贝叶斯网络与证明网：贝叶斯推断的证明论

贝叶斯网络与证明网：贝叶斯推理的证明论阐释

Bayesian Networks and Proof-Nets: a proof-theoretical account of Bayesian Inference

本文揭示贝叶斯网络与乘法线性逻辑证明网在联合概率分布表示和计算层面的对应关系，为贝叶斯推理建立证明论基础。

Unifying Inference for Bayesian and Petri Nets

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 choices within certain subnets called structural branching cells (s-cells). Bayesian nets (BN) are usually structured as partial orders where nodes define conditional probability distributions. In the paper, we unify the two structures in terms of Symmetric Monoidal Categories (SMC), so that we can apply to PN ordinary analysis techniques developed for BN. …

Updating Probabilistic Knowledge on Condition/Event Nets using Bayesian Networks

The paper extends Bayesian networks (BNs) by a mechanism for dynamic changes to the probability distributions represented by BNs. One application scenario is the process of knowledge acquisition of an observer interacting with a system. In particular, the paper considers condition/event nets where the observer's knowledge about the current marking is a probability distribution over markings. The observer can interact with the net to deduce information about the marking by requesting certain transitions to fire and observing their success or failure. Aiming for an efficient implementation of dy…

量子贝叶斯网络：通过线性逻辑的组合性与类型化

Quantum Bayesian Networks: Compositionality and Typing via Linear Logic

本文通过线性逻辑证明网为量子贝叶斯网络引入组合原则和类型化机制，确保系统组合的良好行为，并在经典和纯量子情况下分别退化为标准贝叶斯网络和张量网络。

Picturing classical and quantum Bayesian inference

We introduce a graphical framework for Bayesian inference that is sufficiently general to accommodate not just the standard case but also recent proposals for a theory of quantum Bayesian inference wherein one considers density operators rather than probability distributions as representative of degrees of belief. The diagrammatic framework is stated in the graphical language of symmetric monoidal categories and of compact structures and Frobenius structures therein, in which Bayesian inversion boils down to transposition with respect to an appropriate compact structure. We characterize classi…