Related papers: Novel Algorithms for Sampling Abstract Simplicial …
We consider the problem of uniform sampling of points on an algebraic variety. Specifically, we develop a randomized algorithm that, given a small set of multivariate polynomials over a sufficiently large finite field, produces a common…
Symbolic regression automates the process of learning closed-form mathematical models from data. Standard approaches to symbolic regression, as well as newer deep learning approaches, rely on heuristic model selection criteria, heuristic…
At the intersection of dynamical systems, control theory, and formal methods lies the construction of symbolic abstractions: these typically represent simpler, finite-state models whose behavior mimics that of an underlying concrete system…
Nested sampling is a powerful approach to Bayesian inference ultimately limited by the computationally demanding task of sampling from a heavily constrained probability distribution. An effective algorithm in its own right, Hamiltonian…
Quality by design in pharmaceutical manufacturing hinges on computational methods and tools that are capable of accurate quantitative prediction of the design space. This paper investigates Bayesian approaches to design space…
We present a pair of heuristic algorithms. The first is to generate a random regular graph of fixed size. The second is the introduction of the Metropolis Coupled Simulated Annealer (MCSA) for optimizing spectral gaps in fixed size regular…
Sampling-based motion planners have experienced much success due to their ability to efficiently and evenly explore the state space. However, for many tasks, it may be more efficient to not uniformly explore the state space, especially when…
We introduce the method of stochastic lists to deal with a multi-variable positive function, defined by a self-consistent equation, typical for certain problems in physics and mathematics. In this approach, the function's properties are…
Graph embedding, representing local and global neighborhood information by numerical vectors, is a crucial part of the mathematical modeling of a wide range of real-world systems. Among the embedding algorithms, random walk-based algorithms…
Anytime almost-surely asymptotically optimal planners, such as RRT*, incrementally find paths to every state in the search domain. This is inefficient once an initial solution is found as then only states that can provide a better solution…
Spatially homogeneous random walks in $(\mathbb{Z}_{+})^{2}$ with non-zero jump probabilities at distance at most 1, with non-zero drift in the interior of the quadrant and absorbed when reaching the axes are studied. Absorption…
In this paper, a simulation-based method for the analysis and design of abstracted models for a stochastic hybrid system is proposed. The accuracy of a model is evaluated in terms of its capability to reproduce the system output for all the…
In this paper we present an efficient algorithm to produce a provably dense sample of a smooth compact variety. The procedure is partly based on computing $\textit{bottlenecks}$ of the variety. Using geometric information such as the…
Hypergraph is a topological model for networks. In order to study the topology of hypergraphs, the homology of the associated simplicial complexes and the embedded homology have been invented. In this paper, we give some algorithms to…
Thompson sampling has emerged as an effective heuristic for a broad range of online decision problems. In its basic form, the algorithm requires computing and sampling from a posterior distribution over models, which is tractable only for…
Stratified sampling is a fast and simple method to generate point sets with uniform distribution in hypercubes. However, for the most common paraxial stratfication it has the prominent drawback that the number of sampled points in n…
This paper presents an algorithm for sampling random variables that allows to separation of the sampling process into subproblems by dividing the sample space into overlapping parts. The subproblems can be solved independently of each other…
Tree graphs are routinely used in statistics. When estimating a Bayesian model with a tree component, sampling the posterior remains a core difficulty. Existing Markov chain Monte Carlo methods tend to rely on local moves, often leading to…
We define a model for random (abstract) cell complexes (CCs), similiar to the well-known Erd\H{o}s-R\'enyi model for graphs and its extensions for simplicial complexes. To build a random cell complex, we first draw from an Erd\H{o}s-R\'enyi…
In this manuscript, inspired by a simpler reformulation of primary sample space Metropolis light transport, we derive a novel family of general Markov chain Monte Carlo algorithms called charted Metropolis-Hastings, that introduces the…