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Bob Zhang - One of the best experts on this subject based on the ideXlab platform.
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harmonization shared autoencoder gaussian process Latent Variable Model with relaxed hamming distance
IEEE Transactions on Neural Networks, 2020Co-Authors: Bob Zhang, David ZhangAbstract:Multiview learning has shown its superiority in visual classification compared with the single-view-based methods. Especially, due to the powerful representation capacity, the Gaussian process Latent Variable Model (GPLVM)-based multiview approaches have achieved outstanding performances. However, most of them only follow the assumption that the shared Latent Variables can be generated from or projected to the multiple observations but fail to exploit the harmonization in the back constraint and adaptively learn a classifier according to these learned Variables, which would result in performance degradation. To tackle these two issues, in this article, we propose a novel harmonization shared autoencoder GPLVM with a relaxed Hamming distance (HSAGP-RHD). Particularly, an autoencoder structure with the Gaussian process (GP) prior is first constructed to learn the shared Latent Variable for multiple views. To enforce the agreement among various views in the encoder, a harmonization constraint is embedded into the Model by making consistency for the view-specific similarity. Furthermore, we also propose a novel discriminative prior, which is directly imposed on the Latent Variable to simultaneously learn the fused features and adaptive classifier in a unit Model. In detail, the centroid matrix corresponding to the centroids of different categories is first obtained. A relaxed Hamming distance (RHD)-based measurement is subsequently presented to measure the similarity and dissimilarity between the Latent Variable and centroids, not only allowing us to get the closed-form solutions but also encouraging the points belonging to the same class to be close, while those belonging to different classes to be far. Due to this novel prior, the category of the out-of-sample is also allowed to be simply assigned in the testing phase. Experimental results conducted on three real-world data sets demonstrate the effectiveness of the proposed method compared with state-of-the-art approaches.
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Visual Classification With Multikernel Shared Gaussian Process Latent Variable Model
IEEE Transactions on Cybernetics, 2019Co-Authors: Jinxing Li, Bob Zhang, Guangming Lu, David ZhangAbstract:Multiview learning methods often achieve improvement compared with single-view-based approaches in many applications. Due to the powerful nonlinear ability and probabilistic perspective of Gaussian process (GP), some GP-based multiview efforts were presented. However, most of these methods make a strong assumption on the kernel function (e.g., radial basis function), which limits the capacity of the real data Modeling. In order to address this issue, in this paper, we propose a novel multiview approach by combining a multikernel and GP Latent Variable Model. Instead of designing a deterministic kernel function, multiple kernel functions are established to automatically adapt various types of data. Considering a simple way of obtaining Latent Variables at the testing stage, a projection from the observed space to the Latent space as a back constraint has also been simultaneously introduced into the proposed method. Additionally, different from some existing methods which apply the classifiers off-line, a hinge loss is embedded into the Model to jointly learn the classification hyperplane, encouraging the Latent Variables belonging to the different classes to be separated. An efficient algorithm based on the gradient decent technique is constructed to optimize our method. Finally, we apply the proposed approach to three real-world datasets and the associated results demonstrate the effectiveness and superiority of our Model compared with other state-of-the-art methods.
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shared linear encoder based gaussian process Latent Variable Model for visual classification
ACM Multimedia, 2018Co-Authors: Bob Zhang, David ZhangAbstract:Multi-view learning has shown its powerful potential in many applications and achieved outstanding performances compared with the single-view based methods. In this paper, we propose a novel multi-view learning Model based on the Gaussian Process Latent Variable Model (GPLVM) to learn a shared Latent Variable in the manifold space with a linear and gaussian process prior based back projection. Different from existing GPLVM methods which only consider a mapping from the Latent space to the observed space, the proposed method simultaneously takes a back projection from the observation to the Latent Variable into account. Concretely, due to the various dimensions of different views, a projection for each view is first learned to linearly map its observation to a subspace. The gaussian process prior is then imposed on another transformation to non-linearly and efficiently map the learned subspace to a shared manifold space. In order to apply the proposed approach to the classification, a discriminative regularization is also embedded to exploit the label information. Experimental results on three real-world databases substantiate the effectiveness and superiority of the proposed approach as compared with several state-of-the-art approaches.
