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Generalised Probabilistic Theories (GPTs) provide a unifying framework encompassing classical theories, quantum theories, as well as hypothetical alternatives. We investigate the problem of extending a system with a finite set of…
This book is devoted to the problem of sequential probability forecasting, that is, predicting the probabilities of the next outcome of a growing sequence of observations given the past. This problem is considered in a very general setting…
Factorizable joint shift (FJS) represents a type of distribution shift (or dataset shift) that comprises both covariate and label shift. Recently, it has been observed that FJS actually arises from consecutive label and covariate (or vice…
Proving compositionality of behavioral equivalence on state-based systems with respect to algebraic operations is a classical and widely studied problem. We study a categorical formulation of this problem, where operations on state-based…
Distributive laws of a monad T over a functor F are categorical tools for specifying algebra-coalgebra interaction. They proved to be important for solving systems of corecursive equations, for the specification of well-behaved structural…
In this paper, we provide an explicit probability distribution for classification purposes. It is derived from the Bayesian nonparametric mixture of Dirichlet process model, but with suitable modifications which remove unsuitable aspects of…
Hilbert bimodules are morphisms between C*-algebraic models of quantum systems, while symplectic dual pairs are morphisms between Poisson geometric models of classical systems. Both of these morphisms preserve representation-theoretic…
The interplay between the algebraic structure (operator algebras) for the quantum observables and the convex structure of the state space has been explored for a long time and most advanced results are due to Alfsen and Shultz. Here we…
In particle physics, as in many areas of science, parameter inference relies on simulations to bridge the gap between theory and experiment. Recent developments in simulation-based inference have boosted the sensitivity of analyses;…
Probabilistic bisimulation is a fundamental notion of process equivalence for probabilistic systems. Among others, it has important applications including formalizing the anonymity property of several communication protocols. There is a lot…
The Poisson-binomial distribution is useful in many applied problems in engineering, actuarial science, and data mining. The Poisson-binomial distribution models the distribution of the sum of independent but not identically distributed…
As inductive inference and machine learning methods in computer science see continued success, researchers are aiming to describe ever more complex probabilistic models and inference algorithms. It is natural to ask whether there is a…
We investigate the possibility to separate the bisimulation-invariant fragment of P from that of NP, resp. PSPACE. We build on Otto's Theorem stating that the bisimulation-invariant queries in P are exactly those that are definable in the…
Many recursive functions can be defined elegantly as the unique homomorphisms, between two algebras, two coalgebras, or one each, that are induced by some universal property of a distinguished structure. Besides the well-known applications…
In this paper we present multivariate space-time fractional Poisson processes by considering common random time-changes of a (finite-dimensional) vector of independent classical (non-fractional) Poisson processes. In some cases we also…
The most efficient MC weights for the calculation of physical, canonical expectation values are not necessarily those of the canonical ensemble. The use of suitably generalized ensembles can lead to a much faster convergence of the…
There is an ``algebraisation'' of the notion of weak factorisation system (w.f.s.) known as a natural weak factorisation system. In it, the two classes of maps of a w.f.s. are replaced by two categories of maps-with-structure, where the…
The paper introduces the concept of a cluster structure to define a joint distribution of the sample size and its exchangeable random partitions. The cluster structure allows the probability distribution of the random partitions of a subset…
While distributed systems with transfer of processes have become pervasive, methods for reasoning about their behaviour are underdeveloped. In this paper we propose a bisimulation technique for proving behavioural equivalence of such…
Probability forecasting is common in the geosciences, the finance sector, and elsewhere. It is sometimes the case that one has multiple probability-forecasts for the same target. How is the information in these multiple forecast systems…