Related papers: Probabilistic Stable Functions on Discrete Cones a…
Spaces of convex and concave functions appear naturally in theory and applications. For example, convex regression and log-concave density estimation are important topics in nonparametric statistics. In stochastic portfolio theory, concave…
Quantum mechanics contains some strange unphysical concepts. Among these are complex numbers, Hilbert spaces with their unitary and self-adjoint operators, states represented by complex vectors, superpositions of states, collapse of wave…
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 consider the problem of characterizing entrywise functions that preserve the cone of positive definite matrices when applied to every off-diagonal element. Our results extend theorems of Schoenberg [Duke Math. J. 9], Rudin [Duke Math. J.…
Multimodular functions, primarily used in the literature of queueing theory, discrete-event systems, and operations research, constitute a fundamental function class in discrete convex analysis. The objective of this paper is to clarify the…
We introduce a notion of the ``explanation" of one (generalized) probabilistic model by another as particular kind of span in the category $\Prob$ of probabilistic models and morphisms. We show that explanations compose under a standard…
This paper is about the surprising interaction of a foundational result from model theory, about stability of theories, with algorithmic stability in learning. First, in response to gaps in existing learning models, we introduce a new…
We consider functions of natural numbers which allow a combinatorial interpretation as density functions (speed) of classes of relational structures, s uch as Fibonacci numbers, Bell numbers, Catalan numbers and the like. Many of these…
Probabilistic circuits compute multilinear polynomials that represent multivariate probability distributions. They are tractable models that support efficient marginal inference. However, various polynomial semantics have been considered in…
We extend and improve the existing characterization of the dynamics of general quadratic real polynomial maps with coefficients that depend on a single parameter $\lambda$, and generalize this characterization to cubic real polynomial maps,…
The aim of this paper is to present an elementary computable theory of probability, random variables and stochastic processes. The probability theory is baed on existing approaches using valuations and lower integrals. Various approaches to…
A probabilistic framework to study the dependence structure induced by deterministic discrete-time state-space systems between input and output processes is introduced. General sufficient conditions are formulated under which output…
A stochastic PDE, describing mesoscopic fluctuations in systems of weakly interacting inertial particles of finite volume, is proposed and analysed in any finite dimension $d\in\mathbb{N}$. It is a regularised and inertial version of the…
There is no known way of giving a domain-theoretic semantics to higher-order probabilistic languages, in such a way that the involved domains are continuous or quasi-continuous - the latter is required to do any serious mathematics. We…
We prove two general results concerning spectral sequences of $\mathbf{FI}$-modules. These results can be used to significantly improve stable ranges in a large portion of the stability theorems for $\mathbf{FI}$-modules currently in the…
By discussing several examples, the theory of generalized functional models is shown to be very natural for modeling some situations of reasoning under uncertainty. A generalized functional model is a pair (f, P) where f is a function…
In this paper, we study the probabilistic stability analysis of a subclass of stochastic hybrid systems, called the Planar Probabilistic Piecewise Constant Derivative Systems (Planar PPCD), where the continuous dynamics is deterministic,…
We document a connection between constraint reasoning and probabilistic reasoning. We present an algorithm, called {em probabilistic arc consistency}, which is both a generalization of a well known algorithm for arc consistency used in…
A multidimensional generalization of the Bernstein class of functions and the properties of functions of the introduced class are examined. In particular, a new proof of the integral representation of Bernstein functions of many variables…
Probabilistic Boolean Networks (PBNs) have been previously proposed so as to gain insights into complex dy- namical systems. However, identification of large networks and of the underlying discrete Markov Chain which describes their…