The Generalized A* Architecture

We consider the problem of computing a lightest derivation of a global structure using a set of weighted rules. A large variety of inference problems in AI can be formulated in this framework. We generalize A* search and heuristics derived from abstractions to a broad class of lightest derivation problems. We also describe a new algorithm that searches for lightest derivations using a hierarchy of abstractions. Our generalization of A* gives a new algorithm for searching AND/OR graphs in a bottom-up fashion. We discuss how the algorithms described here provide a general architecture for addressing the pipeline problem --- the problem of passing information back and forth between various stages of processing in a perceptual system. We consider examples in computer vision and natural language processing. We apply the hierarchical search algorithm to the problem of estimating the boundaries of convex objects in grayscale images and compare it to other search methods. A second set of experiments demonstrate the use of a new compositional model for finding salient curves in images

PAC-Bayesian Bounds for Randomized Empirical Risk Minimizers

The aim of this paper is to generalize the PAC-Bayesian theorems proved by Catoni in the classification setting to more general problems of statistical inference. We show how to control the deviations of the risk of randomized estimators. A particular attention is paid to randomized estimators drawn in a small neighborhood of classical estimators, whose study leads to control the risk of the latter. These results allow to bound the risk of very general estimation procedures, as well as to perform model selection

Three Cuts for Accelerated Interval Propagation

This paper addresses the problem of nonlinear multivariate root finding. In an earlier paper we described a system called Newton which finds roots of systems of nonlinear equations using refinements of interval methods. The refinements are inspired by AI constraint propagation techniques. Newton is competative with continuation methods on most benchmarks and can handle a variety of cases that are infeasible for continuation methods. This paper presents three "cuts" which we believe capture the essential theoretical ideas behind the success of Newton. This paper describes the cuts in a concise and abstract manner which, we believe, makes the theoretical content of our work more apparent. Any implementation will need to adopt some heuristic control mechanism. Heuristic control of the cuts is only briefly discussed here

Random-World Semantics and Syntactic Independence for Expressive Languages

We consider three desiderata for a language combining logic and probability: logical expressivity, random-world semantics, and the existence of a useful syntactic condition for probabilistic independence. Achieving these three desiderata simultaneously is nontrivial. Expressivity can be achieved by using a formalism similar to a programming language, but standard approaches to combining programming languages with probabilities sacrifice random-world semantics. Naive approaches to restoring random-world semantics undermine syntactic independence criteria. Our main result is a syntactic independence criterion that holds for a broad class of highly expressive logics under random-world semantics. We explore various examples including Bayesian networks, probabilistic context-free grammars, and an example from Mendelian genetics. Our independence criterion supports a case-factor inference technique that reproduces both variable elimination for BNs and the inside algorithm for PCFGs

Generalization Error in Deep Learning

Deep learning models have lately shown great performance in various fields such as computer vision, speech recognition, speech translation, and natural language processing. However, alongside their state-of-the-art performance, it is still generally unclear what is the source of their generalization ability. Thus, an important question is what makes deep neural networks able to generalize well from the training set to new data. In this article, we provide an overview of the existing theory and bounds for the characterization of the generalization error of deep neural networks, combining both classical and more recent theoretical and empirical results

Colouring random graphs and maximising local diversity

We study a variation of the graph colouring problem on random graphs of finite average connectivity. Given the number of colours, we aim to maximise the number of different colours at neighbouring vertices (i.e. one edge distance) of any vertex. Two efficient algorithms, belief propagation and Walksat are adapted to carry out this task. We present experimental results based on two types of random graphs for different system sizes and identify the critical value of the connectivity for the algorithms to find a perfect solution. The problem and the suggested algorithms have practical relevance since various applications, such as distributed storage, can be mapped onto this problem.Comment: 10 pages, 10 figure

Imunomodulacija i oksidativni stres u radnika u pjeskarenju traper platna: promjene uzrokovane izloženosti silici

