Coping with the Limitations of Rational Inference in the Framework of Possibility Theory

Possibility theory offers a framework where both Lehmann's "preferential inference" and the more productive (but less cautious) "rational closure inference" can be represented. However, there are situations where the second inference does not provide expected results either because it cannot produce them, or even provide counter-intuitive conclusions. This state of facts is not due to the principle of selecting a unique ordering of interpretations (which can be encoded by one possibility distribution), but rather to the absence of constraints expressing pieces of knowledge we have implicitly in mind. It is advocated in this paper that constraints induced by independence information can help finding the right ordering of interpretations. In particular, independence constraints can be systematically assumed with respect to formulas composed of literals which do not appear in the conditional knowledge base, or for default rules with respect to situations which are "normal" according to the other default rules in the base. The notion of independence which is used can be easily expressed in the qualitative setting of possibility theory. Moreover, when a counter-intuitive plausible conclusion of a set of defaults, is in its rational closure, but not in its preferential closure, it is always possible to repair the set of defaults so as to produce the desired conclusion.Comment: Appears in Proceedings of the Twelfth Conference on Uncertainty in Artificial Intelligence (UAI1996

Pinning model in random correlated environment: appearance of an infinite disorder regime

We study the influence of a correlated disorder on the localization phase transition in the pinning model. When correlations are strong enough, a strong disorder regime arises: large and frequent attractive regions appear in the environment. We present here a pinning model in random binary ({-1,1}-valued) environment. Defining strong disorder via the requirement that the probability of the occurrence of a large attractive region is sub-exponential in its size, we prove that it coincides with the fact that the critical point is equal to its minimal possible value. We also stress that in the strong disorder regime, the phase transition is smoother than in the homogeneous case, whatever the critical exponent of the homogeneous model is: disorder is therefore always relevant. We illustrate these results with the example of an environment based on the sign of a Gaussian correlated sequence, in which we show that the phase transition is of infinite order in presence of strong disorder. Our results contrast with results known in the literature, in particular in the case of an IID disorder, where the question of the influence of disorder on the critical properties is answered via the so-called Harris criterion, and where a conventional relevance/irrelevance picture holds.Comment: 27 pages, some corrections made in v

The random pinning model with correlated disorder given by a renewal set

We investigate the effect of correlated disorder on the localization transition undergone by a renewal sequence with loop exponent $\alpha$ > 0, when the correlated sequence is given by another independent renewal set with loop exponent $\alpha$ > 0. Using the renewal structure of the disorder sequence, we compute the annealed critical point and exponent. Then, using a smoothing inequality for the quenched free energy and second moment estimates for the quenched partition function, combined with decoupling inequalities, we prove that in the case $\alpha$ > 2 (summable correlations), disorder is irrelevant if $\alpha$ 1/2, which extends the Harris criterion for independent disorder. The case $\alpha$ $\in$ (1, 2) (non-summable correlations) remains largely open, but we are able to prove that disorder is relevant for $\alpha$ > 1/ $\alpha$, a condition that is expected to be non-optimal. Predictions on the criterion for disorder relevance in this case are discussed. Finally, the case $\alpha$ $\in$ (0, 1) is somewhat special but treated for completeness: in this case, disorder has no effect on the quenched free energy, but the annealed model exhibits a phase transition

Epistemic irrelevance in credal networks : the case of imprecise Markov trees

We replace strong independence in credal networks with the weaker notion of epistemic irrelevance. Focusing on directed trees, we show how to combine local credal sets into a global model, and we use this to construct and justify an exact message-passing algorithm that computes updated beliefs for a variable in the tree. The algorithm, which is essentially linear in the number of nodes, is formulated entirely in terms of coherent lower previsions. We supply examples of the algorithm's operation, and report an application to on-line character recognition that illustrates the advantages of our model for prediction

Fifty years of irrelevance: the wild goose chase of management science

Modern management science has existed since 1959 when two reports (by Pierson and Gordon & Howell) on the future of business education were published in the US. At least since 1980, there has been a practically continuous, but somewhat fragmented discussion on the relevance of management research. Although many different proposals have been made to rectify the situation, the mainstream of management research seems to be relatively untroubled and unaffected by this widely sensed irrelevance. The paper aims at initial understanding of the reasons for this spectacular failure of (general) management research to reach relevant results in the period of 1960-2010. Two related questions are considered in more detail. How was the social science turn of management science in 1959 justified and achieved? Which correctives have been proposed for management research, up to now

Disorder relevance for the random walk pinning model in dimension 3

We study the continuous time version of the random walk pinning model, where conditioned on a continuous time random walk Y on Z^d with jump rate \rho>0, which plays the role of disorder, the law up to time t of a second independent random walk X with jump rate 1 is Gibbs transformed with weight e^{\beta L_t(X,Y)}, where L_t(X,Y) is the collision local time between X and Y up to time t. As the inverse temperature \beta varies, the model undergoes a localization-delocalization transition at some critical \beta_c>=0. A natural question is whether or not there is disorder relevance, namely whether or not \beta_c differs from the critical point \beta_c^{ann} for the annealed model. In Birkner and Sun [BS09], it was shown that there is disorder irrelevance in dimensions d=1 and 2, and disorder relevance in d>=4. For d>=5, disorder relevance was first proved by Birkner, Greven and den Hollander [BGdH08]. In this paper, we prove that if X and Y have the same jump probability kernel, which is irreducible and symmetric with finite second moments, then there is also disorder relevance in the critical dimension d=3, and \beta_c-\beta^{ann}_c is at least of the order e^{-C(\zeta)\rho^{-\zeta}}, C(\zeta)>0, for any \zeta>2. Our proof employs coarse graining and fractional moment techniques, which have recently been applied by Lacoin [L09] to the directed polymer model in random environment, and by Giacomin, Lacoin and Toninelli [GLT09] to establish disorder relevance for the random pinning model in the critical dimension. Along the way, we also prove a continuous time version of Doney's local limit theorem [D97] for renewal processes with infinite mean.Comment: 36 pages, revised version following referee's comments. Change of title. Added a monotonicity result (Theorem 1.3) on the critical point shift shown to us by the referee