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Journal articles on the topic 'Belief approximation'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

Leike, Reimar, and Torsten Enßlin. "Optimal Belief Approximation." Entropy 19, no. 8 (2017): 402. http://dx.doi.org/10.3390/e19080402.

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Guo, Yuanzhen, Hao Xiong, and Nicholas Ruozzi. "Marginal Inference in Continuous Markov Random Fields Using Mixtures." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 7834–41. http://dx.doi.org/10.1609/aaai.v33i01.33017834.

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Exact marginal inference in continuous graphical models is computationally challenging outside of a few special cases. Existing work on approximate inference has focused on approximately computing the messages as part of the loopy belief propagation algorithm either via sampling methods or moment matching relaxations. In this work, we present an alternative family of approximations that, instead of approximating the messages, approximates the beliefs in the continuous Bethe free energy using mixture distributions. We show that these types of approximations can be combined with numerical quadra

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WEILER, THOMAS. "APPROXIMATION OF BELIEF FUNCTIONS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 11, no. 06 (2003): 749–77. http://dx.doi.org/10.1142/s021848850300251x.

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This paper addresses the approximation of belief functions by probability functions where the approximation is based on minimizing the Euclidean distance. First of all, we simplify this optimization problem so it becomes equivalent to a standard problem in linear algebra. For the simplified optimization problem, we provide the analytic solution. Furthermore, we show that for Dempster-Shafer belief the simplified optimization problem is equivalent to the original one. In terms of semantics, we compare the approximation of belief functions to various alternative approaches, e.g. pignistic transf

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Zhang, Yan-Lan, and Chang-Qing Li. "Interpretations of belief functions in approximation operators by covering." Journal of Intelligent & Fuzzy Systems 41, no. 6 (2021): 5903–13. http://dx.doi.org/10.3233/jifs-201887.

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The rough set theory and the evidence theory are two important methods used to deal with uncertainty. The relationships between the rough set theory and the evidence theory have been discussed. In covering rough set theory, several pairs of covering approximation operators are characterized by belief and plausibility functions. The purpose of this paper is to review and examine interpretations of belief functions in covering approximation operators. Firstly, properties of the belief structures induced by two pairs of covering approximation operators are presented. Then, for a belief structure

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Gormley, Matthew R., Mark Dredze, and Jason Eisner. "Approximation-Aware Dependency Parsing by Belief Propagation." Transactions of the Association for Computational Linguistics 3 (December 2015): 489–501. http://dx.doi.org/10.1162/tacl_a_00153.

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We show how to train the fast dependency parser of Smith and Eisner (2008) for improved accuracy. This parser can consider higher-order interactions among edges while retaining O( n3) runtime. It outputs the parse with maximum expected recall—but for speed, this expectation is taken under a posterior distribution that is constructed only approximately, using loopy belief propagation through structured factors. We show how to adjust the model parameters to compensate for the errors introduced by this approximation, by following the gradient of the actual loss on training data. We find this grad

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Bhattacharyya, C., and S. S. Keerthi. "Mean Field Methods for a Special Class of Belief Networks." Journal of Artificial Intelligence Research 15 (August 1, 2001): 91–114. http://dx.doi.org/10.1613/jair.734.

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The chief aim of this paper is to propose mean-field approximations for a broad class of Belief networks, of which sigmoid and noisy-or networks can be seen as special cases. The approximations are based on a powerful mean-field theory suggested by Plefka. We show that Saul, Jaakkola and Jordan' s approach is the first order approximation in Plefka's approach, via a variational derivation. The application of Plefka's theory to belief networks is not computationally tractable. To tackle this problem we propose new approximations based on Taylor series. Small scale experiments show that the prop

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Straszak, Damian, and Nisheeth K. Vishnoi. "Belief Propagation, Bethe Approximation and Polynomials." IEEE Transactions on Information Theory 65, no. 7 (2019): 4353–63. http://dx.doi.org/10.1109/tit.2019.2901854.

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Cevolani, G. "Truth approximation via abductive belief change." Logic Journal of IGPL 21, no. 6 (2013): 999–1016. http://dx.doi.org/10.1093/jigpal/jzt010.