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Shared Autoencoder Gaussian Process Latent Variable Model for Visual Classification
IEEE Transactions on Neural Networks and Learning Systems, 2018Co-Authors: Jinxing Li, Bob ZhangAbstract:Multiview learning reveals the Latent correlation among different modalities and utilizes the complementary information to achieve a better performance in many applications. In this paper, we propose a novel multiview learning Model based on the Gaussian process Latent Variable Model (GPLVM) to learn a set of nonlinear and nonparametric mapping functions and obtain a shared Latent Variable in the manifold space. Different from the previous work on the GPLVM, the proposed shared autoencoder Gaussian process (SAGP) Latent Variable Model assumes that there is an additional mapping from the observed data to the shared manifold space. Due to the introduction of the autoencoder framework, both nonlinear projections from and to the observation are considered simultaneously. Additionally, instead of fully connecting used in the conventional autoencoder, the SAGP achieves the mappings utilizing the GP, which remarkably reduces the number of estimated parameters and avoids the phenomenon of overfitting. To make the proposed method adaptive for classification, a discriminative regularization is embedded into the proposed method. In the optimization process, an efficient algorithm based on the alternating direction method and gradient decent techniques is designed to solve the encoder and decoder parts alternatively. Experimental results on three real-world data sets substantiate the effectiveness and superiority of the proposed approach as compared with the state of the art.
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Shared Linear Encoder-Based Multikernel Gaussian Process Latent Variable Model for Visual Classification
IEEE Transactions on Cybernetics, 2024Co-Authors: Jinxing Li, Guangming Lu, Bob ZhangAbstract:Multiview learning has been widely studied in various fields and achieved outstanding performances in comparison to many single-view-based approaches. In this paper, a novel multiview learning method based on the Gaussian process Latent Variable Model (GPLVM) is proposed. In contrast to existing GPLVM methods which only assume that there are transformations from the Latent Variable to the multiple observed inputs, our proposed method simultaneously takes a back constraint into account, encoding multiple observations to the Latent Variable by enjoying the Gaussian process (GP) prior. Particularly, to overcome the difficulty of the covariance matrix calculation in the encoder, a linear projection is designed to map different observations to a consistent subspace first. The obtained Variable in this subspace is then projected to the Latent Variable in the manifold space with the GP prior. Furthermore, different from most GPLVM methods which strongly assume that the covariance matrices follow a certain kernel function, for example, radial basis function (RBF), we introduce a multikernel strategy to design the covariance matrix, being more reasonable and adaptive for the data representation. In order to apply the presented approach to the classification, a discriminative prior is also embedded to the learned Latent Variables to encourage samples belonging to the same category to be close and those belonging to different categories to be far. Experimental results on three real-world databases substantiate the effectiveness and superiority of the proposed method compared with state-of-the-art approaches.
David Zhang - One of the best experts on this subject based on the ideXlab platform.
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harmonization shared autoencoder gaussian process Latent Variable Model with relaxed hamming distance
IEEE Transactions on Neural Networks, 2020Co-Authors: Bob Zhang, David ZhangAbstract:Multiview learning has shown its superiority in visual classification compared with the single-view-based methods. Especially, due to the powerful representation capacity, the Gaussian process Latent Variable Model (GPLVM)-based multiview approaches have achieved outstanding performances. However, most of them only follow the assumption that the shared Latent Variables can be generated from or projected to the multiple observations but fail to exploit the harmonization in the back constraint and adaptively learn a classifier according to these learned Variables, which would result in performance degradation. To tackle these two issues, in this article, we propose a novel harmonization shared autoencoder GPLVM with a relaxed Hamming distance (HSAGP-RHD). Particularly, an autoencoder structure with the Gaussian process (GP) prior is first constructed to learn the shared Latent Variable for multiple views. To enforce the agreement among various views in the encoder, a harmonization constraint is embedded into the Model by making consistency for the view-specific similarity. Furthermore, we also propose a novel discriminative prior, which is directly imposed on the Latent Variable to simultaneously learn the fused features and adaptive classifier in a unit Model. In detail, the centroid matrix corresponding to the centroids of different categories is first obtained. A relaxed Hamming distance (RHD)-based measurement is subsequently presented to measure the similarity and dissimilarity between the Latent Variable and centroids, not only allowing us to get the closed-form solutions but also encouraging the points belonging to the same class to be close, while those belonging to different classes to be far. Due to this novel prior, the category of the out-of-sample is also allowed to be simply assigned in the testing phase. Experimental results conducted on three real-world data sets demonstrate the effectiveness of the proposed method compared with state-of-the-art approaches.