Workers in denim sandblasting are at a high risk of developing silicosis, an occupational lung disease caused by inhaling crystalline silica dust. The development and progress of silicosis is associated with the activation of the immune system and oxidative stress. In the former, interferon-gamma induces both neopterin release and the enzyme indoleamine [2,3]-dioxygenase (IDO) in various cells. The determination of the kynurenine-to-tryptophan ratio and neopterin concentration has proven to be an efficient method to monitor the activation status of IDO and cellular immunity. The present study aimed to investigate whether occupational silica exposure leads to any alterations in neopterin levels, tryptophan degradation, and activities of superoxide dismutase (SOD) and catalase (CAT), agents in the antioxidant defence system. Fifty-five male denim sandblasting workers and twenty-two healthy men as controls were included. Mean neopterin and kynurenine levels, kynurenine-to-tryptophan ratio, and SOD activity were higher in subjects with silicosis compared to non-exposed controls (all, p<0.05). Neopterin levels and kynurenine-totryptophan ratios were positively correlated (p<0.05); however, no correlation was observed between length of employment and the measured parameters. Some of the measured parameters were significantly affected by the severity of the pathology. Our results suggest that silica exposure activates the cellular immune response. The increased neopterin levels and tryptophan degradation confirm the possibility of their use as an indicator of cellular immune response.Radnici u pjeskarenju traper platna izloženi su visokom riziku od silikoze, profesionalne plućne bolesti uzrokovane udisanjem čestica silikatne prašine. Razvoj i progresija silikoze povezani su s aktivacijom imunosnog sustava i oksidativnim stresom. Pri aktivaciji imunosnoga sustava, interferon-gama potiče otpuštanje neopterina i enzima indoleamina [2, 3]-dioksigenaze (IDO) u različitim vrstama stanica. Određivanje omjera kinurenina i triptofana te koncentracije neopterina pokazale su se učinkovitim metodama praćenja aktivacijskoga statusa IDO-a i staničnog imuniteta. Ovaj rad istražuje uzrokuje li profesionalna izloženost silici promjene u razinama neopterina, degradaciji triptofana i aktivnosti superoksid dismutaze (SOD) i katalaze (CAT), agenata u antioksidativnom obrambenom sustavu. U istraživanju je sudjelovalo 55 muških radnika u pjeskarenju traper platna i 22 zdrava muškarca u kontrolnoj skupini. Srednje vrijednosti razina neopterina i kinurenina, omjera kinurenina i triptofana, te aktivnosti SOD-a bile su više u radnika oboljelih od silikoze nego u kontrolnoj skupini (p<0,05). Razina neopterina i omjer kinurenina i triptofana bile su u pozitivnoj korelaciji (p<0,05). Međutim, korelacija nije uočena između mjerenih vrijednosti i radnog staža. Neke od mjerenih vrijednosti bitno su ovisile o težini patologije. Dobiveni rezultati daju naslutiti da izloženost silici uzrokuje aktivaciju staničnog imunosnog odgovora. Povećane razine neopterina i degradacije triptofana potvrđuju mogućnost njihova korištenja kao pokazatelja staničnog imunosnog odgovora

A system of relational syllogistic incorporating full Boolean reasoning

We present a system of relational syllogistic, based on classical propositional logic, having primitives of the following form: Some A are R-related to some B; Some A are R-related to all B; All A are R-related to some B; All A are R-related to all B. Such primitives formalize sentences from natural language like `All students read some textbooks'. Here A and B denote arbitrary sets (of objects), and R denotes an arbitrary binary relation between objects. The language of the logic contains only variables denoting sets, determining the class of set terms, and variables denoting binary relations between objects, determining the class of relational terms. Both classes of terms are closed under the standard Boolean operations. The set of relational terms is also closed under taking the converse of a relation. The results of the paper are the completeness theorem with respect to the intended semantics and the computational complexity of the satisfiability problem.Comment: Available at http://link.springer.com/article/10.1007/s10849-012-9165-