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Page 6803 of Mathematical Reviews Vol. , Issue 2002I [page]

2002 Mathematical Reviews  
We begin by examining the tractable cases of Boolean constraint- satisfaction problems and show that they do uniformize.  ...  ., probabilistic program) as a finite set of p-rules (i.e., probabilistic rules).  ... 

Tractable Boolean and Arithmetic Circuits [article]

Adnan Darwiche
2022 arXiv   pre-print
Tractable Boolean and arithmetic circuits have been studied extensively in AI for over two decades now.  ...  These circuits were initially proposed as "compiled objects," meant to facilitate logical and probabilistic reasoning, as they permit various types of inference to be performed in linear-time and a feed-forward  ...  We saw in the previous section how counting the models of a tractable Boolean circuit is done through the application of arithmetic operations at Boolean gates: additions at or-gates and multiplications  ... 
arXiv:2202.02942v1 fatcat:fq33u2ct4vgwngxan3k7dojxam

Intentional Communication: Computationally Easy or Difficult?

Iris van Rooij, Johan Kwisthout, Mark Blokpoel, Jakub Szymanik, Todd Wareham, Ivan Toni
2011 Frontiers in Human Neuroscience  
It is thus of importance for cognitive neuroscience to know how computationally complex intentional communication actually is.  ...  We illustrate our methodology for a model of the problems solved by receivers and senders during a communicative exchange.  ...  In Section "A Probabilistic Model of Intentional Communication," we will describe in detail the original BIP model of goal inference and our adaptations of this model in the form of a Receiver model and  ... 
doi:10.3389/fnhum.2011.00052 pmid:21747765 pmcid:PMC3129534 fatcat:hnvahy4dgbfndngzxvkllkohw4

Crucial components in probabilistic inference pipelines

Dimitar Shterionov, Gerda Janssens
2015 Proceedings of the 30th Annual ACM Symposium on Applied Computing - SAC '15  
Each probabilistic fact can be either true or false in different models of the ProbLog program.  ...  This step ignores the probabilistic information of a ProbLog program, i.e. the probability label of each probabilistic fact.  ... 
doi:10.1145/2695664.2696006 dblp:conf/sac/ShterionovJ15 fatcat:z2xoj2atkbbgrhgvebvc4ye5ru

Neural Semirings

Pedro Zuidberg Dos Martires
2021 International Workshop on Neural-Symbolic Learning and Reasoning  
Usually, the reasoning task, e.g. probabilistic reasoning or fuzzy reasoning, is fixed upfront as part of the problem specification.  ...  From an abstract algebra perspective, reasoning tasks in symbolic artificial intelligence can be formulated in terms of commutative semiring operations.  ...  In the case of the Boolean literals representing probabilistic Boolean variables, the probability semiring allows for the computation of the probability of a Boolean function being satisfied: 𝑝( ⋁ 𝐼  ... 
dblp:conf/nesy/Martires21 fatcat:jmkwhvi2b5he5lhvjx3utyxo6q

Ordering Variables for Weighted Model Integration

Vincent Derkinderen, Evert Heylen, Pedro Zuidberg Dos Martires, Samuel Kolb, Luc De Raedt
2020 Conference on Uncertainty in Artificial Intelligence  
State-of-the-art probabilistic inference algorithms, such as variable elimination and search-based approaches, rely heavily on the order in which variables are marginalized.  ...  We empirically demonstrate its performance on a set of benchmark problems.  ...  Acknowledgements This work has received support from the Research Foundation -Flanders (1SA5520N), the Special Research Fund of the KU Leuven, the European Research Council (ERC) under the European Union's  ... 
dblp:conf/uai/DerkinderenHMKR20 fatcat:xlylz3hpvnhd3dyfavt6r5j2dq

Comparing Boolean and probabilistic information retrieval systems across queries and disciplines

Robert M. Losee
1997 Journal of the American Society for Information Science  
The performance of models failing to meet statistical and other assumptions is examined.  ...  Using these performance predicting techniques, sample performance figures are provided for queries using the Boolean and and or, as well as for probabilistic systems assuming statistical term independence  ...  Statements composed of a single Boolean operator can be modeled probabilistically and compound Boolean statements can be treated as nested simpler Boolean expressions placed into CNF.  ... 
doi:10.1002/(sici)1097-4571(199702)48:2<143::aid-asi5>3.0.co;2-y fatcat:l6vk37ddvnbyppua4fkqfyhrhi

On Tractable Representations of Binary Neural Networks [article]

Weijia Shi and Andy Shih and Adnan Darwiche and Arthur Choi
2020 arXiv   pre-print
We consider the compilation of a binary neural network's decision function into tractable representations such as Ordered Binary Decision Diagrams (OBDDs) and Sentential Decision Diagrams (SDDs).  ...  First, we consider the task of verifying the robustness of a neural network, and show how we can compute the expected robustness of a neural network, given an OBDD/SDD representation of it.  ...  In general, determining whether an input of a Boolean function is unate/monotone or unused are computationally hard problems.  ... 
arXiv:2004.02082v2 fatcat:ujwdghblefe77oiczmdhuql5uy

