相关论文: Recombining Tree Approximations for Optimal Stoppi…
We study the NP-hard problem of approximating a Minimum Routing Cost Spanning Tree in the message passing model with limited bandwidth (CONGEST model). In this problem one tries to find a spanning tree of a graph $G$ over $n$ nodes that…
The probabilistic diffusion model has become highly effective across various domains. Typically, sampling from a diffusion model involves using a denoising distribution characterized by a Gaussian with a learned mean and either fixed or…
We study the problem of stopping a Brownian motion at a given distribution $\nu$ while optimizing a reward function that depends on the (possibly randomized) stopping time and the Brownian motion. Our first result establishes that the set…
We develop a diffusion approximation for systems subject to fast random resetting by small amplitudes. Equivalently, this describes systems with frequent but small catastrophes. We demonstrate the validity of the approximation by computing…
Diffusion models have recently emerged as a powerful approach for trajectory planning. However, their inherently non-sequential nature limits their effectiveness in long-horizon reasoning tasks at test time. The recently proposed Monte…
This article explores an optimal stopping problem for branching diffusion processes. It consists in looking for optimal stopping lines, a type of stopping time that maintains the branching structure of the processes under analysis. By using…
We provide, in a general setting, explicit solutions for optimal stopping problems that involve a diffusion process and its running maximum. Besides, a new feature includes absorbing boundaries that vary with the value of the running…
We propose and analyze a one-dimensional multi-species cross-diffusion system with non-zero-flux boundary conditions on a moving domain, motivated by the mod- eling of a Physical Vapor Deposition process. Using the boundedness by entropy…
We obtain new transport-entropy inequalities and, as a by-product, new deviation estimates for the laws of two kinds of discrete stochastic approximation schemes. The first one refers to the law of an Euler like discretization scheme of a…
We present a numerical framework to approximate the $\mu$-domain in the planar Skorokhod embedding problem (PSEP), recently appeared in \cite{gross2019}. Our approach investigates the continuity and convergence properties of the solutions…
We describe a variational approach to solving optimal stopping problems for diffusion processes, as an alternative to the traditional approach based on the solution of the free-boundary problem. We study smooth pasting conditions from a…
We address an original approach for the convergence analysis of a finite-volume scheme for the approximation of a stochastic diffusion-convection equation with multiplicative noise in a bounded domain of $\mathbb{R}^d$ (with $d=2$ or $3$)…
Training diffusion models is always a computation-intensive task. In this paper, we introduce a novel speed-up method for diffusion model training, called, which is based on a closer look at time steps. Our key findings are: i) Time steps…
We describe a maximum entropy approach for computing volumes and counting integer points in polyhedra. To estimate the number of points from a particular set X in R^n in a polyhedron P in R^n, by solving a certain entropy maximization…
Data structures known as $k$-d trees have numerous applications in scientific computing, particularly in areas of modern statistics and data science such as range search in decision trees, clustering, nearest neighbors search, local…
The graph edit distance is used for comparing graphs in various domains. Due to its high computational complexity it is primarily approximated. Widely-used heuristics search for an optimal assignment of vertices based on the distance…
In this paper, we deal with distributed estimation problems in diffusion networks with heterogeneous nodes, i.e., nodes that either implement different adaptive rules or differ in some other aspect such as the filter structure or length, or…
In this article, we consider diffusion approximations for a general class of stochastic recursions. Such recursions arise as models for population growth, genetics, financial securities, multiplicative time series, numerical schemes and…
In computational optics, numerical modeling of diffraction between arbitrary planes offers unparalleled flexibility. However, existing methods suffer from the trade-off between computational accuracy and efficiency. To resolve this dilemma,…
Efficient index structures for fast approximate nearest neighbor queries are required in many applications such as recommendation systems. In high-dimensional spaces, many conventional methods suffer from excessive usage of memory and slow…