arXiv research

Suppose $f(x,y) + \fracκ{2} \|x\|^2 - \fracσ{2}\|y\|^2$ is convex where $σ>0$, and the argmin function $γ(x) = \{ γ: \inf_y f(x,y) = f(x,γ)\}$ exists and is single valued. We will prove $γ$ is differentiable almost everywhere. As an application we deduce a minimum principle for certain semiconcave subsolutions.

New method learns binary decision trees efficiently.

Proposes a new risk measurement method for risk-averse stochastic optimization.

New method finds minimum in noisy data, useful for model selection.

Paper proposes new loss functions for training energy networks.

EGO-MDA identifies optimal spectral-bands for process discrimination.

We describe a novel family of models of multi- layer feedforward neural networks in which the activation functions are encoded via penalties in the training problem. Our approach is based on representing a non-decreasing activation function as the argmin of an appropriate convex optimiza- tion problem. The new framewor…

This paper introduces a novel generative encoder (GE) model for generative imaging and image processing with applications in compressed sensing and imaging, image compression, denoising, inpainting, deblurring, and super-resolution. The GE model consists of a pre-training phase and a solving phase. In the pre-training …