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Visual Classification With Multikernel Shared Gaussian Process Latent Variable Model
IEEE Transactions on Cybernetics, 2019Co-Authors: Jinxing Li, Bob Zhang, Guangming Lu, David ZhangAbstract:Multiview learning methods often achieve improvement compared with single-view-based approaches in many applications. Due to the powerful nonlinear ability and probabilistic perspective of Gaussian process (GP), some GP-based multiview efforts were presented. However, most of these methods make a strong assumption on the kernel function (e.g., radial basis function), which limits the capacity of the real data Modeling. In order to address this issue, in this paper, we propose a novel multiview approach by combining a multikernel and GP Latent Variable Model. Instead of designing a deterministic kernel function, multiple kernel functions are established to automatically adapt various types of data. Considering a simple way of obtaining Latent Variables at the testing stage, a projection from the observed space to the Latent space as a back constraint has also been simultaneously introduced into the proposed method. Additionally, different from some existing methods which apply the classifiers off-line, a hinge loss is embedded into the Model to jointly learn the classification hyperplane, encouraging the Latent Variables belonging to the different classes to be separated. An efficient algorithm based on the gradient decent technique is constructed to optimize our method. Finally, we apply the proposed approach to three real-world datasets and the associated results demonstrate the effectiveness and superiority of our Model compared with other state-of-the-art methods.
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shared linear encoder based gaussian process Latent Variable Model for visual classification
ACM Multimedia, 2018Co-Authors: Bob Zhang, David ZhangAbstract:Multi-view learning has shown its powerful potential in many applications and achieved outstanding performances compared with the single-view based methods. In this paper, we propose a novel multi-view learning Model based on the Gaussian Process Latent Variable Model (GPLVM) to learn a shared Latent Variable in the manifold space with a linear and gaussian process prior based back projection. Different from existing GPLVM methods which only consider a mapping from the Latent space to the observed space, the proposed method simultaneously takes a back projection from the observation to the Latent Variable into account. Concretely, due to the various dimensions of different views, a projection for each view is first learned to linearly map its observation to a subspace. The gaussian process prior is then imposed on another transformation to non-linearly and efficiently map the learned subspace to a shared manifold space. In order to apply the proposed approach to the classification, a discriminative regularization is also embedded to exploit the label information. Experimental results on three real-world databases substantiate the effectiveness and superiority of the proposed approach as compared with several state-of-the-art approaches.
Maneesh Sahani - One of the best experts on this subject based on the ideXlab platform.
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Bayesian Manifold Learning: Locally Linear Latent Variable Model (LL-LVM)
2016Co-Authors: Mijung Park, Ahmad Qamar, Lars Buesing, Maneesh SahaniAbstract:Problems with high-dimensional data optimisation in high-d parameter space is computationally expensive and hard to find a global optimum Good news: in many cases, the intrinsic dimensionality is actually low datapoints are sampled from a low-dimensional manifold embedded in a high-dimensional space example: swiss roll Adapted from Roweis & Saul, Science, 2000 Manifold learning: attempts to uncover the manifold structure Non-probabilistic prior work idea: preserve geometric properties of local neighbourhoods limits: sensitive to noise due to lack of explicit Model heuristic methods to evaluate manifold dimensionality no measure of uncertainties in the estimates out-of-sample extension requires extra approximations Gaussian process Latent Variable Model (GP-LVM) idea: define a functional mapping from Latent space to data space using GP [1, 2] for data Y = [y1,...,ydy] ∈ Rn×dy and Latents X = [x1,...,xdx] ∈ Rn×dx, p(Y|X) = dy∏ k=1 N (yk|0,Knn + β−1In), where the i, jth element of the covariance matrix is k(xi,xj) = σ 2 f exp −12 dx∑ q=1 αq(xi,q − xj,q)2 where αq’s determine dimensionality of Latent space. limits: no intuitive preservation of local neighbourhood properties smoothness of manifold constrained by pre-chosen covariance function auxiliary Variable for variational inference (also restricts choice of cov func) Question Can we learn a manifold in a probabilistic and possibly Bayesian way, while preserving geometric properties of local neighbourhoods? Our approach: LL-LVM Key idea: there is a locally linear mapping between tangent spaces in low and high dimensional spaces high-dimensional space low-dimension space T yi yi y
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bayesian manifold learning the locally linear Latent Variable Model
Neural Information Processing Systems, 2015Co-Authors: Mijung Park, Wittawat Jitkrittum, Ahmad Qamar, Z Szabo, Lars Buesing, Maneesh SahaniAbstract:We introduce the Locally Linear Latent Variable Model (LL-LVM), a probabilistic Model for non-linear manifold discovery that describes a joint distribution over observations, their manifold coordinates and locally linear maps conditioned on a set of neighbourhood relationships. The Model allows straightforward variational optimisation of the posterior distribution on coordinates and locally linear maps from the Latent space to the observation space given the data. Thus, the LL-LVM encapsulates the local-geometry preserving intuitions that underlie non-probabilistic methods such as locally linear embedding (LLE). Its probabilistic semantics make it easy to evaluate the quality of hypothesised neighbourhood relationships, select the intrinsic dimensionality of the manifold, construct out-of-sample extensions and to combine the manifold Model with additional probabilistic Models that capture the structure of coordinates within the manifold.
