Publications related to Norm (mathematics)

Convergence of adaptive algorithms for constrained weakly convex optimization

Volkan Cevher, Ahmet Alacaoglu, Yurii Malitskyi

We analyze the adaptive first order algorithm AMSGrad, for solving a constrained stochastic optimization problem with a weakly convex objective. We prove the

\tilde O(t^{-1/2})

rate of convergence for the squared norm of the gradient of Moreau envelope, ...

2021

Convex optimization in sums of Banach spaces

Michaël Unser, Shayan Aziznejad

We characterize the solution of a broad class of convex optimization problems that address the reconstruction of a function from a finite number of linear measurements. The underlying hypothesis is that the solution is decomposable as a finite sum of compo ...

2021

Proximity Results and Faster Algorithms for Integer Programming Using the Steinitz Lemma

Friedrich Eisenbrand

We consider integer programming problems in standard form max{c(T)x : Ax = b, x >= 0, x is an element of Z(n)} where A is an element of Z(mxn), b is an element of Z(m), and c is an element of Z(n). We show that such an integer program can be solved in time ...

ASSOC COMPUTING MACHINERY2020

A Unifying Representer Theorem for Inverse Problems and Machine Learning

Michaël Unser

Regularization addresses the ill-posedness of the training problem in machine learning or the reconstruction of a signal from a limited number of measurements. The method is applicable whenever the problem is formulated as an optimization task. The standar ...

2020

Determinants of Different Types of Positive Environmental Behaviors: An Analysis of Public and Private Sphere Actions

Claudia Rebeca Binder Signer, Ralph Hansmann

A survey of 1206 participants investigated determinants of positive environmental behaviors (PEBs) in Switzerland. Based on a principle component analysis on data for 23 different PEBs, three behavior types were distinguished: (i) public sphere PEBs with p ...

2020

Effective Models and Numerical Homogenization for Wave Propagation in Heterogeneous Media on Arbitrary Timescales

Timothée Noé Pouchon, Assyr Abdulle

A family of effective equations for wave propagation in periodic media for arbitrary timescales O(epsilon-alpha), where epsilon MUCH LESS-THAN1 is the period of the tensor describing the medium, is proposed. The well-posedness of the effective equations of ...

SPRINGER2020

Efficient Proximal Mapping of the 1-path-norm of Shallow Networks

Volkan Cevher, Paul Thierry Yves Rolland, Fabian Ricardo Latorre Gomez, Shaul Nadav Hallak

We demonstrate two new important properties of the 1-path-norm of shallow neural networks. First, despite its non-smoothness and non-convexity it allows a closed form proximal operator which can be efficiently computed, allowing the use of stochastic proxi ...

2020

Procrustes Metrics and Optimal Transport for Covariance Operators

Valentina Masarotto

Covariance operators play a fundamental role in functional data analysis, providing the canonical means to analyse functional variation via the celebrated Karhunen-Loève expansion. These operators may themselves be subject to variation, for instance in con ...

EPFL2019

A spectral refinement of the Bergelson–Host–Kra decomposition and new multiple ergodic theorems

Florian Karl Richter

We investigate how spectral properties of a measure-preserving system (X, B, mu, T) are reflected in the multiple ergodic averages arising from that system. For certain sequences a :N -> N, we provide natural conditions on the spectrum sigma (T) such that, ...

2019

Kernel Regression for Graph Signal Prediction in Presence of Sparse Noise

Pascal Frossard, Arun Venkitaraman

In presence of sparse noise we propose kernel regression for predicting output vectors which are smooth over a given graph. Sparse noise models the training outputs being corrupted either with missing samples or large perturbations. The presence of sparse ...

IEEE2019

Norm (mathematics)

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Convergence of adaptive algorithms for constrained weakly convex optimization

Convex optimization in sums of Banach spaces

Proximity Results and Faster Algorithms for Integer Programming Using the Steinitz Lemma

A Unifying Representer Theorem for Inverse Problems and Machine Learning

Determinants of Different Types of Positive Environmental Behaviors: An Analysis of Public and Private Sphere Actions

Effective Models and Numerical Homogenization for Wave Propagation in Heterogeneous Media on Arbitrary Timescales

Efficient Proximal Mapping of the 1-path-norm of Shallow Networks

Procrustes Metrics and Optimal Transport for Covariance Operators

A spectral refinement of the Bergelson–Host–Kra decomposition and new multiple ergodic theorems

Kernel Regression for Graph Signal Prediction in Presence of Sparse Noise

A Unifying Representer Theorem for Inverse Problems and Machine Learning

Proximity Results and Faster Algorithms for Integer Programming Using the Steinitz Lemma

Convergence of adaptive algorithms for constrained weakly convex optimization

Effective Models and Numerical Homogenization for Wave Propagation in Heterogeneous Media on Arbitrary Timescales

Efficient Proximal Mapping of the 1-path-norm of Shallow Networks

Procrustes Metrics and Optimal Transport for Covariance Operators

A spectral refinement of the Bergelson–Host–Kra decomposition and new multiple ergodic theorems

Kernel Regression for Graph Signal Prediction in Presence of Sparse Noise

Determinants of Different Types of Positive Environmental Behaviors: An Analysis of Public and Private Sphere Actions

Convex optimization in sums of Banach spaces