### Citations

160 | Fixing max-product: Convergent message passing algorithms for MAP LP-relaxations
- Globerson, Jaakkola
- 2008
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Citation Context ... computations that can be solved using any off-the-shelf linear program solver. More importantly, this connects lifted inference and linear program relaxations for the MAP inference problem, see e.g. =-=[22]-=-. In a distinct yet related work, Sen et al. [55] proposed the idea of bisimulated variable elimination (VE). In a nutshell, VE [73] works as follows. To compute a single node marginal, we iterate the... |

142 |
Recursive conditioning
- Darwiche
- 2001
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Citation Context ...babilistic Inference36 networks that can be solved independently. Each of these subnetworks is then solved recursively using the same method, until we reach a simple enough network that can be solved =-=[11]-=-. Recently, several top-down lifted search-based methods have been proposed [23, 24, 68, 48]. Gogate and Domingos [24] reduced the problem of lifted probabilistic inference to weighted model counting ... |

120 | Model minimization in Markov decision processes
- Dean, Givan
- 1997
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Citation Context ...s not too complicated” [27]. Therefore, it is not surprising that symmetries have also been explored in many AI tasks such as (mixed–)integer programming [37, 4], SAT and CSP [54, 64] as well as MDPs =-=[17, 50]-=-. Surprisingly, symmetries have not been the subject of interest within probabilistic inference. Only recently the first efforts were 1 Institute of Geodesy and Geoinformation, University of Bonn, Ger... |

73 |
Asymmetric graphs
- Erdős, Rényi
- 1963
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Citation Context ...imple insight is important. It illustrates that lifting is not always beneficial. There are simply asymmetric situations. In fact, Erdös and Rényi showed that almost all large graphs are asymmetric =-=[18]-=-, but it is readily observed that many graphs representing structures of real interest contain symmetry. Generally, it is difficult to preserve the full joint distribution by lifting. Consequently, li... |

66 | Probabilistic Theorem Proving
- Gogate, Domingos
- 2011
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Citation Context ...]. This was the starting point of the very active research field called ”lifted probabilistic inference”. Since then, several inference approaches that exploit symmetries have been proposed, see e.g. =-=[14, 40, 55, 8, 68, 24]-=- among others, and proven successful in many AI tasks and applications such as information retrieval, satisfiability, boolean model counting, semantic role labeling, Kalman filtering, Page Rank, Label... |

50 | Counting Belief Propagation
- Kersting, Ahmadi, et al.
- 2009
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Citation Context ...aches have rendered many of these large, previously intractable problems quickly solvable by exploiting the induced redundancies. As a sneak preview, lifted (loopy) belief propagation (BP) approaches =-=[58, 30, 16, 31, 25, 3]-=- intuitively automatically group variables and factors of a graphical model together if they have identical computation trees (i.e., the tree-structured “unrolling” of the graphical model computations... |

28 | MPE and partial inversion in lifted probabilistic variable elimination
- Braz, Amir, et al.
- 2006
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Citation Context ...E for relational models, moving essentially from O(2n) to O(n); ultimately being independent of the domain size. Of course, in a similar way, one can lift MAP and MPE inference approaches based on VE =-=[15]-=-. Even more efficiency can be gained if we not only employ sharing of potentials across interchangeable random variables but also to exploit interchangeability within individual potentials. To do so, ... |

21 | Lifted Inference Seen from the Other Side: The Tractable Features
- Jha, Gogate, et al.
- 2010
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Citation Context ...at we do not touch upon methods for preprocessing [57, 38, 63] and lazy inference [49, 52] that can also reduce the running time of inference drastically, upon theoretical results on lifted inference =-=[34, 29, 65]-=-, nor upon the use of lifted inference for relational probabilistic conditional logic [62] and for solving relational MDPs, see e.g. [53, 32]. We also do not touch upon graphical models with symmetrie... |

16 | Lifted inference for relational continuous models
- Choi, Hill, et al.
- 2010
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Citation Context ...]. This was the starting point of the very active research field called ”lifted probabilistic inference”. Since then, several inference approaches that exploit symmetries have been proposed, see e.g. =-=[14, 40, 55, 8, 68, 24]-=- among others, and proven successful in many AI tasks and applications such as information retrieval, satisfiability, boolean model counting, semantic role labeling, Kalman filtering, Page Rank, Label... |

