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Financial structures such as securitisations, insurance contracts, and other hierarchical claims systems can be interpreted as deterministic allocation mechanisms acting on stochastic inflow processes. This paper develops a general…
We describe a representation and a set of inference methods that combine logic programming techniques with probabilistic network representations for uncertainty (influence diagrams). The techniques emphasize the dynamic construction and…
Parameter identification problems are formulated in a probabilistic language, where the randomness reflects the uncertainty about the knowledge of the true values. This setting allows conceptually easily to incorporate new information, e.g.…
Multi-model ensembles provide a pragmatic approach to the representation of model uncertainty in climate prediction. However, such representations are inherently ad hoc, and, as shown, probability distributions of climate variables based on…
We review the mathematical formalism underlying the modelling of stochasticity in biological systems. Beginning with a description of the system in terms of its basic constituents, we derive the mesoscopic equations governing the dynamics…
Stochasticity is a key characteristic of intracellular processes such as gene regulation and chemical signalling. Therefore, characterising stochastic effects in biochemical systems is essential to understand the complex dynamics of living…
The black-box nature of neural models has motivated a line of research that aims to generate natural language rationales to explain why a model made certain predictions. Such rationale generation models, to date, have been trained on…
This chapter presents probability logic as a rationality framework for human reasoning under uncertainty. Selected formal-normative aspects of probability logic are discussed in the light of experimental evidence. Specifically, probability…
In stochastic decision problems, one often wants to estimate the underlying probability measure statistically, and then to use this estimate as a basis for decisions. We shall consider how the uncertainty in this estimation can be…
Probabilistic argumentation allows reasoning about argumentation problems in a way that is well-founded by probability theory. However, in practice, this approach can be severely limited by the fact that probabilities are defined by adding…
Discrete mathematics is the foundation of computer science. It focuses on concepts and reasoning methods that are studied using math notations. It has long been argued that discrete math is better taught with programming, which takes…
Stochastic thermodynamics is a framework for describing non-equilibrium processes at the level of fluctuating trajectories, where the state of a system evolves as a stochastic time series, allowing thermodynamic quantities such as work,…
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…
While generative methods have progressed rapidly in recent years, generating expressive prosody for an utterance remains a challenging task in text-to-speech synthesis. This is particularly true for systems that model prosody explicitly…
Real-valued logics underlie an increasing number of neuro-symbolic approaches, though typically their logical inference capabilities are characterized only qualitatively. We provide foundations for establishing the correctness and power of…
An increasing number of scientific experiments support the view of perception as Bayesian inference, which is rooted in Helmholtz's view of perception as unconscious inference. Recent study of logic presents a view of logical reasoning as…
Description logics are a powerful tool for describing ontological knowledge bases. That is, they give a factual account of the world in terms of individuals, concepts and relations. In the presence of uncertainty, such factual accounts are…
Symbolic dynamics has proven to be an invaluable tool in analyzing the mechanisms that lead to unpredictability and random behavior in nonlinear dynamical systems. Surprisingly, a discrete partition of continuous state space can produce a…
Many real-world systems exhibit ``noisy'' evolution in time; interpreting their finitely-sampled behavior as arising from continuous-time processes (in the It\^o or Stratonovich sense) has led to significant success in modeling and analysis…
Symbolic regression automates the process of learning closed-form mathematical models from data. Standard approaches to symbolic regression, as well as newer deep learning approaches, rely on heuristic model selection criteria, heuristic…