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A Bayesian network is a graphical model that encodes probabilistic relationships among variables of interest. When used in conjunction with statistical techniques, the graphical model has several advantages for data analysis. One, because…

Explainable AI (XAI) aims to provide interpretations for predictions made by learning machines, such as deep neural networks, in order to make the machines more transparent for the user and furthermore trustworthy also for applications in…

This chapter offers an accessible introduction to the channel-based approach to Bayesian probability theory. This framework rests on algebraic and logical foundations, inspired by the methodologies of programming language semantics. It…

Biological networks are a very convenient modelling and visualisation tool to discover knowledge from modern high-throughput genomics and postgenomics data sets. Indeed, biological entities are not isolated, but are components of complex…

There is a brief description of the probabilistic causal graph model for representing, reasoning with, and learning causal structure using Bayesian networks. It is then argued that this model is closely related to how humans reason with and…

We showed how to use trained neural networks to perform Bayesian reasoning in order to solve tasks outside their initial scope. Deep generative models provide prior knowledge, and classification/regression networks impose constraints. The…

Motivated by inferring cellular signaling networks using noisy flow cytometry data, we develop procedures to draw inference for Bayesian networks based on error-prone data. Two methods for inferring causal relationships between nodes in a…

In this paper, we present two methods to provide explanations for reasoning with belief functions in the valuation-based systems. One approach, inspired by Strat's method, is based on sensitivity analysis, but its computation is simpler…

The currently dominating artificial intelligence and machine learning technology, neural networks, builds on inductive statistical learning. Neural networks of today are information processing systems void of understanding and reasoning…

Explainable artificial intelligence techniques are developed at breakneck speed, but suitable evaluation approaches lag behind. With explainers becoming increasingly complex and a lack of consensus on how to assess their utility, it is…

Explanation methods aim to make neural networks more trustworthy and interpretable. In this paper, we demonstrate a property of explanation methods which is disconcerting for both of these purposes. Namely, we show that explanations can be…

We analyze a model of learning and belief formation in networks in which agents follow Bayes rule yet they do not recall their history of past observations and cannot reason about how other agents' beliefs are formed. They do so by making…

We study the stability of posterior predictive inferences to the specification of the likelihood model and perturbations of the data generating process. In modern big data analyses, useful broad structural judgements may be elicited from…

The vast majority of network datasets contains errors and omissions, although this is rarely incorporated in traditional network analysis. Recently, an increasing effort has been made to fill this methodological gap by developing network…

Defeasible reasoning is the mode of reasoning where conclusions can be overturned by taking into account new evidence. A commonly used method in cognitive science and logic literature is to handcraft argumentation supporting inference…

Network data are increasingly collected along with other variables of interest. Our motivation is drawn from neurophysiology studies measuring brain connectivity networks for a sample of individuals along with their membership to a low or…

Causal Bayesian networks are 'causal' models since they make predictions about interventional distributions. To connect such causal model predictions to real-world outcomes, we must determine which actions in the world correspond to which…

In the existing evidential networks with belief functions, the relations among the variables are always represented by joint belief functions on the product space of the involved variables. In this paper, we use conditional belief functions…

State-of-the-art deep-learning systems use decision rules that are challenging for humans to model. Explainable AI (XAI) attempts to improve human understanding but rarely accounts for how people typically reason about unfamiliar agents. We…

Large language models (LLMs) are increasingly used as agents that interact with users and with the world. To do so successfully, LLMs must construct representations of the world and form probabilistic beliefs about them. To provide…