An Expectation-Maximization Algorithm to Estimate the Integrated Choice and Latent Variable Model

2017 ◽  
Vol 51 (3) ◽  
pp. 946-967 ◽  
Author(s):  
Keemin Sohn
Keyword(s):  
Expectation Maximization ◽  
Latent Variable ◽  
Expectation Maximization Algorithm ◽  
Latent Variable Model ◽  
Variable Model

Mixtures of Probabilistic Principal Component Analyzers

1999 ◽  
Vol 11 (2) ◽  
pp. 443-482 ◽  
Author(s):  
Michael E. Tipping ◽  
Christopher M. Bishop
Keyword(s):  
Expectation Maximization ◽  
Latent Variable ◽  
Ad Hoc ◽  
Expectation Maximization Algorithm ◽  
Principal Component ◽  
Latent Variable Model ◽  
Variable Model ◽  
Digit Recognition ◽  
Handwritten Digit ◽  
Density Modeling

Principal component analysis (PCA) is one of the most popular techniques for processing, compressing, and visualizing data, although its effectiveness is limited by its global linearity. While nonlinear variants of PCA have been proposed, an alternative paradigm is to capture data complexity by a combination of local linear PCA projections. However, conventional PCA does not correspond to a probability density, and so there is no unique way to combine PCA models. Therefore, previous attempts to formulate mixture models for PCA have been ad hoc to some extent. In this article, PCA is formulated within a maximum likelihood framework, based on a specific form of gaussian latent variable model. This leads to a well-defined mixture model for probabilistic principal component analyzers, whose parameters can be determined using an expectation-maximization algorithm. We discuss the advantages of this model in the context of clustering, density modeling, and local dimensionality reduction, and we demonstrate its application to image compression and handwritten digit recognition.

A diversified shared latent variable model for efficient image characteristics extraction and modelling

2021 ◽  
Vol 421 ◽  
pp. 244-259
Author(s):  
Hao Xiong ◽  
Yuan Yan Tang ◽  
Fionn Murtagh ◽  
Leszek Rutkowski ◽  
Shlomo Berkovsky
Keyword(s):  
Latent Variable ◽  
Latent Variable Model ◽  
Variable Model ◽  
Image Characteristics

scholarly journals Efficient Dimensionality Reduction Methods in Reservoir History Matching

Energies ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 3137
Author(s):  
Amine Tadjer ◽  
Reider B. Bratvold ◽  
Remus G. Hanea
Keyword(s):  
Data Assimilation ◽  
Dimensionality Reduction ◽  
Gaussian Process ◽  
Latent Variable ◽  
History Matching ◽  
Production Performance ◽  
Latent Variable Model ◽  
Variable Model ◽  
Multiple Data ◽  
Ensemble Smoother

Production forecasting is the basis for decision making in the oil and gas industry, and can be quite challenging, especially in terms of complex geological modeling of the subsurface. To help solve this problem, assisted history matching built on ensemble-based analysis such as the ensemble smoother and ensemble Kalman filter is useful in estimating models that preserve geological realism and have predictive capabilities. These methods tend, however, to be computationally demanding, as they require a large ensemble size for stable convergence. In this paper, we propose a novel method of uncertainty quantification and reservoir model calibration with much-reduced computation time. This approach is based on a sequential combination of nonlinear dimensionality reduction techniques: t-distributed stochastic neighbor embedding or the Gaussian process latent variable model and clustering K-means, along with the data assimilation method ensemble smoother with multiple data assimilation. The cluster analysis with t-distributed stochastic neighbor embedding and Gaussian process latent variable model is used to reduce the number of initial geostatistical realizations and select a set of optimal reservoir models that have similar production performance to the reference model. We then apply ensemble smoother with multiple data assimilation for providing reliable assimilation results. Experimental results based on the Brugge field case data verify the efficiency of the proposed approach.

scholarly journals Chinese Character Image Completion Using a Generative Latent Variable Model

2021 ◽  
Vol 11 (2) ◽  
pp. 624
Author(s):  
In-su Jo ◽  
Dong-bin Choi ◽  
Young B. Park
Keyword(s):  
Latent Variable ◽  
Chinese Character ◽  
Image Inpainting ◽  
Latent Variable Model ◽  
Chinese Characters ◽  
Image Completion ◽  
Variable Model ◽  
Variational Autoencoder ◽  
Convolution Model ◽  
Detection Technologies

Chinese characters in ancient books have many corrupted characters, and there are cases in which objects are mixed in the process of extracting the characters into images. To use this incomplete image as accurate data, we use image completion technology, which removes unnecessary objects and restores corrupted images. In this paper, we propose a variational autoencoder with classification (VAE-C) model. This model is characterized by using classification areas and a class activation map (CAM). Through the classification area, the data distribution is disentangled, and then the node to be adjusted is tracked using CAM. Through the latent variable, with which the determined node value is reduced, an image from which unnecessary objects have been removed is created. The VAE-C model can be utilized not only to eliminate unnecessary objects but also to restore corrupted images. By comparing the performance of removing unnecessary objects with mask regions with convolutional neural networks (Mask R-CNN), one of the prevalent object detection technologies, and also comparing the image restoration performance with the partial convolution model (PConv) and the gated convolution model (GConv), which are image inpainting technologies, our model is proven to perform excellently in terms of removing objects and restoring corrupted areas.

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