no code implementations • 11 Jan 2021 • Patrick L. Combettes, Zev C. Woodstock
Under investigation is the problem of finding the best approximation of a function in a Hilbert space subject to convex constraints and prescribed nonlinear transformations.
Functional Analysis Optimization and Control
1 code implementation • 2 Nov 2020 • Léo Simpson, Patrick L. Combettes, Christian L. Müller
The underlying statistical forward model is assumed to be of the following form: \[ y = X \beta + \sigma \epsilon \qquad \textrm{subject to} \qquad C\beta=0 \] Here, $X \in \mathbb{R}^{n\times d}$is a given design matrix and the vector $y \in \mathbb{R}^{n}$ is a continuous or binary response vector.
no code implementations • 5 Aug 2020 • Patrick L. Combettes, Jean-Christophe Pesquet
The goal of this paper is to promote the use of fixed point strategies in data science by showing that they provide a simplifying and unifying framework to model, analyze, and solve a great variety of problems.
Optimization and Control
1 code implementation • 4 Mar 2019 • Patrick L. Combettes, Christian L. Müller
This model describes the response as a linear combination of log-ratios of the original compositions and has been extended to the high-dimensional setting via regularization.
Statistics Theory Statistics Theory
no code implementations • 3 Mar 2019 • Patrick L. Combettes, Jean-Christophe Pesquet
Deriving sharp Lipschitz constants for feed-forward neural networks is essential to assess their robustness in the face of adversarial inputs.
Optimization and Control
no code implementations • 22 Aug 2018 • Patrick L. Combettes, Jean-Christophe Pesquet
Motivated by structures that appear in deep neural networks, we investigate nonlinear composite models alternating proximity and affine operators defined on different spaces.
Optimization and Control
1 code implementation • 16 May 2018 • Patrick L. Combettes, Christian L. Müller
We introduce an optimization model for maximum likelihood-type estimation (M-estimation) that generalizes a large class of existing statistical models, including Huber's concomitant M-estimator, Owen's Huber/Berhu concomitant estimator, the scaled lasso, support vector machine regression, and penalized estimation with structured sparsity.
Statistics Theory Statistics Theory
no code implementations • 6 Jun 2015 • Michel Barlaud, Wafa Belhajali, Patrick L. Combettes, Lionel Fillatre
This paper deals with sparse feature selection and grouping for classification and regression.
no code implementations • 30 Jun 2011 • Patrick L. Combettes, Jean-Christophe Pesquet
We propose a primal-dual splitting algorithm for solving monotone inclusions involving a mixture of sums, linear compositions, and parallel sums of set-valued and Lipschitzian operators.
Optimization and Control 47H05, 90C25
1 code implementation • 17 Dec 2009 • Patrick L. Combettes, Jean-Christophe Pesquet
The proximity operator of a convex function is a natural extension of the notion of a projection operator onto a convex set.
Optimization and Control Numerical Analysis 90C25, 65K05, 90C90, 94A08