4 papers
Distributed Function Minimization in Apache Spark
Andrea Schioppa
We report on an open-source implementation for distributed function minimization on top of Apache Spark by using gradient and quasi-Newton methods. We show-case it with an applicat…
Learning to Transport with Neural Networks
Andrea Schioppa
We compare several approaches to learn an Optimal Map, represented as a neural network, between probability distributions. The approaches fall into two categories: ``Heuristics'' a…
Optimality of the final model found via Stochastic Gradient Descent
Andrea Schioppa
We study convergence properties of Stochastic Gradient Descent (SGD) for convex objectives without assumptions on smoothness or strict convexity. We consider the question of establ…
PI spaces with analytic dimension 1 and arbitrary topological dimension
Bruce Kleiner, Andrea Schioppa
For every n, we construct a metric measure space that is doubling, satisfies a Poincare inequality in the sense of Heinonen-Koskela, has topological dimension n, and has a measurab…