### Citations

3374 | Conditional random fields: Probabilistic models for segmenting and labeling sequence data - Lafferty, McCallum, et al. - 2001 |

1454 | P.: Gradient-based learning applied to document recognition
- LeCun, Bottou, et al.
- 1998
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Citation Context ...d (4): 〈xi〉 ≈ ˆxi and 〈xixj〉 ≈ ˆxiˆxj. It is interesting to note that with the saddle point approximation of Z, the gradient ascent updates are similar to the perceptron-learning type updates used in =-=[10]-=- and [11] in nonprobabilistic settings. 3.3 Maximum Marginal Approximation (MMA) This is the second approximation based on BP inference in which MPM label estimates are used for approximating the expe... |

1234 | On the statistical analysis of dirty pictures
- Besag
- 1986
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Citation Context ... Section 4, a test set of 200 noisy images was generated using 50 noisy images each from four base images. For comparison, we also obtain the local MAP solution using Iterated Conditional Modes (ICM) =-=[12]-=- which has been shown to be robust to incorrect parameter settings. In addition, we also compare results with parameters learned through pseudo-Likelihood (PL), which uses a factored approximation of ... |

820 | Training products of experts by minimizing contrastive divergence. Neural computation
- Hinton
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Citation Context ...Chain Monte Carlo (MCMC), can be used to approximate the true expectation. But, MCMC techniques have two main problems, i.e. long ’burn-in’ period which make them slow, and high variance in estimates =-=[5]-=-. To avoid MCMC drawbacks, Contrastive Divergence (CD) was proposed by Hinton [5]. In CD, only a single MCMC move is made from the current empirical distribution of the data (P 0 ) leading to new dist... |

637 | Discriminative training methods for hidden markov models: Theory and experiments with perceptron algorithms
- Collins
- 2002
(Show Context)
Citation Context ...i〉 ≈ ˆxi and 〈xixj〉 ≈ ˆxiˆxj. It is interesting to note that with the saddle point approximation of Z, the gradient ascent updates are similar to the perceptron-learning type updates used in [10] and =-=[11]-=- in nonprobabilistic settings. 3.3 Maximum Marginal Approximation (MMA) This is the second approximation based on BP inference in which MPM label estimates are used for approximating the expectations.... |

570 | Shallow Parsing with Conditional Random Fields
- Sha, Pereira
- 2003
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Citation Context ...e developed in the context of analyzing 1D sequence data for which exact maximum likelihood parameter learning is feasible using efficient techniques, e.g. iterative scaling [2], quasi-Newton methods =-=[3]-=- etc. However, when the graphs contain loops, it is not feasible to exactly maximize the likelihood with respect to the parameters. Therefore, a critical issue for the discriminative fields to be prac... |

468 | Generalized belief propagation
- Yedidia, Freeman, et al.
- 2000
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Citation Context ... DRFs, approximate MAP estimates can be obtained using the min-cut/max-flow algorithms as explained in [1]. We use the sum-product version of loopy Belief Propagation (BP) to obtain the MPM estimates =-=[9]-=-. The approximations described below are designed to match these two classes of inference techniques.s3.1 Pseudo Marginal Approximation (PMA) It is easy to see that, if we had true marginal distributi... |

142 | Discriminative fields for modeling spatial dependencies in natural images
- Kumar, Hebert
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Citation Context ... Introduction In language processing, natural image analysis etc., the input data shows significant dependencies, which should be modeled appropriately to achieve good classification. In earlier work =-=[1]-=-, we presented the Discriminative Random Field (DRF) model for image analysis, which is a type of Conditional Random Field (CRF) proposed by Lafferty et al. [2]. These fields discriminatively model th... |

32 |
Tree-reweighted belief propagation and approximate ML estimation by pseudo-moment matching
- Wainwright, Jaakkola, et al.
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Citation Context ...µ ij(y m ). (6) m i∈Sm j∈Ni Here, fi and gij are functions that approximate the true expectations in the gradient. Several approaches have been proposed that compute fi and gij using pseudo-marginals =-=[7]-=-[8]. In this work, we propose to directly construct fi and gij using label estimates obtained through inference at the current parameter estimates as explained in Section 3.2 and 3.3. The first questi... |

28 | Dynamic conditional random fields for jointly labeling multiple sequences
- McCallum, Rohanimanesh
- 2003
(Show Context)
Citation Context ...j(y m ). (6) m i∈Sm j∈Ni Here, fi and gij are functions that approximate the true expectations in the gradient. Several approaches have been proposed that compute fi and gij using pseudo-marginals [7]=-=[8]-=-. In this work, we propose to directly construct fi and gij using label estimates obtained through inference at the current parameter estimates as explained in Section 3.2 and 3.3. The first question ... |

12 | Multiclass discriminative fields for parts-based object detection
- Kumar, Hebert
- 2004
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Citation Context ... of inference method. 1.1 Discriminative fields In this section, we review the formulation of discriminative fields. Although the formulation is general to arbitrary graphs with multiple class labels =-=[4]-=-, we will discuss the problem of learning in the context of binary classification on 2D image lattices. Let y be the observed data from an input image, where y = {yi} i∈S , yi is the data from ith sit... |

3 |
An Analysis of Contrastive Divergence Learning
- Williams, Agakov
- 2002
(Show Context)
Citation Context ...ain beyond burn-in. According to this, 〈xi〉 ≈ 〈xi〉 P 1 and 〈xixj〉 ≈ 〈xixj〉 P 1. Even though CD is computationally simple and yields estimates with low variance, the bias in estimates can be a problem =-=[6]-=-, which was also verified in our experiments in Section 6. However, this approximation of expectation using single sample forms the basis for different approximations we use in this work, as shown in ... |