Related papers: A Monad for Probabilistic Point Processes

Gaussian processes are the leading class of distributions on random functions, but they suffer from well known issues including difficulty scaling and inflexibility with respect to certain shape constraints (such as nonnegativity). Here we…

A growing body of research on probabilistic programs and causal models has highlighted the need to reason compositionally about model classes that extend directed graphical models. Both probabilistic programs and causal models define a…

Like notions of process equivalence, behavioural preorders on processes come in many flavours, ranging from fine-grained comparisons such as ready simulation to coarse-grained ones such as trace inclusion. Often, such behavioural preorders…

The log-likelihood of a generative model often involves both positive and negative terms. For a temporal multivariate point process, the negative term sums over all the possible event types at each time and also integrates over all the…

We construct a factorization of the Giry monad through the category of convex spaces, and show that, provided that no measurable cardinals exist, probability measures can be viewed as natural transformations. Using the adjunction of this…

In process mining, precision measures are used to quantify how much a process model overapproximates the behavior seen in an event log. Although several measures have been proposed throughout the years, no research has been done to validate…

We develop a model for point processes on the real line, where the intensity can be locally unbounded without inducing an explosion. In contrast to an orderly point process, for which the probability of observing more than one event over a…

We apply random matrix theory to study the impact of measurement uncertainty on dynamic mode decomposition. Specifically, when the measurements follow a normal probability density function, we show how the moments of that density propagate…

This is the first paper of a series of two devoted to develop a practical method to describe the growth history of bound virialized objects in the gravitational instability scenario without resorting to $N$-body simulations. Here we present…

The normalised partial sums of values of a nonnegative multiplicative function over divisors with appropriately restricted sizes of a random permutation from the symmetric group define trajectories of a stochastic process. We prove a…

The algebraic properties of the combination of probabilistic choice and nondeterministic choice have long been a research topic in program semantics. This paper explains a formalization in the Coq proof assistant of a monad equipped with…

We propose an approach to compute the boundary crossing probabilities for a class of diffusion processes which can be expressed as piecewise monotone (not necessarily one-to-one) functionals of a standard Brownian motion. This class…

This thesis describes work on two applications of probabilistic programming: the learning of probabilistic program code given specifications, in particular program code of one-dimensional samplers; and the facilitation of sequential Monte…

We treat observable operator models (OOM) and their non-commutative generalisation, which we call NC-OOMs. A natural characteristic of a stochastic process in the context of classical OOM theory is the process dimension. We investigate its…

The conventional definition of a topological metric over a space specifies properties that must be obeyed by any measure of "how separated" two points in that space are. Here it is shown how to extend that definition, and in particular the…

We show that the dimension of the geometric shape formed by the phenomenologically valid points inside a multi-dimensional parameter space can be used to characterise different new physics models and to define a quantitative measure for the…

In this paper, we propose a simple yet effective method to represent point clouds as sets of samples drawn from a cloud-specific probability distribution. This interpretation matches intrinsic characteristics of point clouds: the number of…

Gaussian processes can be treated as subsets of a standard Hilbert space, however, the volume size relation between the underlying index space of random processes and its convex hull is not clear. The understanding of such volume size…

Let $X$ be a locally compact Polish space. A random measure on $X$ is a probability measure on the space of all (nonnegative) Radon measures on $X$. Denote by $\mathbb K(X)$ the cone of all Radon measures $\eta$ on $X$ which are of the form…

The purpose of this paper is to estimate the intensity of some random measure by a piecewise constant function on a finite partition of the underlying measurable space. Given a (possibly large) family of candidate partitions, we build a…