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Schwöbel, Sarah, Stefan Kiebel, and Dimitrije Marković. "Active Inference, Belief Propagation, and the Bethe Approximation." Neural Computation 30, no. 9 (2018): 2530–67. http://dx.doi.org/10.1162/neco_a_01108.

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When modeling goal-directed behavior in the presence of various sources of uncertainty, planning can be described as an inference process. A solution to the problem of planning as inference was previously proposed in the active inference framework in the form of an approximate inference scheme based on variational free energy. However, this approximate scheme was based on the mean-field approximation, which assumes statistical independence of hidden variables and is known to show overconfidence and may converge to local minima of the free energy. To better capture the spatiotemporal properties

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Cevolani, Gustavo. "Truth approximation, belief merging, and peer disagreement." Synthese 191, no. 11 (2014): 2383–401. http://dx.doi.org/10.1007/s11229-014-0486-2.

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Lim, Michael H., Tyler J. Becker, Mykel J. Kochenderfer, Claire J. Tomlin, and Zachary N. Sunberg. "Optimality Guarantees for Particle Belief Approximation of POMDPs." Journal of Artificial Intelligence Research 77 (August 27, 2023): 1591–636. http://dx.doi.org/10.1613/jair.1.14525.

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Partially observable Markov decision processes (POMDPs) provide a flexible representation for real-world decision and control problems. However, POMDPs are notoriously difficult to solve, especially when the state and observation spaces are continuous or hybrid, which is often the case for physical systems. While recent online sampling-based POMDP algorithms that plan with observation likelihood weighting have shown practical effectiveness, a general theory characterizing the approximation error of the particle filtering techniques that these algorithms use has not previously been proposed. Ou

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Syau, Yu-Ru, En-Bing Lin, and Churn-Jung Liau. "An Order-Theoretic Study on Formal Concept Analysis." Axioms 12, no. 12 (2023): 1099. http://dx.doi.org/10.3390/axioms12121099.

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This paper employs an order-theoretic framework to explore the intricacies of formal concepts. Initially, we establish a natural correspondence among formal contexts, preorders, and the resulting partially ordered sets (posets). Leveraging this foundation, we provide insightful characterizations of atoms and coatoms within finite concept lattices, drawing upon object intents. Expanding from the induced poset originating from a formal context, we extend these characterizations to discern join-irreducible and meet-irreducible elements within finite concept lattices. Contrary to a longstanding mi

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Bonet, B., and H. Geffner. "Belief Tracking for Planning with Sensing: Width, Complexity and Approximations." Journal of Artificial Intelligence Research 50 (August 31, 2014): 923–70. http://dx.doi.org/10.1613/jair.4475.

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We consider the problem of belief tracking in a planning setting where states are valuations over a set of variables that are partially observable, and beliefs stand for the sets of states that are possible. While the problem is intractable in the worst case, it has been recently shown that in deterministic conformant and contingent problems, belief tracking is exponential in a width parameter that is often bounded and small. In this work, we extend these results in two ways. First, we introduce a width notion that applies to non-deterministic problems as well, develop a factored belief tracki

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DENŒUX, THIERRY. "INNER AND OUTER APPROXIMATION OF BELIEF STRUCTURES USING A HIERARCHICAL CLUSTERING APPROACH." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 09, no. 04 (2001): 437–60. http://dx.doi.org/10.1142/s0218488501000880.

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A hierarchical clustering approach is proposed for reducing the number of focal elements in a crisp or fuzzy belief function, yielding strong inner and outer approximations. At each step of the proposed algorithm, two focal elements are merged, and the mass is transfered to their intersection or their union. The resulting approximations allow the calculation of lower and upper bounds on the belief and plausibility degrees induced by the conjunctive or disjunctive sum of any number of belief structures. Numerical experiments demonstrate the effectiveness of this approach.

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Emanuel, Amber S., Cristina A. Godinho, Christopher Steinman, and John A. Updegraff. "Education differences in cancer fatalism: The role of information-seeking experiences." Journal of Health Psychology 23, no. 12 (2016): 1533–44. http://dx.doi.org/10.1177/1359105316664129.

