Related papers: Testing Probabilistic Processes: Can Random Choice…
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…
Probabilistic bisimulation is a fundamental notion of process equivalence for probabilistic systems. Among others, it has important applications including formalizing the anonymity property of several communication protocols. There is a lot…
This paper presents a theory of systemic undecidability, reframing incomputability as a structural property of systems rather than a localized feature of specific functions or problems. We define a notion of causal embedding and prove a…
A causal set is a partially ordered set on a countably infinite ground-set such that each element is above finitely many others. A natural extension of a causal set is an enumeration of its elements which respects the order. We bring…
Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…
The definition of the conditional probability is very important in the theory of the probability. This definition is based on the fact, that random events can be simultaneously measurable. This paper deal with the problem of conditioning…
Topological models of empirical and formal inquiry are increasingly prevalent. They have emerged in such diverse fields as domain theory [1, 16], formal learning theory [18], epistemology and philosophy of science [10, 15, 8, 9, 2],…
A random set is a generalisation of a random variable, i.e. a set-valued random variable. The random set theory allows a unification of other uncertainty descriptions such as interval variable, mass belief function in Dempster-Shafer theory…
Uncertainty representation and quantification are paramount in machine learning and constitute an important prerequisite for safety-critical applications. In this paper, we propose novel measures for the quantification of aleatoric and…
Various strategies for active learning have been proposed in the machine learning literature. In uncertainty sampling, which is among the most popular approaches, the active learner sequentially queries the label of those instances for…
It is often claimed that the fundamental laws of physics are deterministic and time-symmetric and that therefore our experience of the passage of time is an illusion. This paper will critically discuss these claims and show that they are…
Models of a generalized nondeterminism are defined by limitations on nonde- terministic behavior of a computing device. A regular realizability problem is a problem of verifying existence of a special sort word in a regular language. These…
We study stochastic choice across decision problems, each represented as a menu of action labels paired with observable outcome vectors. We propose a consistency condition for behavior in decision problems composed of two separable…
A semi-process is an analog of the semi-flow for non-autonomous differential equations or inclusions. We prove an abstract result on the existence of measurable semi-processes in the situations where there is no uniqueness. Also, we allow…
Determinantal point processes (DPPs) are probability models over subsets of a ground set that favor diverse selections while suppressing redundancy. That is, they tend to assign higher likelihood to collections whose elements complement one…
Observability is a modelling property that describes the possibility of inferring the internal state of a system from observations of its output. A related property, structural identifiability, refers to the theoretical possibility of…
This paper proposes a notion of branching bisimilarity for non-deterministic probabilistic processes. In order to characterize the corresponding notion of rooted branching probabilistic bisimilarity, an equational theory is proposed for a…
The probabilistic reachability problems of nondeterministic systems are studied. Based on the existing studies, the definition of probabilistic reachable sets is generalized by taking into account time-varying target set and obstacle. A…
Methods for learning optimal policies in autonomous agents often assume that the way the domain is conceptualised---its possible states and actions and their causal structure---is known in advance and does not change during learning. This…
Decision making under uncertainty is a key component of many AI settings, and in particular of voting scenarios where strategic agents are trying to reach a joint decision. The common approach to handle uncertainty is by maximizing expected…