Related papers: Computable infinite dimensional filters with appli…
The problem of learning a computational model from examples has been receiving growing attention. For the particularly challenging problem of learning models of distributed systems, existing results are restricted to models with a fixed…
We consider deep multivariate models for heterogeneous collections of random variables. In the context of computer vision, such collections may e.g. consist of images, segmentations, image attributes, and latent variables. When developing…
We consider diffusion of independent molecules in an insulated Euclidean domain with unknown diffusivity parameter. At a random time and position, the molecules may bind and stop diffusing in dependence of a given `binding potential'. The…
We use the martingale-theoretic approach of game-theoretic probability to incorporate imprecision into the study of randomness. In particular, we define a notion of computable randomness associated with interval, rather than precise,…
Diffusion models are a remarkably effective way of learning and sampling from a distribution $p(x)$. In posterior sampling, one is also given a measurement model $p(y \mid x)$ and a measurement $y$, and would like to sample from $p(x \mid…
Existing monitoring tools for multivariate data are often asymptotically distribution-free, computationally intensive, or require a large stretch of stable data. Many of these methods are not applicable to 'high dimension, low sample size'…
We develop exact Markov chain Monte Carlo methods for discretely-sampled, directly and indirectly observed diffusions. The qualification "exact" refers to the fact that the invariant and limiting distribution of the Markov chains is the…
We prove that under H\"ormander's type conditions on the coefficients of the unobservable component of a partially observable diffusion process the filtering density is infinitely differentiable and can be represented as the integral of an…
The use of cross-diffusion systems as mathematical models of different image processes is investigated. The present paper is concerned with linear filtering. First, those systems satisfying the most important scale-space properties are…
We study the numerical solution of nonlinear partially observed optimal stopping problems. The system state is taken to be a multi-dimensional diffusion and drives the drift of the observation process, which is another multi-dimensional…
Continuous measurements play a pivotal role in the study of dynamical open quantum systems. `Dyne' detections are among the most widespread and efficient measurement schemes, and give rise to quantum diffusion of the conditioned state. In…
The study of continuous-time information diffusion has been an important area of research for many applications in recent years. When only the diffusion traces (cascades) are accessible, cascade-based network inference and influence…
In this article, we consider computing expectations w.r.t. probability measures which are subject to discretization error. Examples include partially observed diffusion processes or inverse problems, where one may have to discretize time…
This paper is concerned with a partially observed hybrid optimal control problem, where continuous dynamics and discrete events coexist and in particular, the continuous dynamics can be observed while the discrete events, described by a…
Generative diffusions are a powerful class of Monte Carlo samplers that leverage bridging Markov processes to approximate complex, high-dimensional distributions, such as those found in image processing and language models. Despite their…
Inferring the causal structure of a set of random variables from a finite sample of the joint distribution is an important problem in science. Recently, methods using additive noise models have been suggested to approach the case of…
Particle probability hypothesis density filtering has become a promising means for multi-target tracking due to its capability of handling an unknown and time-varying number of targets in non-linear non-Gaussian system. However, its…
Bayesian filtering is a key tool in many problems that involve the online processing of data, including data assimilation, optimal control, nonlinear tracking and others. Unfortunately, the implementation of filters for nonlinear, possibly…
Pathwise predictability of continuous time processes is studied in deterministic setting. We discuss uniform prediction in some weak sense with respect to certain classes of inputs. More precisely, we study possibility of approximation of…
For a one dimensional diffusion process $X=\{X(t) ; 0\leq t \leq T \}$, we suppose that $X(t)$ is hidden if it is below some fixed and known threshold $\tau$, but otherwise it is visible. This means a partially hidden diffusion process. The…