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bayesian manifold learning the locally linear Latent Variable Model ll lvm
arXiv: Machine Learning, 2014Co-Authors: Mijung Park, Wittawat Jitkrittum, Ahmad Qamar, Z Szabo, Lars Buesing, Maneesh SahaniAbstract:We introduce the Locally Linear Latent Variable Model (LL-LVM), a probabilistic Model for non-linear manifold discovery that describes a joint distribution over observations, their manifold coordinates and locally linear maps conditioned on a set of neighbourhood relationships. The Model allows straightforward variational optimisation of the posterior distribution on coordinates and locally linear maps from the Latent space to the observation space given the data. Thus, the LL-LVM encapsulates the local-geometry preserving intuitions that underlie non-probabilistic methods such as locally linear embedding (LLE). Its probabilistic semantics make it easy to evaluate the quality of hypothesised neighbourhood relationships, select the intrinsic dimensionality of the manifold, construct out-of-sample extensions and to combine the manifold Model with additional probabilistic Models that capture the structure of coordinates within the manifold.
Neil D. Lawrence - One of the best experts on this subject based on the ideXlab platform.
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bayesian gaussian process Latent Variable Model
International Conference on Artificial Intelligence and Statistics, 2010Co-Authors: Michalis K. Titsias, Neil D. LawrenceAbstract:We introduce a variational inference framework for training the Gaussian process Latent Variable Model and thus performing Bayesian nonlinear dimensionality reduction. This method allows us to variationally integrate out the input Variables of the Gaussian process and compute a lower bound on the exact marginal likelihood of the nonlinear Latent Variable Model. The maximization of the variational lower bound provides a Bayesian training procedure that is robust to overfitting and can automatically select the dimensionality of the nonlinear Latent space. We demonstrate our method on real world datasets. The focus in this paper is on dimensionality reduction problems, but the methodology is more general. For example, our algorithm is immediately applicable for training Gaussian process Models in the presence of missing or uncertain inputs.
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learning for larger datasets with the gaussian process Latent Variable Model
International Conference on Artificial Intelligence and Statistics, 2007Co-Authors: Neil D. LawrenceAbstract:In this paper we apply the latest techniques in sparse Gaussian process regression (GPR) to the Gaussian process Latent Variable Model (GPLVM). We review three techniques and discuss how they may be implemented in the context of the GP-LVM. Each approach is then implemented on a well known benchmark data set and compared with earlier attempts to sparsify the Model.
Raquel Urtasun - One of the best experts on this subject based on the ideXlab platform.
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np draw a non parametric structured Latent Variable Model for image generation
Uncertainty in Artificial Intelligence, 2021Co-Authors: Xiaohui Zeng, Raquel Urtasun, Richard S Zemel, Sanja Fidler, Renjie LiaoAbstract:In this paper, we present a non-parametric structured Latent Variable Model for image generation, called NP-DRAW, which sequentially draws on a Latent canvas in a part-by-part fashion and then decodes the image from the canvas. Our key contributions are as follows. 1) We propose a non-parametric prior distribution over the appearance of image parts so that the Latent Variable ``what-to-draw'' per step becomes a categorical random Variable. This improves the expressiveness and greatly eases the learning compared to Gaussians used in the literature. 2) We Model the sequential dependency structure of parts via a Transformer, which is more powerful and easier to train compared to RNNs used in the literature; 3) We propose an effective heuristic parsing algorithm to pre-train the prior. Experiments on MNIST, Omniglot, CIFAR-10, and CelebA show that our method significantly outperforms previous structured image Models like DRAW and AIR and is competitive to other generic generative Models. Moreover, we show that our Model's inherent compositionality and interpretability bring significant benefits in the low-data learning regime and Latent space editing. Code is available at \url{https://github.com/ZENGXH/NPDRAW}.