15 | Fastest mixing Markov chain on graphs with symmetries
- Boyd, Diaconis, et al.
- 2009
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Citation Context ...r relational probabilistic conditional logic [62] and for solving relational MDPs, see e.g. [53, 32]. We also do not touch upon graphical models with symmetries outside the SRL/StarAI context such as =-=[5, 36, 19, 20]-=-. K. Kersting / Lifted Probabilistic Inference34 Figure 3. From left to right, the steps of lifting the factor graph in Fig. 1(Left). The colore... |

14 | Multi-evidence lifted message passing, with application to PageRank and the Kalman filter
- Ahmadi, Kersting, et al.
- 2011
(Show Context)
Citation Context ...aches have rendered many of these large, previously intractable problems quickly solvable by exploiting the induced redundancies. As a sneak preview, lifted (loopy) belief propagation (BP) approaches =-=[58, 30, 16, 31, 25, 3]-=- intuitively automatically group variables and factors of a graphical model together if they have identical computation trees (i.e., the tree-structured “unrolling” of the graphical model computations... |

12 |
Anytime lifted belief propagation
- Braz, Natarajan, et al.
- 2009
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Citation Context ...aches have rendered many of these large, previously intractable problems quickly solvable by exploiting the induced redundancies. As a sneak preview, lifted (loopy) belief propagation (BP) approaches =-=[58, 30, 16, 31, 25, 3]-=- intuitively automatically group variables and factors of a graphical model together if they have identical computation trees (i.e., the tree-structured “unrolling” of the graphical model computations... |

11 |
Algorithms for highly symmetric linear and integer programs
- Bödi, Herr, et al.
- 2013
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Citation Context ...many symmetries to be uniform and regular, thus not too complicated” [27]. Therefore, it is not surprising that symmetries have also been explored in many AI tasks such as (mixed–)integer programming =-=[37, 4]-=-, SAT and CSP [54, 64] as well as MDPs [17, 50]. Surprisingly, symmetries have not been the subject of interest within probabilistic inference. Only recently the first efforts were 1 Institute of Geod... |

11 |
Lifted First Order Probabilistic Inference
- Braz, Amir, et al.
- 2005
(Show Context)
Citation Context ...]. This was the starting point of the very active research field called ”lifted probabilistic inference”. Since then, several inference approaches that exploit symmetries have been proposed, see e.g. =-=[14, 40, 55, 8, 68, 24]-=- among others, and proven successful in many AI tasks and applications such as information retrieval, satisfiability, boolean model counting, semantic role labeling, Kalman filtering, Page Rank, Label... |

10 |
Template-based inference in symmetric relational Markov random fields
- Jaimovich, Meshi, et al.
- 2007
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Citation Context ...eady highly efficient, BP does not make use of symmetries. Reconsider our example shown Fig. 2. To exploit the symmetries present in the graph structure, lifted BP variants [58, 30], (that build upon =-=[28]-=-) essentially perform two steps: Given a factor graph, they first compute a lifted factor graph and then run a modified BP on it. In the first step, we simulate BP keeping track of which nodes and fac... |

10 | Informed lifting for message-passing
- Kersting, Massaoudi, et al.
- 2010
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Citation Context |

8 | Exploiting Logical Structure in Lifted Probabilistic Inference
- Gogate, Domingos
- 2010
(Show Context)
Citation Context ...subnetworks is then solved recursively using the same method, until we reach a simple enough network that can be solved [11]. Recently, several top-down lifted search-based methods have been proposed =-=[23, 24, 68, 48]-=-. Gogate and Domingos [24] reduced the problem of lifted probabilistic inference to weighted model counting in a lifted graph. Van den Broeck et al. [68] employ circuits in first-order deterministic d... |

6 | Lifted online training of relational models with stochastic gradient methods
- Ahmadi, Kersting, et al.
- 2012
(Show Context)
Citation Context ... break the global model in to local ones and then to train and recombine the local models. This breaks long-range dependencies and allows to exploit lifting within and across the local training tasks =-=[2]-=-. Recently, Bui et al. [6] have shown that for MAP inference we can exploit the symmetries of the model before evidence is obtained. To conclude, one of the key challenges in building intelligent agen... |

5 | Lifted belief propagation: Pairwise marginals and beyond
- Ahmadi, Kersting, et al.
- 2010
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Citation Context ... from scratch, therefore often canceling the benefits of lifted inference. Online lifting approaches avoid this by reusing already known liftings when computing the lifting of the next inference task =-=[1, 42, 25]-=- and can also be used to realize lifted sampling. Lifted BP approaches are also appealing because they are simple, efficient, and parallelizable. Moreover, they have paved the way for lifted solutions... |

