Related papers: Quantum Convex Support
It is well known that correlations predicted by quantum mechanics cannot be explained by any classical (local-realistic) theory. The relative strength of quantum and classical correlations is usually studied in the context of Bell…
Quantum coherence is an important quantum resource which plays a pivotal role in the field of quantum information. Based on metric adjusted skew information, we define a measure of quantum uncertainty to study average coherence under…
We define what it means for a state in a convex cone of states on a space of observables to be generalized-entangled relative to a subspace of the observables, in a general ordered linear spaces framework for operational theories. This…
Quantum machine learning is often motivated by the idea that quantum systems can expose useful high-dimensional structure that is difficult to access with classical models. We isolate one central component of this claim: the fixed…
Generalized quantum measurements with N distinct outcomes are used for determining the density matrix, of order d, of an ensemble of quantum systems. The resulting probabilities are represented by a point in an N-dimensional space. It is…
Advances in statistical learning theory present the opportunity to develop statistical models of quantum many-body systems exhibiting remarkable predictive power. The potential of such ``theory-thin'' approaches is illustrated with the…
We investigate metric projections and distance functions referring to convex bodies in finite-dimensional normed spaces. For this purpose we identify the vector space with its dual space by using, instead of the usual identification via the…
In this work we deal with the problem of support estimation under shape restrictions. The shape restriction we deal with is an extension of the notion of convexity named alpha-convexity. Instead of assuming, as in the convex case, the…
A support vector machine (SVM) is an algorithm that finds a hyperplane which optimally separates labeled data points in $\mathbb{R}^n$ into positive and negative classes. The data points on the margin of this separating hyperplane are…
We study multivariate normal models that are described by linear constraints on the inverse of the covariance matrix. Maximum likelihood estimation for such models leads to the problem of maximizing the determinant function over a…
Current work on human-machine alignment aims at understanding machine-learned latent spaces and their correspondence to human representations. G{\"a}rdenfors' conceptual spaces is a prominent framework for understanding human…
In the framework of shape constrained estimation, we review methods and works done in convex set estimation. These methods mostly build on stochastic and convex geometry, empirical process theory, functional analysis, linear programming,…
Uncertainty relations are usually stated as bounds on selected combinations of variances, but the full covariance matrix contains substantially richer information about the geometry of quantum state space and about the operational…
The geometric problem of estimating an unknown compact convex set from evaluations of its support function arises in a range of scientific and engineering applications. Traditional approaches typically rely on estimators that minimize the…
Little known relations of the renown concept of the halfspace depth for multivariate data with notions from convex and affine geometry are discussed. Halfspace depth may be regarded as a measure of symmetry for random vectors. As such, the…
Quantum information geometry studies families of quantum states by means of differential geometry. A new approach is followed with the intention to facilitate the introduction of a more general theory in subsequent work. To this purpose,…
With the ubiquity of sensors in the IoT era, statistical observations are becoming increasingly available in the form of massive (multivariate) time-series. Formulated as unsupervised anomaly detection tasks, an abundance of applications…
Convex geometry has recently attracted great attention as a framework to formulate general probabilistic theories. In this framework, convex sets and affine maps represent the state spaces of physical systems and the possible dynamics,…
Deciding whether the union of two convex polyhedra is itself a convex polyhedron is a basic problem in polyhedral computations; having important applications in the field of constrained control and in the synthesis, analysis, verification…
In decision-making problems under uncertainty, probabilistic constraints are a valuable tool to express safety of decisions. They result from taking the probability measure of a given set of random inequalities depending on the decision…