相关论文: Probability Bracket Notation, Markov Chains, Stoch…

A new class of nonparametric prior distributions, termed Beta-Binomial stick-breaking process, is proposed. By allowing the underlying length random variables to be dependent through a Beta marginals Markov chain, an appealing discrete…

The projected belief network (PBN) is a generative stochastic network with tractable likelihood function based on a feed-forward neural network (FFNN). The generative function operates by "backing up" through the FFNN. The PBN is two…

The probabilistic symbol is defined as the right-hand side derivative at time zero of the characteristic functions corresponding to the one-dimensional marginals of a time-homogeneous stochastic process. As described in various…

The stochastic theory of non-relativistic quantum mechanics presented here relies heavily upon the theory of stochastic processes, with its definitions, theorems and specific vocabulary as well. Its main hypothesis states indeed that the…

The Pairwise Markov Chain (PMC) is a probabilistic graphical model extending the well-known Hidden Markov Model. This model, although highly effective for many tasks, has been scarcely utilized for continuous value prediction. This is…

A theory of systems with long-range correlations based on the consideration of binary N-step Markov chains is developed. In the model, the conditional probability that the i-th symbol in the chain equals zero (or unity) is a linear function…

It is of some interest to understand how statistically based mechanisms for signal processing might be integrated with biologically motivated mechanisms such as neural networks. This paper explores a novel hybrid approach for classifying…

Although quantum systems are generally described by quantum state vectors, we show that in certain cases their measurement processes can be reformulated as probabilistic equations expressed in terms of probabilistic state vectors. These…

Stochastic processes that involve the creation of objects and relations over time are widespread, but relatively poorly studied. For example, accurate fault diagnosis in factory assembly processes requires inferring the probabilities of…

This paper proposes various new analysis techniques for Bayes networks in which conditional probability tables (CPTs) may contain symbolic variables. The key idea is to exploit scalable and powerful techniques for synthesis problems in…

Recent work by the authors equips Petri occurrence nets (PN) with probability distributions which fully replace nondeterminism. To avoid the so-called confusion problem, the construction imposes additional causal dependencies which restrict…

We describe here the new concept of $\epsilon$-Homomorphisms of Probabilistic Regulatory Gene Networks(PRN). The $\epsilon$-homomorphisms are special mappings between two probabilistic networks, that consider the algebraic action of the…

Understanding the complex and stochastic nature of Gene Regulatory Networks (GRNs) remains a central challenge in systems biology. Existing modeling paradigms often struggle to effectively capture the intricate, multi-factor regulatory…

The projected belief network (PBN) is a layered generative network (LGN) with tractable likelihood function, and is based on a feed-forward neural network (FFNN). There are two versions of the PBN: stochastic and deterministic (D-PBN), and…

In this paper we introduce the idea of probability in the definition of Sequential Dynamical Systems, thus obtaining a new concept, Probabilistic Sequential System. The introduction of a probabilistic structure on Sequential Dynamical…

This paper generalizes the notion of stochastic order to a relation between probability measures over arbitrary measurable spaces. This generalization is motivated by the observation that for the stochastic ordering of two stationary Markov…

In this article, the following results are obtained: the process of a randomly wandering particle having a size and a continuous trajectory of motion is considered; (b) based on the study of this probabilistic process, a derivation of the…

We consistently formalize the probabilistic description of multipartite joint measurements performed on systems of any nature. This allows us: (1) to specify in probabilistic terms the difference between nonsignaling, the Einstein-…

We provide two applications of an elementary (yet seemingly unknown) probabilistic representation of matrix ordered exponentials, which generalizes the Feynman-Kac formula in finite dimensions and the change of measure formula between two…

Probabilistic circuits (PCs) have gained prominence in recent years as a versatile framework for discussing probabilistic models that support tractable queries and are yet expressive enough to model complex probability distributions.…