4 |
Relax, compensate and then recover
- Choi, Darwiche
- 2011
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Citation Context ... how to realize a lifted Kalman filter based on lifted VE [10]. Recently, Van den Broeck et al. [66] built a bridge between lifted VE and lifted BP by lifting the ”relax, compensate and then recover” =-=[7]-=-. An alternative to variable elimination is to use search-based methods based on recursive conditioning. That is, we decompose by conditioning on parameterized variables a lifted network into smaller ... |

4 | Lifted relational kalman filtering
- Choi, Guzmn-Rivera, et al.
(Show Context)
Citation Context ...entials and the marginals that are not in pairwise form are converted to pairwise form and then eliminated. Recently, the same group has shown how to realize a lifted Kalman filter based on lifted VE =-=[10]-=-. Recently, Van den Broeck et al. [66] built a bridge between lifted VE and lifted BP by lifting the ”relax, compensate and then recover” [7]. An alternative to variable elimination is to use search-b... |

4 | Lattices of graphical Gaussian models with symmetries
- Gehrmann
- 2011
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Citation Context ...r relational probabilistic conditional logic [62] and for solving relational MDPs, see e.g. [53, 32]. We also do not touch upon graphical models with symmetries outside the SRL/StarAI context such as =-=[5, 36, 19, 20]-=-. K. Kersting / Lifted Probabilistic Inference34 Figure 3. From left to right, the steps of lifting the factor graph in Fig. 1(Left). The colore... |

4 | Estimation of means in graphical Gaussian models with symmetries
- Gehrmann, Lauritzen
- 2011
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Citation Context ...r relational probabilistic conditional logic [62] and for solving relational MDPs, see e.g. [53, 32]. We also do not touch upon graphical models with symmetries outside the SRL/StarAI context such as =-=[5, 36, 19, 20]-=-. K. Kersting / Lifted Probabilistic Inference34 Figure 3. From left to right, the steps of lifting the factor graph in Fig. 1(Left). The colore... |

3 | Efficient methods for lifted inference with aggregate factors
- Choi, Braz, et al.
- 2011
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Citation Context ...cted first-order models that require an aggregation operator when a parent random variable is parameterized by logical variables that are not present in a child random variable. Recently, Choi et al. =-=[9]-=- have shown how to perform lifted VE in the presence of aggregate factors such as SUM, AVERAGE, and AND in probabilistic relational models. Taghipour et al. [61] have lifted the restriction of having ... |

3 | Efficient sequential clamping for lifted message passing
- Hadiji, Ahmadi, et al.
- 2011
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Citation Context |

2 | Symmetries in linear and integer programs
- Herr, Bödi
- 2010
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Citation Context ... theory, and much of modern cosmology lies one concept: symmetry.” In mathematics, as Herr and Bödi note, ”we expect objects with many symmetries to be uniform and regular, thus not too complicated” =-=[27]-=-. Therefore, it is not surprising that symmetries have also been explored in many AI tasks such as (mixed–)integer programming [37, 4], SAT and CSP [54, 64] as well as MDPs [17, 50]. Surprisingly, sym... |

1 |
Salvo Braz, ‘Exact lifted inference with distinct soft evidence on every object
- Bui, Huynh, et al.
- 2012
(Show Context)
Citation Context ... to local ones and then to train and recombine the local models. This breaks long-range dependencies and allows to exploit lifting within and across the local training tasks [2]. Recently, Bui et al. =-=[6]-=- have shown that for MAP inference we can exploit the symmetries of the model before evidence is obtained. To conclude, one of the key challenges in building intelligent agents is closing the gap betw... |

1 | Lifted message passing for satisfiability
- Hadiji, Kersting, et al.
- 2010
(Show Context)
Citation Context ...llelizable. Moreover, they have paved the way for lifted solutions of many important AI tasks. For instance, one can lift variants of BP for solving satisfiability problems such as survey propagation =-=[26]-=- or when the underlying distributions are Gaussian [3]. In turn, one can realize lifted variants of Kalman filters, PageRank, Label Propagation, and Clustering-on-demand [3, 43]. Even linear programmi... |

1 | Stochastic planning and lifted inference
- Khardon
(Show Context)
Citation Context ...stically, upon theoretical results on lifted inference [34, 29, 65], nor upon the use of lifted inference for relational probabilistic conditional logic [62] and for solving relational MDPs, see e.g. =-=[53, 32]-=-. We also do not touch upon graphical models with symmetries outside the SRL/StarAI context such as [5, 36, 19, 20]. K. Kersting / Lifted Probabilistic Inference34 ... |