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Cancer fatalism is the belief that cancer is uncontrollable and lethal. Individuals with less education are more likely to hold fatalistic beliefs about cancer, but the mechanism accounting for the relationship is unknown. We tested whether negative health information seeking experiences explain this relationship. Structural equation modeling was used to test this relationship across three datasets from the Health Information National Trends Survey. Across all datasets, the model showed good fit: Cycle 1 (coefficient of determination = .11, comparative fit index = .96, root mean square error o

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Haenni, Rolf, and Norbert Lehmann. "Resource bounded and anytime approximation of belief function computations." International Journal of Approximate Reasoning 31, no. 1-2 (2002): 103–54. http://dx.doi.org/10.1016/s0888-613x(02)00074-9.

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Golovko, Nikita V. "LAURENCE BONJOURS’S COHERENTISM, INTERNALISM AND EPISTEMIC BASING RELATION." Vestnik Tomskogo gosudarstvennogo universiteta. Filosofiya, sotsiologiya, politologiya, no. 82 (2024): 30–43. https://doi.org/10.17223/1998863x/82/3.

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The article aims to show that Laurence BonJour’s theory of coherentist justification of empirical knowledge can be reconciled with the concept of doxastic epistemic basing relation (R. Audi, R. Fumerton, H. Longino), which will allow responding to Alan Goldman’s claim that “coherence within BonJour’s theory is neither a necessary nor a sufficient condition of knowledge”. The main emphasis is placed on the fact that an attempt to speak about justification only in terms of beliefs, reasons and basing relation, at least as at first approximation, is devoid of the need to appeal to any predetermin

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18

Roy, N., G. Gordon, and S. Thrun. "Finding Approximate POMDP solutions Through Belief Compression." Journal of Artificial Intelligence Research 23 (January 1, 2005): 1–40. http://dx.doi.org/10.1613/jair.1496.

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Standard value function approaches to finding policies for Partially Observable Markov Decision Processes (POMDPs) are generally considered to be intractable for large models. The intractability of these algorithms is to a large extent a consequence of computing an exact, optimal policy over the entire belief space. However, in real-world POMDP problems, computing the optimal policy for the full belief space is often unnecessary for good control even for problems with complicated policy classes. The beliefs experienced by the controller often lie near a structured, low-dimensional subspace emb

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19

Saul, L. K., T. Jaakkola, and M. I. Jordan. "Mean Field Theory for Sigmoid Belief Networks." Journal of Artificial Intelligence Research 4 (March 1, 1996): 61–76. http://dx.doi.org/10.1613/jair.251.

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We develop a mean field theory for sigmoid belief networks based on ideas from statistical mechanics. Our mean field theory provides a tractable approximation to the true probability distribution in these networks; it also yields a lower bound on the likelihood of evidence. We demonstrate the utility of this framework on a benchmark problem in statistical pattern recognition---the classification of handwritten digits.

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Pakzad, Payam, and Venkat Anantharam. "Estimation and Marginalization Using the Kikuchi Approximation Methods." Neural Computation 17, no. 8 (2005): 1836–73. http://dx.doi.org/10.1162/0899766054026693.

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In this letter, we examine a general method of approximation, known as the Kikuchi approximation method, for finding the marginals of a product distribution, as well as the corresponding partition function. The Kikuchi approximation method defines a certain constrained optimization problem, called the Kikuchi problem, and treats its stationary points as approximations to the desired marginals. We show how to associate a graph to any Kikuchi problem and describe a class of local message-passing algorithms along the edges of any such graph, which attempt to find the solutions to the problem. Imp

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21

Ma, Chuang, Xiao-Long Yang, Han-Shuang Chen, and Hai-Feng Zhang. "A mean-field approximation based BP algorithm for solving the stochastic block model." Acta Physica Sinica 70, no. 22 (2021): 228901. http://dx.doi.org/10.7498/aps.70.20210511.

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As a mainstream algorithm for inferring probabilistic graphical models, belief propagation (BP) algorithm is one of the most important methods to solve the joint probability distribution in the stochastic block model. However, existing methods either lead to low accuracy in dealing with the core-periphery structure problem, or the theoretical derivation is difficult to understand due to a large number of approximation, or both exist. Of course, the reason for low accuracy comes from too many approximations. The main reason for many approximations and complex theoretical derivation is that the

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22

Yan, Minlun. "Multigranulations Rough Set Method of Attribute Reduction in Information Systems Based on Evidence Theory." Journal of Applied Mathematics 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/857186.

