Bayesian Inference for Graphical Factor Analysis Models

Giudici, Paolo; Stanghellini, Elena

doi:10.1007/bf02296197

Cited by 12 publications

(7 citation statements)

References 19 publications

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“…Extensions of graphical models which includes latent variables have recently been proposed in the sphere of cross‐sectional analysis (see, e.g. the graphical factor analysis models in Giudici and Stanghellini, 2002). We are currently working on similar extensions within the fields of time series analysis with particular emphasis on the common trends model for partially non‐stationary processes (Stock and Watson, 1988).…”

Section: Discussionmentioning

confidence: 99%

A Bayesian Approach to Modelling Graphical Vector Autoregressions

Corander

Villani

2006

Journal Time Series Analysis

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Section: Discussionmentioning

confidence: 99%

A Bayesian Approach to Modelling Graphical Vector Autoregressions

Corander

Villani

2006

Journal Time Series Analysis

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“…We also remark that an extension of the reversible jump algorithm for undirected decomposable graphs with latent variables is presented and discussed in a recent paper by Giudici and Stanghellini (1999), the extension the directed case is not available yet, but can be accomplished along similar lines. Finally, the reversible jump approach also permits extensions for non-conjugate priors, such as hierarchical ones, which may diminish the sensitivity of inferences to the prior distribution (see e.g.…”

Section: Discussionmentioning

confidence: 99%

Markov Chain Monte Carlo model selection for DAG models

Fronk

Giudici

2004

Statistical Methods & Applications

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We present a methodology for Bayesian model choice and averaging in Gaussian directed acyclic graphs (dags). The dimension-changing move involves adding or dropping a (directed) edge from the graph. The methodology employs the results in Geiger and Heckerman and searches directly in the space of all dags. Model determination is carried out by implementing a reversible jump Markov Chain Monte Carlo sampler. To achieve this aim we rely on the concept of adjacency matrices, which provides a relatively inexpensive check for acyclicity. The performance of our procedure is illustrated by means of two simulated datasets, as well as one real dataset.

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“…The supervised extraction techniques include Linear Discriminant Analysis (LDA) [33], Kernel Fisher Discriminant (KFD) Analysis [34], and an extraction framework in a kernel space [14], etc. In unsupervised learning, linear methods (such as Principle Component Analysis (PCA) [19] and factor analysis [20]) and nonlinear methods (metric learning [21] and manifold learning [22], [26], [27], [28]) are proposed.…”

Section: Related Workmentioning

confidence: 99%

Beyond Redundancies: A Metric-Invariant Method for Unsupervised Feature Selection

Hou

Zhang

Yan

et al. 2010

IEEE Trans. Knowl. Data Eng.

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A fundamental goal of unsupervised feature selection is denoising, which aims to identify and reduce noisy features that are not discriminative. Due to the lack of information about real classes, denoising is a challenging task. The noisy features can disturb the reasonable distance metric and result in unreasonable feature spaces, i.e., the feature spaces in which common clustering algorithms cannot effectively find real classes. To overcome the problem, we make a primary observation that the relevance of features is intrinsic and independent of any metric scaling on the feature space. This observation implies that feature selection should be invariant, at least to some extent, with respect to metric scaling. In this paper, we clarify the necessity of considering the metric invariance in unsupervised feature selection and propose a novel model incorporating metric invariance. Our proposed method is motivated by the following observations: if the statistic that guides the unsupervised feature selection process is invariant with respect to possible metric scaling, the solution of this model will also be invariant. Hence, if a metric-invariant model can distinguish discriminative features from noisy ones in a reasonable feature space, it will also work on the unreasonable counterpart transformed from the reasonable one by metric scaling. A theoretical justification of the metric invariance of our proposed model is given and the empirical evaluation demonstrates its promising performance.

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Bayesian Inference for Graphical Factor Analysis Models

Abstract: factor analysis, graphical Gaussian models, identification, model comparison, reversible jump MCMC,

Cited by 12 publications

References 19 publications

A Bayesian Approach to Modelling Graphical Vector Autoregressions

A Bayesian Approach to Modelling Graphical Vector Autoregressions

Markov Chain Monte Carlo model selection for DAG models

Beyond Redundancies: A Metric-Invariant Method for Unsupervised Feature Selection

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