scholarly journals Variational Bayesian Multinomial Probit Regression with Gaussian Process Priors

2006 ◽  
Vol 18 (8) ◽  
pp. 1790-1817 ◽  
Author(s):  
Mark Girolami ◽  
Simon Rogers
Keyword(s):  
Gaussian Process ◽  
Latent Variables ◽  
Data Augmentation ◽  
A Priori ◽  
Covariance Structure ◽  
Variational Approximation ◽  
Probit Regression ◽  
Variational Bayesian ◽  
Augmentation Strategy ◽  
Sparse Approximations

It is well known in the statistics literature that augmenting binary and polychotomous response models with gaussian latent variables enables exact Bayesian analysis via Gibbs sampling from the parameter posterior. By adopting such a data augmentation strategy, dispensing with priors over regression coefficients in favor of gaussian process (GP) priors over functions, and employing variational approximations to the full posterior, we obtain efficient computational methods for GP classification in the multiclass setting.1 The model augmentation with additional latent variables ensures full a posteriori class coupling while retaining the simple a priori independent GP covariance structure from which sparse approximations, such as multiclass informative vector machines (IVM), emerge in a natural and straightforward manner. This is the first time that a fully variational Bayesian treatment for multiclass GP classification has been developed without having to resort to additional explicit approximations to the nongaussian likelihood term. Empirical comparisons with exact analysis use Markov Chain Monte Carlo (MCMC) and Laplace approximations illustrate the utility of the variational approximation as a computationally economic alternative to full MCMC and it is shown to be more accurate than the Laplace approximation.

Collaborative Fuzzy Clustering of Variational Bayesian Generative Topographic Mapping

2015 ◽  
Vol 14 (01) ◽  
pp. 1550001 ◽  
Author(s):  
Mohamad Ghassany ◽  
Younès Bennani
Keyword(s):  
Latent Variables ◽  
Input Data ◽  
Analytical Approximation ◽  
Variational Approximation ◽  
Topographic Mapping ◽  
Data Sets ◽  
Sources Of Information ◽  
Generative Topographic Mapping ◽  
Variational Bayesian ◽  
Collaborative Clustering

In this paper, we propose a Collaborative Clustering method based on Variational Bayesian Generative Topographic Mapping (VBGTM). To do so, we first propose a method that combines VBGTM and Fuzzy c-means (FCM). Collaborative clustering is useful to achieve interaction between different sources of information for the purpose of revealing underlying structures and regularities within data sets. It can be treated as a process of consensus building where we attempt to reveal a structure that is common across all sets of data. VBGTM was introduced as a variational approximation of Generative Topographic Mapping (GTM) to control data overfitting. It provides an analytical approximation to the posterior probability of the latent variables and the distribution of the input data in the latent space. It can be effectively applied to visualize and explore properties of the data. But when the number of latent points is large, similar units need to be grouped (i.e., clustered) to facilitate quantitative analysis of the map and the data. We use FCM to determine the prototypes as well as the resultant clusters and the corresponding membership functions of the input data, based on the latent variables obtained from VBGTM. So, by combining the two algorithms, we develop a method that can do visualization and clustering at the same time. We observe that the hybrid method (F-VBGTM) performs very well in terms of many cluster-validity indexes.

scholarly journals Scalable Variational Bayesian Kernel Selection for Sparse Gaussian Process Regression

2020 ◽  
Vol 34 (04) ◽  
pp. 5997-6004
Author(s):  
Tong Teng ◽  
Jie Chen ◽  
Yehong Zhang ◽  
Bryan Kian Hsiang Low
Keyword(s):  
Lower Bound ◽  
Gaussian Process ◽  
Marginal Likelihood ◽  
Gaussian Process Regression ◽  
Random Variable ◽  
Variational Approximation ◽  
Variational Bayesian ◽  
Kernel Selection ◽  
Real World Datasets ◽  
Posterior Belief

This paper presents a variational Bayesian kernel selection (VBKS) algorithm for sparse Gaussian process regression (SGPR) models. In contrast to existing GP kernel selection algorithms that aim to select only one kernel with the highest model evidence, our VBKS algorithm considers the kernel as a random variable and learns its belief from data such that the uncertainty of the kernel can be interpreted and exploited to avoid overconfident GP predictions. To achieve this, we represent the probabilistic kernel as an additional variational variable in a variational inference (VI) framework for SGPR models where its posterior belief is learned together with that of the other variational variables (i.e., inducing variables and kernel hyperparameters). In particular, we transform the discrete kernel belief into a continuous parametric distribution via reparameterization in order to apply VI. Though it is computationally challenging to jointly optimize a large number of hyperparameters due to many kernels being evaluated simultaneously by our VBKS algorithm, we show that the variational lower bound of the log-marginal likelihood can be decomposed into an additive form such that each additive term depends only on a disjoint subset of the variational variables and can thus be optimized independently. Stochastic optimization is then used to maximize the variational lower bound by iteratively improving the variational approximation of the exact posterior belief via stochastic gradient ascent, which incurs constant time per iteration and hence scales to big data. We empirically evaluate the performance of our VBKS algorithm on synthetic and massive real-world datasets.