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Attribute reduction is one of the most important problems in rough set theory. However, from the granular computing point of view, the classical rough set theory is based on a single granulation. It is necessary to study the issue of attribute reduction based on multigranulations rough set. To acquire brief decision rules from information systems, this paper firstly investigates attribute reductions by combining the multigranulations rough set together with evidence theory. Concepts of belief and plausibility consistent set are proposed, and some important properties are addressed by the view

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23

Galesloot, Maris F. L., Thiago D. Simão, Sebastian Junges, and Nils Jansen. "Factored Online Planning in Many-Agent POMDPs." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 16 (2024): 17407–15. http://dx.doi.org/10.1609/aaai.v38i16.29689.

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In centralized multi-agent systems, often modeled as multi-agent partially observable Markov decision processes (MPOMDPs), the action and observation spaces grow exponentially with the number of agents, making the value and belief estimation of single-agent online planning ineffective. Prior work partially tackles value estimation by exploiting the inherent structure of multi-agent settings via so-called coordination graphs. Additionally, belief estimation methods have been improved by incorporating the likelihood of observations into the approximation. However, the challenges of value estimat

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24

Le Roux, Nicolas, and Yoshua Bengio. "Deep Belief Networks Are Compact Universal Approximators." Neural Computation 22, no. 8 (2010): 2192–207. http://dx.doi.org/10.1162/neco.2010.08-09-1081.

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Deep belief networks (DBN) are generative models with many layers of hidden causal variables, recently introduced by Hinton, Osindero, and Teh ( 2006 ), along with a greedy layer-wise unsupervised learning algorithm. Building on Le Roux and Bengio ( 2008 ) and Sutskever and Hinton ( 2008 ), we show that deep but narrow generative networks do not require more parameters than shallow ones to achieve universal approximation. Exploiting the proof technique, we prove that deep but narrow feedforward neural networks with sigmoidal units can represent any Boolean expression.

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Ghufron, M. Nur, Rini Risnawita Suminta, and Jamaludin Hadi Kusuma. "Knowledge and Learning of Interreligious and Intercultural Understanding in an Indonesian Islamic College Sample: An Epistemological Belief Approach." Religions 11, no. 8 (2020): 411. http://dx.doi.org/10.3390/rel11080411.

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Epistemological beliefs are the basis of how someone acquires knowledge and are used as a guide for behavior in everyday life. For religious fundamentalists, however, their belief in religious knowledge is very strong, causing them to negate different opinions and ideas. Since the radicalization process is closely related to the education process, two important epistemological concepts of belief about knowledge and belief about learning need to be tested to analyze the extent to which these two factors might be predictors of an individual’s tendency towards religious fundamentalism. The purpos

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Montúfar, Guido F. "Universal Approximation Depth and Errors of Narrow Belief Networks with Discrete Units." Neural Computation 26, no. 7 (2014): 1386–407. http://dx.doi.org/10.1162/neco_a_00601.

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We generalize recent theoretical work on the minimal number of layers of narrow deep belief networks that can approximate any probability distribution on the states of their visible units arbitrarily well. We relax the setting of binary units (Sutskever & Hinton, 2008 ; Le Roux & Bengio, 2008 , 2010 ; Montúfar & Ay, 2011 ) to units with arbitrary finite state spaces and the vanishing approximation error to an arbitrary approximation error tolerance. For example, we show that a q-ary deep belief network with [Formula: see text] layers of width [Formula: see text] for some [Formula:

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DESTERCKE, SEBASTIEN, DIDIER DUBOIS, and ERIC CHOJNACKI. "A CONSONANT APPROXIMATION OF THE PRODUCT OF INDEPENDENT CONSONANT RANDOM SETS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 17, no. 06 (2009): 773–92. http://dx.doi.org/10.1142/s0218488509006261.

