Arthur Van Camp
Ghent University
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Publication
Featured researches published by Arthur Van Camp.
Fuzzy Sets and Systems | 2016
Jasper De Bock; Arthur Van Camp; Marcio Alves Diniz; Gert de Cooman
We provide representation theorems for both finite and countable sequences of finite-valued random variables that are considered to be partially exchangeable. In their most general form, our results are presented in terms of sets of desirable gambles, a very general framework for modelling uncertainty. Its key advantages are that it allows for imprecision, is more expressive than almost every other imprecise-probabilistic framework and makes conditioning on events with (lower) probability zero non-problematic. We translate our results to more conventional, although less general frameworks as well: lower previsions, linear previsions and probability measures. The usual, precise-probabilistic representation theorems for partially exchangeable random variables are obtained as special cases.
international conference information processing | 2012
Arthur Van Camp; Gert de Cooman
We present a method for learning imprecise local uncertainty models in stationary hidden Markov models. If there is enough data to justify precise local uncertainty models, then existing learning algorithms, such as the Baum–Welch algorithm, can be used. When there is not enough evidence to justify precise models, the method we suggest here has a number of interesting features.
Fuzzy Sets and Systems | 2017
Arthur Van Camp; Gert de Cooman; Enrique Miranda; Erik Quaeghebeur
We investigate how to model indifference with choice functions. We take the coherence axioms for choice functions proposed by Seidenfeld, Schervisch and Kadane as a source of inspiration, but modify them to strengthen the connection with desirability. We discuss the properties of choice functions that are coherent under our modified set of axioms and the connection with desirability. Once this is in place, we present an axiomatisation of indifference in terms of desirability. On this we build our definition of indifference in terms of choice functions, which we discuss in some detail.
International Journal of Approximate Reasoning | 2018
Arthur Van Camp; Gert de Cooman; Enrique Miranda
Abstract We investigate a generalisation of the coherent choice functions considered by Seidenfeld et al. [35] , by sticking to the convexity axiom but imposing no Archimedeanity condition. We define our choice functions on vector spaces of options, which allows us to incorporate as special cases both Seidenfeld et al.s [35] choice functions on horse lotteries and also pairwise choice—which is equivalent to sets of desirable gambles [29] —, and to investigate their connections. We show that choice functions based on sets of desirable options (gambles) satisfy Seidenfelds convexity axiom only for very particular types of sets of desirable options, which are exactly those that are representable by lexicographic probability systems that have no non-trivial Savage-null events. We call them lexicographic choice functions. Finally, we prove that these choice functions can be used to determine the most conservative convex choice function associated with a given binary relation.
probabilistic graphical models | 2014
Cedric De Boom; Jasper De Bock; Arthur Van Camp; Gert de Cooman
We present an efficient algorithm for estimating hidden state sequences in imprecise hidden Markov models (iHMMs), based on observed output sequences. The main difference with classical HMMs is that the local models of an iHMM are not represented by a single mass function, but rather by a set of mass functions. We consider as estimates for the hidden state sequence those sequences that are maximal. In this way, we generalise the problem of finding a state sequence with highest posterior probability, as is commonly considered in HMMs, and solved efficiently by the Viterbi algorithm. An important feature of our approach is that there may be multiple maximal state sequences, typically for iHMMs that are highly imprecise. We show experimentally that the time complexity of our algorithm tends to be linear in this number of maximal sequences, and investigate how this number depends on the local models.
International Journal of Approximate Reasoning | 2018
Arthur Van Camp; Gert de Cooman
We investigate how to model exchangeability with choice functions. Exchangeability is a structural assessment on a sequence of uncertain variables. We show how such assessments are a special indifference assessment, and how that leads to a counterpart of de Finettis Representation Theorem, both in a finite and a countable context.
soft methods in probability and statistics | 2017
Arthur Van Camp; Enrique Miranda; Gert de Cooman
We investigate the connection between choice functions and lexicographic probabilities, by means of the convexity axiom considered by Seidenfeld et al. (Synthese 172:157–176, 2010 [7]) but without imposing any Archimedean condition. We show that lexicographic probabilities are related to a particular type of sets of desirable gambles, and investigate the properties of the coherent choice function this induces via maximality. Finally, we show that the convexity axiom is necessary but not sufficient for a coherent choice function to be the infimum of a class of lexicographic ones.
european conference on artificial intelligence | 2012
Gert de Cooman; Jasper De Bock; Arthur Van Camp
We summarise and provide pointers to recent advances in inference and identification for specific types of probabilistic graphical models using imprecise probabilities. Robust inferences can be made in so-called credal networks when the local models attached to their nodes are imprecisely specified as conditional lower previsions, by using exact algorithms whose complexity is comparable to that for the precise-probabilistic counterparts.
international conference information processing | 2018
Arthur Van Camp; Enrique Miranda; Gert de Cooman
We extend the notion of natural extension, that gives the least committal extension of a given assessment, from the theory of sets of desirable gambles to that of choice functions. We give an expression of this natural extension and characterise its existence by means of a property called avoiding complete rejection. We prove that our notion reduces indeed to the standard one in the case of choice functions determined by binary comparisons, and that these are not general enough to determine all coherent choice function. Finally, we investigate the compatibility of the notion of natural extension with the structural assessment of indifference between a set of options.
Archive | 2018
Enrique Miranda; Arthur Van Camp; Gert de Cooman
We establish an equivalent representation of coherent choice functions in terms of a family of rejection sets, and investigate how each of the coherence axioms translates into this framework. In addition, we show that this family allows to simplify the verification of coherence in a number of particular cases.