Related papers: Convex Hulls under Uncertainty
We prove that the combinatorial optimization problem of determining the hull number of a partial cube is NP-complete. This makes partial cubes the minimal graph class for which NP-completeness of this problem is known and improves some…
This paper presents a novel end-to-end framework for closed-form computation and visualization of critical point uncertainty in 2D uncertain scalar fields. Critical points are fundamental topological descriptors used in the visualization…
In this work, we investigate the question of how knowledge about expectations $\mathbb{E}(f_i(X))$ of a random vector $X$ translate into inequalities for $\mathbb{E}(g(X))$ for given functions $f_i$, $g$ and a random vector $X$ whose…
Region extraction is necessary in a wide range of applications, from object detection in autonomous driving to analysis of subcellular morphology in cell biology. There exist two main approaches: convex hull extraction, for which exact and…
A common problem in the optimization of structures is the handling of uncertainties in the parameters. If the parameters appear in the constraints, the uncertainties can lead to an infinite number of constraints. Usually the constraints…
In this work we study preprocessing for tractable problems when part of the input is unknown or uncertain. This comes up naturally if, e.g., the load of some machines or the congestion of some roads is not known far enough in advance, or if…
Recent advancements in tabular deep learning have demonstrated exceptional practical performance, yet the field often lacks a clear understanding of why these techniques actually succeed. To address this gap, our paper highlights the…
The main purpose of this paper is to report on the state of the art of computing integer hulls and their facets as well as counting lattice points in convex polytopes. Using the polymake system we explore various algorithms and…
Both the current trends in technology such as smartphones, general mobile devices, stationary sensors, and satellites as well as a new user mentality of using this technology to voluntarily share enriched location information produces a…
We present an algorithm for robust model predictive control with consideration of uncertainty and safety constraints. Our framework considers a nonlinear dynamical system subject to disturbances from an unknown but bounded uncertainty set.…
Geometry constitutes a core set of intuitions present in all humans, regardless of their language or schooling [1]. Could brain's built in machinery for processing geometric information take part in uncertainty representation? For decades…
We consider the convex hull of the perturbed point process comprised of $n$ i.i.d. points, each distributed as the sum of a uniform point on the unit sphere $\S^{d-1}$ and a uniform point in the $d$-dimensional ball centered at the origin…
In this article we present a general framework for non-concave robust stochastic control problems under model uncertainty in a discrete time finite horizon setting. Our framework allows to consider a variety of different path-dependent…
The convex hull of several i.i.d. beta distributed random vectors in $\mathbb R^d$ is called the random beta polytope. Recently, the expected values of their intrinsic volumes, number of faces, normal and tangent angles and other quantities…
As data plays an increasingly pivotal role in decision-making, the emergence of data markets underscores the growing importance of data valuation. Within the machine learning landscape, Data Shapley stands out as a widely embraced method…
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…
In this article we study the problem of quantifying the uncertainty in an experiment with a technical system. We propose new density estimates which combine observed data of the technical system and simulated data from an (imperfect)…
We give a survey of work on the number of vertices of the convex hull of integer points defined by the system of linear inequalities. Also, we present our improvement of some of these.
In this paper, we address the trajectory planning problem in uncertain nonconvex static and dynamic environments that contain obstacles with probabilistic location, size, and geometry. To address this problem, we provide a risk bounded…
Many prediction tasks contain uncertainty. In some cases, uncertainty is inherent in the task itself. In future prediction, for example, many distinct outcomes are equally valid. In other cases, uncertainty arises from the way data is…