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The belief structure resulting from the combination of consonant and independent marginal random sets is not, in general, consonant. Also, the complexity of such a structure grows exponentially with the number of combined random sets, making it quickly intractable for computations. In this paper, we propose a simple guaranteed consonant outer approximation of this structure. The complexity of this outer approximation does not increase with the number of marginal random sets (i.e., of dimensions), making it easier to handle in uncertainty propagation. Features and advantages of this outer appro

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Downton, Jonathan E., and Charles Ursenbach. "Linearized amplitude variation with offset (AVO) inversion with supercritical angles." GEOPHYSICS 71, no. 5 (2006): E49—E55. http://dx.doi.org/10.1190/1.2227617.

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Contrary to popular belief, a linearized approximation of the Zoeppritz equations may be used to estimate the reflection coefficient for angles of incidence up to and beyond the critical angle. These supercritical reflection coefficients are complex, implying a phase variation with offset in addition to amplitude variation with offset (AVO). This linearized approximation is then used as the basis for an AVO waveform inversion. By incorporating this new approximation, wider offset and angle data may be incorporated in the AVO inversion, helping to stabilize the problem and leading to more accur

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Chen, Yu-Wang, Jian-Bo Yang, Dong-Ling Xu, and Shan-Lin Yang. "On the inference and approximation properties of belief rule based systems." Information Sciences 234 (June 2013): 121–35. http://dx.doi.org/10.1016/j.ins.2013.01.022.

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Yang, Yi, and Yuanli Liu. "Iterative Approximation of Basic Belief Assignment Based on Distance of Evidence." PLOS ONE 11, no. 2 (2016): e0147799. http://dx.doi.org/10.1371/journal.pone.0147799.

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Zhang, Shao-Pu, Pin Sun, Ju-Sheng Mi, and Tao Feng. "Belief function of Pythagorean fuzzy rough approximation space and its applications." International Journal of Approximate Reasoning 119 (April 2020): 58–80. http://dx.doi.org/10.1016/j.ijar.2020.01.001.

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32

Chavez, R. Martin, and Gregory F. Cooper. "A randomized approximation algorithm for probabilistic inference on bayesian belief networks." Networks 20, no. 5 (1990): 661–85. http://dx.doi.org/10.1002/net.3230200510.

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Ghosal, S. K., K. K. Nandi, and Papia Chakraborty. "Passage from Einsteinian to Galilean Relativity and Clock Synchrony." Zeitschrift für Naturforschung A 46, no. 3 (1991): 256–58. http://dx.doi.org/10.1515/zna-1991-0307.

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AbstractThere is a general belief that under small velocity approximation. Special Relativity goes over into Galilean Relativity. Should this be interpreted exclusively in terms of the kinematical symmetry transformations (Lorentz vs. Galilei) a misconception could easily arise that would stem from overlooking the role of conventionality ingredients of Special Relativity Theory. It is observed that the small velocity approximation cannot alter the convention of distant simultaneity. In order to exemplify this point further, the Lorentz transformations are critically compared, under the same ap

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Riegler, Erwin, Gunvor Elisabeth Kirkelund, Carles Navarro Manchon, Mihai-Alin Badiu, and Bernard Henri Fleury. "Merging Belief Propagation and the Mean Field Approximation: A Free Energy Approach." IEEE Transactions on Information Theory 59, no. 1 (2013): 588–602. http://dx.doi.org/10.1109/tit.2012.2218573.

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Albrecht, Stefano V., and Subramanian Ramamoorthy. "Exploiting Causality for Selective Belief Filtering in Dynamic Bayesian Networks." Journal of Artificial Intelligence Research 55 (April 28, 2016): 1135–78. http://dx.doi.org/10.1613/jair.5044.

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Dynamic Bayesian networks (DBNs) are a general model for stochastic processes with partially observed states. Belief filtering in DBNs is the task of inferring the belief state (i.e. the probability distribution over process states) based on incomplete and noisy observations. This can be a hard problem in complex processes with large state spaces. In this article, we explore the idea of accelerating the filtering task by automatically exploiting causality in the process. We consider a specific type of causal relation, called passivity, which pertains to how state variables cause changes in oth

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PENG, YUN, and MIAO JIN. "A NEURAL NETWORK APPROACH TO APPROXIMATING MAP IN BELIEF NETWORKS." International Journal of Neural Systems 12, no. 03n04 (2002): 271–90. http://dx.doi.org/10.1142/s0129065702001175.

