An Introduction to Variational Methods for Graphical Models

Jordan, Michael I.; Ghahramani, Zoubin; Jaakkola, Tommi S.; Saul, Lawrence K.

doi:10.1007/978-94-011-5014-9_5

Cited by 1,585 publications

(2,147 citation statements)

References 25 publications

Supporting

Mentioning

2,133

Contrasting

Unclassified

Order By: Relevance

“…As mentioned previously, in graphical models (or Bayesian networks, in particular) a node represents a random variable and links specify the dependency relationships between these variables [22]. The states of the random variables can be hidden in the sense that they are not directly observable, but it is assumed that they may have observations related to the state values.…”

Section: Belief Propagationmentioning

confidence: 99%

Bayesian Networks for Modeling Cortical Integration

Akay

2006

Handbook of Neural Engineering

View full text Add to dashboard Cite

Section: Belief Propagationmentioning

confidence: 99%

Bayesian Networks for Modeling Cortical Integration

Akay

2006

Handbook of Neural Engineering

View full text Add to dashboard Cite

“…1. For general graphical models, the term decomposable and the term triangulated have their own meanings (they are actually equivalent properties [21]). Here, we use the term decomposable triangulated specifically for the graph type defined in this paragraph.…”

Section: Detection and Labelingmentioning

confidence: 99%

“…For general graphical models, the labeling problem is the most-probable-configuration problem on the graph and can be solved through max-propagation on junction trees [18], [21], [28]. The dynamic programming algorithm [2] and the max-propagation algorithm essentially have the same order of complexity which is determined by the maximum clique size of the graph.…”

Section: Decomposable Triangulated Graphs and General Graphical Modelsmentioning

confidence: 99%

Unsupervised learning of human motion

Yang

Gonçalves²,

Perona

2003

IEEE Trans. Pattern Anal. Machine Intell.

146

View full text Add to dashboard Cite

Abstract-An unsupervised learning algorithm that can obtain a probabilistic model of an object composed of a collection of parts (a moving human body in our examples) automatically from unlabeled training data is presented. The training data include both useful "foreground" features as well as features that arise from irrelevant background clutter-the correspondence between parts and detected features is unknown. The joint probability density function of the parts is represented by a mixture of decomposable triangulated graphs which allow for fast detection. To learn the model structure as well as model parameters, an EM-like algorithm is developed where the labeling of the data (part assignments) is treated as hidden variables. The unsupervised learning technique is not limited to decomposable triangulated graphs. The efficiency and effectiveness of our algorithm is demonstrated by applying it to generate models of human motion automatically from unlabeled image sequences, and testing the learned models on a variety of sequences.

show abstract

“…(2) is not tractable, we develop a generalised EM (GEM) algorithm (see e.g. [6]), with approximate E-step. In general terms, for each data point t n , its log-likelihood can be bounded as follows:…”

Section: Structured Variational Em Solutionmentioning

confidence: 99%

“…a fully factorial form [6] is the most common choice. However, under our model definitions, it is feasible to keep some of the posterior dependencies by choosing the following tree-structured…”

Section: Structured Variational Em Solutionmentioning

confidence: 99%

Robust Visual Mining of Data with Error Information

Sun

Kabán

Raychaudhury

Knowledge Discovery in Databases: PKDD 2007

View full text Add to dashboard Cite

Abstract. Recent results on robust density-based clustering have indicated that the uncertainty associated with the actual measurements can be exploited to locate objects that are atypical for a reason unrelated to measurement errors. In this paper, we develop a constrained robust mixture model, which, in addition, is able to nonlinearly map such data for visual exploration. Our robust visual mining approach aims to combine statistically sound density-based analysis with visual presentation of the density structure, and to provide visual support for the identification and exploration of 'genuine' peculiar objects of interest that are not due to the measurement errors. In this model, an exact inference is not possible despite the latent space being discretised, and we resort to employing a structured variational EM. We present results on synthetic data as well as a real application, for visualising peculiar quasars from an astrophysical survey, given photometric measurements with errors.

show abstract

An Introduction to Variational Methods for Graphical Models

Cited by 1,585 publications

References 25 publications

Bayesian Networks for Modeling Cortical Integration

Bayesian Networks for Modeling Cortical Integration

Unsupervised learning of human motion

Robust Visual Mining of Data with Error Information

Contact Info

Product

Resources

About