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np draw a non parametric structured Latent Variable Model for image generation
arXiv: Computer Vision and Pattern Recognition, 2021Co-Authors: Xiaohui Zeng, Raquel Urtasun, Richard S Zemel, Sanja Fidler, Renjie LiaoAbstract:In this paper, we present a non-parametric structured Latent Variable Model for image generation, called NP-DRAW, which sequentially draws on a Latent canvas in a part-by-part fashion and then decodes the image from the canvas. Our key contributions are as follows. 1) We propose a non-parametric prior distribution over the appearance of image parts so that the Latent Variable ``what-to-draw'' per step becomes a categorical random Variable. This improves the expressiveness and greatly eases the learning compared to Gaussians used in the literature. 2) We Model the sequential dependency structure of parts via a Transformer, which is more powerful and easier to train compared to RNNs used in the literature. 3) We propose an effective heuristic parsing algorithm to pre-train the prior. Experiments on MNIST, Omniglot, CIFAR-10, and CelebA show that our method significantly outperforms previous structured image Models like DRAW and AIR and is competitive to other generic generative Models. Moreover, we show that our Model's inherent compositionality and interpretability bring significant benefits in the low-data learning regime and Latent space editing. Code is available at this https URL.
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implicit Latent Variable Model for scene consistent motion forecasting
arXiv: Computer Vision and Pattern Recognition, 2020Co-Authors: Raquel Urtasun, Sergio Casas, Cole Gulino, Simon Suo, Katie Luo, Renjie LiaoAbstract:In order to plan a safe maneuver an autonomous vehicle must accurately perceive its environment, and understand the interactions among traffic participants. In this paper, we aim to learn scene-consistent motion forecasts of complex urban traffic directly from sensor data. In particular, we propose to characterize the joint distribution over future trajectories via an implicit Latent Variable Model. We Model the scene as an interaction graph and employ powerful graph neural networks to learn a distributed Latent representation of the scene. Coupled with a deterministic decoder, we obtain trajectory samples that are consistent across traffic participants, achieving state-of-the-art results in motion forecasting and interaction understanding. Last but not least, we demonstrate that our motion forecasts result in safer and more comfortable motion planning.
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A constrained Latent Variable Model
2012 IEEE Conference on Computer Vision and Pattern Recognition, 2012Co-Authors: Aydin Varol, Mathieu Salzmann, Raquel UrtasunAbstract:Latent Variable Models provide valuable compact representations for learning and inference in many computer vision tasks. However, most existing Models cannot directly encode prior knowledge about the specific problem at hand. In this paper, we introduce a constrained Latent Variable Model whose generated output inherently accounts for such knowledge. To this end, we propose an approach that explicitly imposes equality and inequality constraints on the Model's output during learning, thus avoiding the computational burden of having to account for these constraints at inference. Our learning mechanism can exploit non-linear kernels, while only involving sequential closed-form updates of the Model parameters. We demonstrate the effectiveness of our constrained Latent Variable Model on the problem of non-rigid 3D reconstruction from monocular images, and show that it yields qualitative and quantitative improvements over several baselines.
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discriminative gaussian process Latent Variable Model for classification
International Conference on Machine Learning, 2007Co-Authors: Raquel Urtasun, Trevor DarrellAbstract:Supervised learning is difficult with high dimensional input spaces and very small training sets, but accurate classification may be possible if the data lie on a low-dimensional manifold. Gaussian Process Latent Variable Models can discover low dimensional manifolds given only a small number of examples, but learn a Latent space without regard for class labels. Existing methods for discriminative manifold learning (e.g., LDA, GDA) do constrain the class distribution in the Latent space, but are generally deterministic and may not generalize well with limited training data. We introduce a method for Gaussian Process Classification using Latent Variable Models trained with discriminative priors over the Latent space, which can learn a discriminative Latent space from a small training set.
