Decomposable models and Bayesian networks can be defined as sequences of oligo-dimensional probability measures connected with operators of composition. The preliminary results suggest that the probabilistic models allowing for effective computational procedures are represented by sequences possessing a special property; we shall call them perfect sequences. The paper lays down the elementary foundation necessary for further study of iterative application of operators of composition. We believe to develop a technique describing several graph models in a unifying way. We are convinced that practically all theoretical results and procedures connected with decomposable models and Bayesian networks can be translated into the terminology introduced in this paper. For example, complexity of computational procedures in these models is closely dependent on possibility to change the ordering of oligo-dimensional measures defining the model. Therefore, in this paper, lot of attention is paid to possibility to change ordering of the operators of composition.

Valuation based systems verifying an idempotent property are studied. A partial order is defined between the valuations giving them a lattice structure. Then, two different strategies are introduced to represent valuations: as infimum of the most informative valuations or as supremum of the least informative ones. It is studied how to carry out computations with both representations in an efficient way. The particular cases of finite sets and convex polytopes are considered.

This volume contains the papers presented at CICLOPS'12: 12th International Colloquium on Implementation of Constraint and LOgic Programming Systems held on Tueseday September 4th, 2012 in Budapest. The program included 1 invited talk, 9 technical presentations and a panel discussion on Prolog open standards (open.pl). Each programme paper was reviewed by 3 reviewers. CICLOPS'12 continues a tradition of successful workshops on Implementations of Logic Programming Systems, previously held in Budapest (1993) and Ithaca (1994), the Compulog Net workshops on Parallelism and Implementation Technologies held in Madrid (1993 and 1994), Utrecht (1995) and Bonn (1996), the Workshop on Parallelism and Implementation Technology for (Constraint) Logic Programming Languages held in Port Jefferson (1997), Manchester (1998), Las Cruces (1999), and London (2000), and more recently the Colloquium on Implementation of Constraint and LOgic Programming Systems in Paphos (2001), Copenhagen (2002), Mumbai (2003), Saint Malo (2004), Sitges (2005), Seattle (2006), Porto (2007), Udine (2008), Pasadena (2009), Edinburgh (2010) - together with WLPE, Lexington (2011). We would like to thank all the authors, Tom Schrijvers for his invited talk, the programme committee members, and the ICLP 2012 organisers. We would like to also thank arXiv.org for providing permanent hosting.

The family of Groves mechanisms, which includes the well-known VCG mechanism (also known as the Clarke mechanism), is a family of efficient and strategy-proof mechanisms. Unfortunately, the Groves mechanisms are generally not budget balanced. That is, under such mechanisms, payments may flow into or out of the system of the agents, resulting in deficits or reduced utilities for the agents. We consider the following problem: within the family of Groves mechanisms, we want to identify mechanisms that give the agents the highest utilities, under the constraint that these mechanisms must never incur deficits. We adopt a prior-free approach. We introduce two general measures for comparing mechanisms in prior-free settings. We say that a non-deficit Groves mechanism M individually dominates another non-deficit Groves mechanism M' if for every type profile, every agent's utility under M is no less than that under M', and this holds with strict inequality for at least one type profile and one agent. We say that a non-deficit Groves mechanism M collectively dominates another non-deficit Groves mechanism M' if for every type profile, the agents' total utility under M is no less than that under M', and this holds with strict inequality for at least one type profile. The above definitions induce two partial orders on non-deficit Groves mechanisms. We study the maximal elements corresponding to these two partial orders, which we call the individually undominated mechanisms and the collectively undominated mechanisms, respectively.

The process of diagnosis involves learning about the state of a system from various observations of symptoms or findings about the system. Sophisticated Bayesian (and other) algorithms have been developed to revise and maintain beliefs about the system as observations are made. Nonetheless, diagnostic models have tended to ignore some common sense reasoning exploited by human diagnosticians; In particular, one can learn from which observations have not been made, in the spirit of conversational implicature. There are two concepts that we describe to extract information from the observations not made. First, some symptoms, if present, are more likely to be reported before others. Second, most human diagnosticians and expert systems are economical in their data-gathering, searching first where they are more likely to find symptoms present. Thus, there is a desirable bias toward reporting symptoms that are present. We develop a simple model for these concepts that can significantly improve diagnostic inference.

We investigate a class of hierarchical mixtures-of-experts (HME) models where exponential family regression models with generalized linear mean functions of the form psi(ga+fx^Tfgb) are mixed. Here psi(...) is the inverse link function. Suppose the true response y follows an exponential family regression model with mean function belonging to a class of smooth functions of the form psi(h(fx)) where h(...)in W_2^infty (a Sobolev class over [0,1]^{s}). It is shown that the HME probability density functions can approximate the true density, at a rate of O(m^{-2/s}) in L_p norm, and at a rate of O(m^{-4/s}) in Kullback-Leibler divergence. These rates can be achieved within the family of HME structures with no more than s-layers, where s is the dimension of the predictor fx. It is also shown that likelihood-based inference based on HME is consistent in recovering the truth, in the sense that as the sample size n and the number of experts m both increase, the mean square error of the predicted mean response goes to zero. Conditions for such results to hold are stated and discussed.

Boltzmann machines are undirected graphical models with two-state stochastic variables, in which the logarithms of the clique potentials are quadratic functions of the node states. They have been widely studied in the neural computing literature, although their practical applicability has been limited by the difficulty of finding an effective learning algorithm. One well-established approach, known as mean field theory, represents the stochastic distribution using a factorized approximation. However, the corresponding learning algorithm often fails to find a good solution. We conjecture that this is due to the implicit uni-modality of the mean field approximation which is therefore unable to capture multi-modality in the true distribution. In this paper we use variational methods to approximate the stochastic distribution using multi-modal mixtures of factorized distributions. We present results for both inference and learning to demonstrate the effectiveness of this approach.

We analyze differences between two information-theoretically motivated approaches to statistical inference and model selection: the Minimum Description Length (MDL) principle, and the Minimum Message Length (MML) principle. Based on this analysis, we present two revised versions of MML: a pointwise estimator which gives the MML-optimal single parameter model, and a volumewise estimator which gives the MML-optimal region in the parameter space. Our empirical results suggest that with small data sets, the MDL approach yields more accurate predictions than the MML estimators. The empirical results also demonstrate that the revised MML estimators introduced here perform better than the original MML estimator suggested by Wallace and Freeman.

The efficiency of algorithms using secondary structures for probabilistic inference in Bayesian networks can be improved by exploiting independence relations induced by evidence and the direction of the links in the original network. In this paper we present an algorithm that on-line exploits independence relations induced by evidence and the direction of the links in the original network to reduce both time and space costs. Instead of multiplying the conditional probability distributions for the various cliques, we determine on-line which potentials to multiply when a message is to be produced. The performance improvement of the algorithm is emphasized through empirical evaluations involving large real world Bayesian networks, and we compare the method with the HUGIN and Shafer-Shenoy inference algorithms.

This paper proposes a method to find the actual state of a complex dynamic system from information coming from the sensors on the system himself, or on its environment. The nominal evolution of the system is a priori known and can be modeled (by an expert, for example), by different methods. In this paper, the Petri nets have been chosen. Contrary to the usual use of the Petri nets, the initial state of the system is unknown. So a degree of belief is bound to each places, or set of places. The theory used to model this uncertainty is the Dempster-Shafer's one which is well adapted to this type of problems. From the given Petri net characterizing the nominal evolution of the dynamic system, and from the observation inputs, the proposed method allows to determine according to the reliability of the model and the inputs, the state of the system at any time.