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Large Steps in Inverse Rendering of Geometry

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On Convergence-Diagnostic based Step Sizes for Stochastic Gradient Descent

Nicolas Henri Bernard Flammarion, Scott William Pesme, Aymeric Daphnis Kévin Dieuleveut

Constant step-size Stochastic Gradient Descent exhibits two phases: a transient phase during which iterates make fast progress towards the optimum, followed by a stationary phase during which iterates oscillate around the optimal point. In this paper, we s ...

2020

Despite the widespread use of gradient-based algorithms for optimizing high-dimensional non-convex functions, understanding their ability of finding good minima instead of being trapped in spurious ones remains to a large extent an open problem. Here we fo ...

Curran Associates, Inc.2020

We propose a non-parametric regression method that does not rely on the structure of the ground-truth, but only on its regularity properties. The methodology can be readily used for learning surrogate models of nonlinear dynamical systems from data, while ...

2019

The basis of the discrete element method is to model masses interacting with each other through different forces and constraints. On each mass, the second law of Newton is applied to obtain a differential equation. From this equation and boundary condition ...

2019

Stochastic Gradient Descent for Spectral Embedding with Implicit Orthogonality Constraint

Pascal Frossard, Mireille El Gheche, Giovanni Chierchia

In this paper, we propose a scalable algorithm for spectral embedding. The latter is a standard tool for graph clustering. However, its computational bottleneck is the eigendecomposition of the graph Laplacian matrix, which prevents its application to larg ...

IEEE2019

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Coordinate descent with random coordinate selection is the current state of the art for many large scale optimization problems. However, greedy selection of the steepest coordinate on smooth problems can yield convergence rates independent of the dimension ...

2019

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The reconstruction of the angular and spatial intensity distribution from radiative flux maps measured in high flux solar simulators or optical concentrators is an ill-posed inverse problem requiring special solution strategies. We aimed at providing a sol ...

2019

Efficient Greedy Coordinate Descent for Composite Problems

Martin Jaggi, Sebastian Urban Stich, Anastasiia Koloskova, Sai Praneeth Reddy Karimireddy

MICROTOME PUBLISHING2019

In recent years, Machine Learning based Computer Vision techniques made impressive progress. These algorithms proved particularly efficient for image classification or detection of isolated objects. From a probabilistic perspective, these methods can predi ...

EPFL2018

Multi space reduced basis preconditioners for parametrized partial differential equations

Niccolò Dal Santo

The multiquery solution of parametric partial differential equations (PDEs), that is, PDEs depending on a vector of parameters, is computationally challenging and appears in several engineering contexts, such as PDE-constrained optimization, uncertainty qu ...

EPFL2018