Sparse probabilistic Boolean network problems: A partial proximal-type operator splitting method

Kangkang Deng, Zheng Peng, Jianli Chen
2017 Journal of Industrial and Management Optimization  
The sparse probabilistic Boolean network (SPBN) model has been applied in various fields of industrial engineering and management.  ...  In this paper, a partial proximal-type operator splitting method is proposed to solve a separable minimization problem arising from the study of the SPBN model.  ...  The first version of this work was completed during the second author visiting Prof. Y-H Dai of Academy of Mathematics and Systems Science, Chinese Academy of Sciences.  ... 
doi:10.3934/jimo.2018127 fatcat:z4gswfgph5bedj6vxsw3ny2ey4

Compacting Boolean Formulae for Inference in Probabilistic Logic Programming [chapter]

Theofrastos Mantadelis, Dimitar Shterionov, Gerda Janssens
2015 Lecture Notes in Computer Science  
Knowledge compilation converts Boolean formulae for which some inference tasks are computationally expensive into a representation where the same tasks are tractable.  ...  ProbLog is a state-of-the-art Probabilistic Logic Programming system that uses knowledge compilation to reduce the expensive probabilistic inference to an efficient weighted model counting.  ...  In the context of ProbLog we preserve the weighted model count of the Boolean formulae.  ... 
doi:10.1007/978-3-319-23264-5_35 fatcat:4ku2u2zoxfdkflvyxon2z55yyi

Probabilistic Model Checking Modulo Theories

Bjorn Wachter, Lijun Zhang, Holger Hermanns
2007 Fourth International Conference on the Quantitative Evaluation of Systems (QEST 2007)  
To the best of our knowledge, this is the first time that properties of probabilistic infinite-state models have been verified at this level of automation.  ...  We leverage recent advances in automatic theorem proving to compute tractable finite-state models. Experiments show the feasibility of our approach.  ...  To simplify the presentation, we don't consider nested probabilistic operators.  ... 
doi:10.1109/qest.2007.10 dblp:conf/qest/WachterZH07 fatcat:vy2l2ve6urdwrlcbdsh2oulvou

Mathematical, logical, and formal methods in information retrieval: An introduction to the special issue

Fabio Crestani, Sandor Dominich, Mounia Lalmas, Cornelis Joost (Keith) van Rijsbergen
2003 Journal of the American Society for Information Science and Technology  
In this article we outline some of the major aspects of the subject, and summarise the papers of this special issue with respect to how they relate to these aspects.  ...  We conclude highlighting some directions of future research, which are needed in order to better understand the formal characteristics of Information Retrieval.  ...  In addition, they provide useful practical viewpoints and arguments to building computationally more secure and efficient operational retrieval systems.  ... 
doi:10.1002/asi.10208 fatcat:chbsjnf2ufa6jpmjrr67pw2eta

Most probable explanations in Bayesian networks: Complexity and tractability

Johan Kwisthout
2011 International Journal of Approximate Reasoning  
One of the key computational problems in Bayesian networks is computing the maximal posterior probability of a set of variables in the network, given an observation of the values of another set of variables  ...  In this paper, we give an overview of the computational complexity of many problem variants, including enumeration variants, parameterized problems, and approximation strategies to the MPE-problem with  ...  Acknowledgements The author is supported by the OCTOPUS project under the responsibility of the Embedded Systems Institute.  ... 
doi:10.1016/j.ijar.2011.08.003 fatcat:iz6p52e2jva2pdipnnjd54o65e

Look Ma, No Latent Variables: Accurate Cutset Networks via Compilation

Tahrima Rahman, Shasha Jin, Vibhav Gogate
2019 International Conference on Machine Learning  
Tractable probabilistic models obviate the need for unreliable approximate inference approaches and as a result often yield accurate query answers in practice.  ...  However, most tractable models that achieve state-of-the-art generalization performance (measured using test set likelihood score) use latent variables.  ...  Any opinions, findings, conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views or official policies, either expressed or implied, of DARPA  ... 
dblp:conf/icml/RahmanJG19 fatcat:fy3nh5ntgrgmhbgljoopdsqu54

Parallel Probabilistic Inference by Weighted Model Counting

Giso H. Dal, Alfons W. Laarman, Peter J. F. Lucas
2018 European Workshop on Probabilistic Graphical Models  
Knowledge compilation as part of the Weighted Model Counting approach has proven to be an efficient tool for exact inference in probabilistic graphical models, by exploiting structures that more traditional  ...  In this paper, we explore the possibilities for Weighted Model Counting.  ...  The compilation step in WMC is computationally intensive, and thus, that is where one finds most tractability issues.  ... 
dblp:conf/pgm/DalLL18 fatcat:hw7x77yrt5dw7pzz4dopqnaokm
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