network.
  However, in practice we do not always have i.i.d. samples from our target
  of interest. Data sets often exhibit biases—for example, under-representation of
  certain demographics—and if we ignore this fact our machine learning algorithms
  will propagate these biases. Alternatively, it may be useful to assume our data has
  been gathered via a biased sample selection mechanism in order to manipulate
  properties of the estimating distribution Q.
  In this paper, we construct an estimator for the MMD between P and Q when we
  only have access to P via some biased sample selection mechanism, and suggest
  methods for estimating this sample selection mechanism when it is not already
  known. We show that this estimator can be used to train generative neural networks
  on a biased data sample, to give a simulator that reverses the effect of that
  bias.
authors: Maurice Diesendruck Guy W. Cole Sinead Williamson
hIndex: Sinead Williamson 13