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Bayesian belief networks (BBN) are a widely studied graphical model for representing uncertainty and probabilistic interdependence among variables. One of the factors that restricts the model's wide acceptance in practical applications is that the general inference with BBN is NP-hard. This is also true for the maximum a posteriori probability (MAP) problem, which is to find the most probable joint value assignment to all uninstantiated variables, given instantiation of some variables in a BBN . To circumvent the difficulty caused by MAP's computational complexity, we suggest in this paper a n

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Wakui, Tomoko, Kentaro Watanabe, Hiroyasu Miwa, and Sakiko Itoh. "DEVELOPMENT OF THE TECHNOLOGY INTEGRATION BELIEF INDEX FOR FAMILY CAREGIVERS." Innovation in Aging 8, Supplement_1 (2024): 1104–5. https://doi.org/10.1093/geroni/igae098.3547.

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Abstract In highly aged societies, the technology integration into community care settings is promoted. Despite this, real-world adoption faces hurdles because of the common belief that care provided by humans is inherently superior. This gap highlights the absence of specific measures to assess this belief. This study aims to develop the Technology Integration Belief Index for Family Caregivers (TIBI-FC), which evaluates family caregivers’ attitudes towards technology use in long-term care. We conducted a survey with 2,002 family caregivers of older adults living in the community, selected in

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Lim, Seung-Chan, and Hyuncheol Park. "Gaussian Approximation-Based Belief Propagation Receiver for Uplink SCMA Systems With Imperfect CSIR." IEEE Communications Letters 22, no. 12 (2018): 2611–14. http://dx.doi.org/10.1109/lcomm.2018.2874441.

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Montufar, Guido, and Nihat Ay. "Refinements of Universal Approximation Results for Deep Belief Networks and Restricted Boltzmann Machines." Neural Computation 23, no. 5 (2011): 1306–19. http://dx.doi.org/10.1162/neco_a_00113.

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We improve recently published results about resources of restricted Boltzmann machines (RBM) and deep belief networks (DBN) required to make them universal approximators. We show that any distribution [Formula: see text] on the set [Formula: see text] of binary vectors of length [Formula: see text] can be arbitrarily well approximated by an RBM with [Formula: see text] hidden units, where [Formula: see text] is the minimal number of pairs of binary vectors differing in only one entry such that their union contains the support set of [Formula: see text]. In important cases this number is half t

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Yoo, Yongseok, and Sriram Vishwanath. "On Resolving Simultaneous Congruences Using Belief Propagation." Neural Computation 27, no. 3 (2015): 748–70. http://dx.doi.org/10.1162/neco_a_00702.

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Graphical models and related algorithmic tools such as belief propagation have proven to be useful tools in (approximately) solving combinatorial optimization problems across many application domains. A particularly combinatorially challenging problem is that of determining solutions to a set of simultaneous congruences. Specifically, a continuous source is encoded into multiple residues with respect to distinct moduli, and the goal is to recover the source efficiently from noisy measurements of these residues. This problem is of interest in multiple disciplines, including neural codes, decent

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Parks, Beth, and Hans Benze. "Visualizing Double-Slit Interference on a Shoestring." Physics Teacher 60, no. 5 (2022): 338–39. http://dx.doi.org/10.1119/5.0050803.

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Student misconceptions of the double-slit experiment (Fig. 1) are abundant. The most common ones that we observe include: (1) belief that constructive interference requires both pathlengths to be integer multiples of the wavelength (“ L1 = n1λ” and “ L2 = n2λ”) rather than only the pathlength difference (Δ L ≡ | L1 – L2| = nλ); (2) failure to understand that the justification for d sin θ = nλ is that d sin θ is a good approximation to Δ L; (3) confusion about the limits in which the approximation d sin θ = nλ is valid; and (4) confusion about the limits in which the approximation sin θ = tan θ

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Theocharous, Georgios, and Sridhar Mahadevan. "Compressing POMDPs Using Locality Preserving Non-Negative Matrix Factorization." Proceedings of the AAAI Conference on Artificial Intelligence 24, no. 1 (2010): 1147–52. http://dx.doi.org/10.1609/aaai.v24i1.7750.

