Related papers: Hausdorff Moment Transforms and Their Performance
This paper is a continuation of our previous investigation on the truncated matrix trigonometric moment problem in Ukrainian Math. J., 2011, 63, no.6, 786-797. In the present paper we obtain a Nevanlinna-type formula for this moment problem…
Consistency models have recently been introduced to accelerate sampling from diffusion models by directly predicting the solution (i.e., data) of the probability flow ODE (PF ODE) from initial noise. However, the training of consistency…
We use the method of Maximum (relative) Entropy to process information in the form of observed data and moment constraints. The generic "canonical" form of the posterior distribution for the problem of simultaneous updating with data and…
Gradient descent-based optimization methods underpin the parameter training of neural networks, and hence comprise a significant component in the impressive test results found in a number of applications. Introducing stochasticity is key to…
In this paper we present an enhancement of the regression-based variance reduction approaches recently proposed in Belomestny et al. This enhancement is based on a truncation of the control variate and allows for a significant reduction of…
We study the truncated multidimensional moment problem with a general type of truncations. The operator approach to the moment problem is presented. A way to construct atomic solutions of the moment problem is indicated.
Hamiltonian Monte Carlo (HMC) algorithms which combine numerical approximation of Hamiltonian dynamics on finite intervals with stochastic refreshment and Metropolis correction are popular sampling schemes, but it is known that they may…
A highly efficient formulation of moment equations for stochastic reaction networks is introduced. It is based on a set of binomial moments that capture the combinatorics of the reaction processes. The resulting set of equations can be…
The paper is devoted to introducing an approach to compute the approximate minimum time function of control problems which is based on reachable set approximation and uses arithmetic operations for convex compact sets. In particular, in…
The moment-SOS hierarchy is a widely applicable framework to address polynomial optimization problems over basic semi-algebraic sets based on positivity certificates of polynomial. Recent works show that the convergence rate of this…
The Hausdorff distance is a measure of (dis-)similarity between two sets which is widely used in various applications. Most of the applied literature is devoted to the computation for sets consisting of a finite number of points. This has…
Approximate solutions of the chemical master equation and the chemical Fokker-Planck equation are an important tool in the analysis of biomolecular reaction networks. Previous studies have highlighted a number of problems with the…
Moment-closure approximations are an important tool in the analysis of the dynamics on both static and adaptive networks. Here, we provide a broad survey over different approximation schemes by applying each of them to the adaptive voter…
We study a truncated two-dimensional moment problem in terms of the Stieltjes transform. The set of the solutions is described by the Schur step-by-step algorithm, which is based on the continued fraction expansion of the solution. In…
The truncation and approximation errors for the set of numerical solutions computed by methods based on the algorithms of different structure are calculated and analyzed for the case of the two-dimensional steady inviscid compressible flow.…
This paper deals with (1) the truncated matrix Hamburger moment problem from the point of view of reproducing kernel Hilbert spaces of vector valued entire functions of the kind introduced and extensively studied by Louis de Branges and (2)…
Completely random measures (CRM) represent the key building block of a wide variety of popular stochastic models and play a pivotal role in modern Bayesian Nonparametrics. A popular representation of CRMs as a random series with decreasing…
The first part of this paper is devoted to introducing an approach to compute the approximate minimum time function of control problems which is based on reachable set approximation and uses arithmetic operations for convex compact sets. In…
We consider the problem of decomposing higher-order moment tensors, i.e., the sum of symmetric outer products of data vectors. Such a decomposition can be used to estimate the means in a Gaussian mixture model and for other applications in…
The main goal of this paper is to reconsider a phenomenon which was treated in earlier work of the authors' on several truncated matricial moment problems. Using a special kind of Schur complement we obtain a more transparent insight into…