109 citations · 522 across the 51 of their papers we have counts for
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No-collision Transportation Maps
Levon Nurbekyan, Alexander Iannantuono, Adam M. Oberman
Transportation maps between probability measures are critical objects in numerous areas of mathematics and applications such as PDE, fluid mechanics, geometry, machine learning, co…
Nesterov's method with decreasing learning rate leads to accelerated stochastic gradient descent
Maxime Laborde, Adam M. Oberman
We present a coupled system of ODEs which, when discretized with a constant time step/learning rate, recovers Nesterov's accelerated gradient descent algorithm. The same ODEs, when…
Stochastic Gradient Descent with Polyak's Learning Rate
Adam M. Oberman, Mariana Prazeres
Stochastic gradient descent (SGD) for strongly convex functions converges at the rate $\bO(1/k)$. However, achieving good results in practice requires tuning the parameters (for ex…
Stochastic Backward Euler: An Implicit Gradient Descent Algorithm for -means Clustering
Penghang Yin, Minh Pham, Adam Oberman +1
In this paper, we propose an implicit gradient descent algorithm for the classic -means problem. The implicit gradient step or backward Euler is solved via stochastic fixed-poin…
Anisotropic Total Variation Regularized L^1-Approximation and Denoising/Deblurring of 2D Bar Codes
Rustum Choksi, Yves van Gennip, Adam Oberman
We consider variations of the Rudin-Osher-Fatemi functional which are particularly well-suited to denoising and deblurring of 2D bar codes. These functionals consist of an anisotro…