Related papers: Random Marked Sets
Covariance regression analysis is an approach to linking the covariance of responses to a set of explanatory variables $X$, where $X$ can be a vector, matrix, or tensor. Most of the literature on this topic focuses on the "Fixed-$X$"…
Point processes are stochastic models generating interacting points or events in time, space, etc. Among characteristics of these models, first-order intensity and conditional intensity functions are often considered. We focus on…
We introduce multi-kangaroo Markov processes and provide a general procedure for evaluating a certain type of stochastic functionals. We calculate analytically the large deviation properties. Applications include zero-crossing statistics…
We consider random processes that are history-dependent, in the sense that the distribution of the next step of the process at any time depends upon the entire past history of the process. In general, therefore, the Markov property cannot…
Statistical learning theory provides the foundation to applied machine learning, and its various successful applications in computer vision, natural language processing and other scientific domains. The theory, however, does not take into…
We treat the class of universal Markov processes on the d-dimensional Euklidean space which do not depend on random. For these, as well as for several subclasses, we prove criteria whether a function f, defined on the positive half-line,…
Determinantal point processes have arisen in diverse settings in recent years and have been investigated intensively. We study basic combinatorial and probabilistic aspects in the discrete case. Our main results concern relationships with…
The problem of (pathwise) large deviations for conditionally continuous Gaussian processes is investigated. The theory of large deviations for Gaussian processes is extended to the wider class of random processes -- the conditionally…
This paper generalizes stochastic collocation methods to handle correlated non-Gaussian random parameters. The key challenge is to perform a multivariate numerical integration in a correlated parameter space when computing the coefficient…
From the Bayesian perspective, the category of conditional probabilities (a variant of the Kleisli category of the Giry monad, whose objects are measurable spaces and arrows are Markov kernels) gives a nice framework for conceptualization…
Many problems arising in applications result in the need to probe a probability distribution for functions. Examples include Bayesian nonparametric statistics and conditioned diffusion processes. Standard MCMC algorithms typically become…
The problem of characterization of Gibbs random fields is considered. Various Gibbsianness criteria are obtained using the earlier developed one-point framework which in particular allows to describe random fields by means of either…
Random projections offer an appealing and flexible approach to a wide range of large-scale statistical problems. They are particularly useful in high-dimensional settings, where we have many covariates recorded for each observation. In…
We propose a new method to construct a stationary process and random field with a given decreasing covariance function and any one-dimensional marginal distribution. The result is a new class of stationary processes and random fields. The…
We introduce the notion of a stochastic probabilistic program and present a reference implementation of a probabilistic programming facility supporting specification of stochastic probabilistic programs and inference in them. Stochastic…
Various approaches to stochastic processes exist, noting that key properties such as measurability and continuity are not trivially satisfied. We introduce a new theory for Gaussian processes using improper linear functionals. Using a…
Set prediction is about learning to predict a collection of unordered variables with unknown interrelations. Training such models with set losses imposes the structure of a metric space over sets. We focus on stochastic and underdefined…
We present a novel, yet rather simple construction within the traditional framework of Scott domains to provide semantics to probabilistic programming, thus obtaining a solution to a long-standing open problem in this area. Unlike current…
We consider a stochastic process $Y$ defined by an integral in quadratic mean of a deterministic function $f$ with respect to a Gaussian process $X$, which need not have stationary increments. For a class of Gaussian processes $X$, it is…
We introduce the notion of domain-structured chaos and apply it to establish a connection between stochastic dynamics and deterministic chaos.