Integrating Improved U-Net and Continuous Maximum Flow Algorithm for 3D Brain Tumor Image Segmentation

2020 ◽  
Vol 64 (4) ◽  
pp. 40412-1-40412-11
Author(s):  
Kexin Bai ◽  
Qiang Li ◽  
Ching-Hsin Wang
Keyword(s):  
Brain Tumor ◽  
Data Augmentation ◽  
A Priori ◽  
Class Imbalance ◽  
Maximum Flow ◽  
Magnetic Resonance Images ◽  
Tumor Segmentation ◽  
Similarity Coefficients ◽  
Segmentation Algorithms ◽  
Flow Algorithm

Abstract To address the issues of the relatively small size of brain tumor image datasets, severe class imbalance, and low precision in existing segmentation algorithms for brain tumor images, this study proposes a two-stage segmentation algorithm integrating convolutional neural networks (CNNs) and conventional methods. Four modalities of the original magnetic resonance images were first preprocessed separately. Next, preliminary segmentation was performed using an improved U-Net CNN containing deep monitoring, residual structures, dense connection structures, and dense skip connections. The authors adopted a multiclass Dice loss function to deal with class imbalance and successfully prevented overfitting using data augmentation. The preliminary segmentation results subsequently served as the a priori knowledge for a continuous maximum flow algorithm for fine segmentation of target edges. Experiments revealed that the mean Dice similarity coefficients of the proposed algorithm in whole tumor, tumor core, and enhancing tumor segmentation were 0.9072, 0.8578, and 0.7837, respectively. The proposed algorithm presents higher accuracy and better stability in comparison with some of the more advanced segmentation algorithms for brain tumor images.

scholarly journals Adversarial Data Augmentation on Breast MRI Segmentation

2021 ◽  
Vol 11 (10) ◽  
pp. 4554
Author(s):  
João F. Teixeira ◽  
Mariana Dias ◽  
Eva Batista ◽  
Joana Costa ◽  
Luís F. Teixeira ◽  
...  
Keyword(s):  
Data Augmentation ◽  
Medical Image Analysis ◽  
Synthetic Data ◽  
Breast Mri ◽  
Semantic Segmentation ◽  
Adversarial Networks ◽  
Augmentation Strategy ◽  
Magnetic Resonance Imaging Mri ◽  
Segmentation Task ◽  
The Impact

The scarcity of balanced and annotated datasets has been a recurring problem in medical image analysis. Several researchers have tried to fill this gap employing dataset synthesis with adversarial networks (GANs). Breast magnetic resonance imaging (MRI) provides complex, texture-rich medical images, with the same annotation shortage issues, for which, to the best of our knowledge, no previous work tried synthesizing data. Within this context, our work addresses the problem of synthesizing breast MRI images from corresponding annotations and evaluate the impact of this data augmentation strategy on a semantic segmentation task. We explored variations of image-to-image translation using conditional GANs, namely fitting the generator’s architecture with residual blocks and experimenting with cycle consistency approaches. We studied the impact of these changes on visual verisimilarity and how an U-Net segmentation model is affected by the usage of synthetic data. We achieved sufficiently realistic-looking breast MRI images and maintained a stable segmentation score even when completely replacing the dataset with the synthetic set. Our results were promising, especially when concerning to Pix2PixHD and Residual CycleGAN architectures.

scholarly journals Feature Re-Learning for Video Recommendation

2021 ◽  
Vol 9 (VI) ◽  
pp. 3143-3149
Author(s):  
Chanjal C
Keyword(s):  
Data Augmentation ◽  
Video Retrieval ◽  
Poor Performance ◽  
Training Data ◽  
Video Annotation ◽  
Video Copy Detection ◽  
Copy Detection ◽  
Augmentation Strategy ◽  
Ranking Loss ◽  
Video Recommendation

Predicting the relevance between two given videos with respect to their visual content is a key component for content-based video recommendation and retrieval. The application is in video recommendation, video annotation, Category or near-duplicate video retrieval, video copy detection and so on. In order to estimate video relevance previous works utilize textual content of videos and lead to poor performance. The proposed method is feature re-learning for video relevance prediction. This work focus on the visual contents to predict the relevance between two videos. A given feature is projected into a new space by an affine transformation. Different from previous works this use a standard triplet ranking loss that optimize the projection process by a novel negative-enhanced triplet ranking loss. In order to generate more training data, propose a data augmentation strategy which works directly on video features. The multi-level augmentation strategy works for video features, which benefits the feature relearning. The proposed augmentation strategy can be flexibly used for frame-level or video-level features. The loss function that consider the absolute similarity of positive pairs and supervise the feature re-learning process and a new formula for video relevance computation.

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