On the nonconvexity of some push-forward constraints and its consequences in machine learning

arXiv:2403.07471v1 Announce Type: cross
Abstract: The push-forward operation enables one to redistribute a probability measure through a deterministic map. It plays a key role in statistics and optimization: many learning problems (notably from optimal transport, generative modeling, and algorithmic fairness) include constraints or penalties framed as push-forward conditions on the model. However, the literature lacks general theoretical insights on the (non)convexity of such constraints and its consequences on the associated learning problems. This paper aims at filling this gap. In …

abstract algorithmic fairness arxiv consequences constraints cs.lg fairness generative generative modeling key machine machine learning map math.pr modeling optimization probability role statistics stat.ml through transport type