Concept
Extreme point
Related publications (18)
On the number of regions of piecewise linear neural networks
Michaël Unser, Alexis Marie Frederic Goujon
Many feedforward neural networks (NNs) generate continuous and piecewise-linear (CPWL) mappings. Specifically, they partition the input domain into regions on which the mapping is affine. The number of these so-called linear regions offers a natural metric ...
2024Data-Driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations
Daniel Kuhn, Peyman Mohajerin Esfahani
We consider stochastic programs where the distribution of the uncertain parameters is only observable through a finite training dataset. Using the Wasserstein metric, we construct a ball in the space of (multivariate and non-discrete) probability distribut ...
2018On some algebraic and extremal problems in discrete geometry
Seyed Hossein Nassajianmojarrad
In the present thesis, we delve into different extremal and algebraic problems arising from combinatorial geometry. Specifically, we consider the following problems. For any integer , we define to be the minimum positive integer such that an ...
EPFL2017Extreme points in non-positive curvature
A natural analogue of the Krein-Milman theorem is shown to fail for CAT(0) spaces. ...
Polish Acad Sciences Inst Mathematics-Impan2016Separation with restricted families of sets
János Pach, Gábor Tardos, Márton Naszódi, Zsolt Langi
Given a finite n-element set X, a family of subsets F subset of 2(X) is said to separate X if any two elements of X are separated by at least one member of F. It is shown that if vertical bar F vertical bar > 2(n-1), then one can select vertical bar log n ...
Academic Press Inc Elsevier Science2016Inner approximations of the region of attraction for polynomial dynamical systems
In a previous work we developed a convex infinite dimensional linear programming (LP) approach to approximating the region of attraction (ROA) of polynomial dynamical systems subject to compact basic semialgebraic state constraints. Finite dimensional rela ...
2013Sparse projections onto the simplex
Volkan Cevher, Christoph Koch, Anastasios Kyrillidis
Most learning methods with rank or sparsity constraints use convex relaxations, which lead to optimization with the nuclear norm or the`1-norm. However, several important learning applications cannot benet from this approach as they feature these convex no ...
JMLR W&CP2013