Related papers: A practical algorithm for volume estimation based …
In this work we introduce a novel weighted message-passing algorithm based on the cavity method to estimate volume-related properties of random polytopes, properties which are relevant in various research fields ranging from metabolic…
We propose efficient numerical algorithms for approximating statistical solutions of scalar conservation laws. The proposed algorithms combine finite volume spatio-temporal approximations with Monte Carlo and multi-level Monte Carlo…
With the goal of obtaining strong relaxations for binary polynomial optimization problems, we introduce the pseudo-Boolean polytope defined as the convex hull of the set of binary points satisfying a collection of equations containing…
This study presents a novel algorithm for identifying the set of extreme points that constitute the exact convex hull of a point set in high-dimensional Euclidean space. The proposed method iteratively solves a sequence of dynamically…
Given an $n$-dimensional convex body by a membership oracle in general, it is known that any polynomial-time deterministic algorithm cannot approximate its volume within ratio $(n/\log n)^n$. There is a substantial progress on randomized…
Approximate Thompson sampling with Langevin Monte Carlo broadens its reach from Gaussian posterior sampling to encompass more general smooth posteriors. However, it still encounters scalability issues in high-dimensional problems when…
Stochastic billiards can be used for approximate sampling from the boundary of a bounded convex set through the Markov Chain Monte Carlo (MCMC) paradigm. This paper studies how many steps of the underlying Markov chain are required to get…
A polyhedral approximation of a convex body can be calculated by solving approximately an associated multiobjective convex program (MOCP). An MOCP can be solved approximately by Benson type algorithms, which compute outer and inner…
The paper proposes a Riemannian Manifold Hamiltonian Monte Carlo sampler to resolve the shortcomings of existing Monte Carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlations. The…
Consider a real-valued function that can only be observed with stochastic noise at a finite set of design points within a Euclidean space. We wish to determine whether there exists a convex function that goes through the true function…
Computer simulation with Monte Carlo is an important tool to investigate the function and equilibrium properties of many systems with biological and soft matter materials solvable in solvents. The appropriate treatment of long-range…
In simulations of crystals, unlike liquids or gases, it may happen that the properties of the studied system depend not only on the volume of the simulation cell but also on its shape. For such cases it is desirable to change the shape of…
The approximation of a high-dimensional vector by a small combination of column vectors selected from a fixed matrix has been actively debated in several different disciplines. In this paper, a sampling approach based on the Monte Carlo…
In general dimension, there is no known total polynomial algorithm for either convex hull or vertex enumeration, i.e. an algorithm whose complexity depends polynomially on the input and output sizes. It is thus important to identify…
We propose a new algorithm for sampling the $N$-body density $|\Psi({\bf R})|^2/\int_{\mathbb{R}^{3N}} |\Psi|^2$ in the Variational Monte Carlo (VMC) framework. This algorithm is based upon a modified Ricci-Ciccotti discretization of the…
Non-linear Trajectory Optimisation (TO) methods require good initial guesses to converge to a locally optimal solution. A feasible guess can often be obtained by allocating a large amount of time for the trajectory to complete. However for…
Polytopes are the basic finite data structures for convex sets: they appear as feasible regions in linear optimization, as geometric summaries in algorithms, and as random objects in stochastic geometry. A natural geometric question is…
Due to the complex characteristics of bottle-brush polymers, it became a challenge to develop an efficient algorithm for studying such macromolecules under various solvent conditions or some constraints in the space by using computer…
We present a polynomial time algorithm to approximately scale tensors of any format to arbitrary prescribed marginals (whenever possible). This unifies and generalizes a sequence of past works on matrix, operator and tensor scaling. Our…
A method for calculating the pressure tensor in constant-volume Monte Carlo simulations of convex bodies is presented. In contrast to other approaches, the method requires only an isotropic scaling of the simulation box, and the counting of…