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Partially Observable Markov Decision Processes (POMDPs) are a well-established and rigorous framework for sequential decision-making under uncertainty. POMDPs are well-known to be intractable to solve exactly, and there has been significant work on finding tractable approximation methods. One well-studied approach is to find a compression of the original POMDP by projecting the belief states to a lower-dimensional space. We present a novel dimensionality reduction method for POMDPs based on locality preserving non-negative matrix factorization. Unlike previous approaches, such as Krylov compre

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Mooij, J. M., and H. J. Kappen. "On the properties of the Bethe approximation and loopy belief propagation on binary networks." Journal of Statistical Mechanics: Theory and Experiment 2005, no. 11 (2005): P11012. http://dx.doi.org/10.1088/1742-5468/2005/11/p11012.

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Vatta, F., A. Soranzo, and F. Babich. "Low‐complexity bound on irregular LDPC belief‐propagation decoding thresholds using a Gaussian approximation." Electronics Letters 54, no. 17 (2018): 1038–40. http://dx.doi.org/10.1049/el.2018.0478.

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Kuipers, Theo A. F. "Basic and Refined Nomic Truth Approximation by Evidence-Guided Belief Revision in AGM-Terms." Erkenntnis 75, no. 2 (2011): 223–36. http://dx.doi.org/10.1007/s10670-011-9292-0.

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Klein, John, Sebastien Destercke, and Olivier Colot. "Interpreting evidential distances by connecting them to partial orders: Application to belief function approximation." International Journal of Approximate Reasoning 71 (April 2016): 15–33. http://dx.doi.org/10.1016/j.ijar.2016.01.001.

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Luckraz, Shravan. "Two Remarks on the Infinite Approximation of a Finite World in Economic Models." Journal of Mathematics 2022 (January 17, 2022): 1–5. http://dx.doi.org/10.1155/2022/2457746.

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While the assumption of infinity is prevalent in almost every area of economics, for two well-known frameworks in decision theory, we note some fundamental differences between the finite versions and their infinite counterpart. The first is on the usage of mixed strategies in finite games, while the second is on a characterization of the truth axiom in models of information and knowledge, where the properties of belief can be related to the properties of preference.

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SONG, Unsok. "Written Records and Artistic Expressions of the Belief in Silla as a Buddha-land." Tae Dong Institute of classic research 54 (June 30, 2025): 9–46. https://doi.org/10.31408/tdicr.2025.54.9.

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This study examines the Belief in Silla as a Buddha-land, deeply rooted in the foundation of Silla's Buddhist beliefs, by dividing it into four categories. Moving beyond the predominantly political and religious perspectives in previous research on the Belief in Silla as a Buddha-land, this study incorporates a new art-historical perspective to restore a closer approximation of its original form. To achieve this, it focuses on the visual outcomes of the Belief in Silla as a Buddha-land, namely its art and culture, and synthesizes political and religious interpretations to more closely approach

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Srivastava, Rajendra P., and Chan Li. "Risk and Reliability Formulas for Systems Security under Dempster-Shafer Theory of Belief Functions." Journal of Emerging Technologies in Accounting 5, no. 1 (2008): 189–219. http://dx.doi.org/10.2308/jeta.2008.5.1.189.

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ABSTRACT: This paper develops comprehensive formulas for assessing the risk and reliability of “Systems Security” under the Dempster-Shafer theory of belief functions, using the Trust Services framework as proposed by the American Institute of Certified Public Accountants (AICPA) and Canadian Institute of Chartered Accountants (CICA). In addition, we discuss how these formulas can be used for planning and evaluation of “Systems Security” risk under the SysTrust services. The analytical formulas are derived for a tree-structured evidential diagram which is constructed by converting the exact ne

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Azevedo, Gilson Xavier de, and Carolina Teles Lemos. "System of Beliefs as Imaginary in Wunenburger." Caminhos 15, no. 2 (2017): 330. http://dx.doi.org/10.18224/cam.v15i2.6072.

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Abstract: the present text aims analyze the question of belief system from concepts of imagery and representation. Your reference with the imaginary and representation is within the approach of Wunenburger, a French philosopher, specialist in studies on the representative imaginary. His work seeks an approximation with structuralist anthropology to analyze symbols and myths in their relations with rationalism in the world contemporary. Part of problem is that belief is a product of human imagination. The basic premise is think that the imaginary would indeed be the source of symbolic construct

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