Multi-View Oriented GPLVM: Expressiveness and Efficiency

• URL: http://arxiv.org/abs/2502.08253v1
• Date: Wed, 12 Feb 2025 09:49:25 GMT
• Title: Multi-View Oriented GPLVM: Expressiveness and Efficiency
• Authors: Zi Yang, Ying Li, Zhidi Lin, Michael Minyi Zhang, Pablo M. Olmos,
• Abstract summary: We introduce a new duality between the spectral density and the kernel function. We derive a generic and expressive kernel termed Next-Gen Spectral Mixture (NG-SM) for MV-GPLVMs. Our proposed method consistently outperforms state-of-the-art models in learning meaningful latent representations.
• Score: 8.459922325396155
• License:
• Abstract: The multi-view Gaussian process latent variable model (MV-GPLVM) aims to learn a unified representation from multi-view data but is hindered by challenges such as limited kernel expressiveness and low computational efficiency. To overcome these issues, we first introduce a new duality between the spectral density and the kernel function. By modeling the spectral density with a bivariate Gaussian mixture, we then derive a generic and expressive kernel termed Next-Gen Spectral Mixture (NG-SM) for MV-GPLVMs. To address the inherent computational inefficiency of the NG-SM kernel, we propose a random Fourier feature approximation. Combined with a tailored reparameterization trick, this approximation enables scalable variational inference for both the model and the unified latent representations. Numerical evaluations across a diverse range of multi-view datasets demonstrate that our proposed method consistently outperforms state-of-the-art models in learning meaningful latent representations.

Related papers

• Variational Learning of Gaussian Process Latent Variable Models through Stochastic Gradient Annealed Importance Sampling [22.256068524699472]
  In this work, we propose an Annealed Importance Sampling (AIS) approach to address these issues. We combine the strengths of Sequential Monte Carlo samplers and VI to explore a wider range of posterior distributions and gradually approach the target distribution. Experimental results on both toy and image datasets demonstrate that our method outperforms state-of-the-art methods in terms of tighter variational bounds, higher log-likelihoods, and more robust convergence.
  arXiv  Detail & Related papers  (2024-08-13T08:09:05Z)
• Preventing Model Collapse in Gaussian Process Latent Variable Models [11.45681373843122]
  This paper theoretically examines the impact of projection variance on model collapse through the lens of a linear FourierVM. We tackle model collapse due to inadequate kernel flexibility by integrating the spectral mixture (SM) kernel and a differentiable random feature (RFF) kernel approximation. The proposedVM, named advisedRFLVM, is evaluated across diverse datasets and consistently outperforms various competing models.
  arXiv  Detail & Related papers  (2024-04-02T06:58:41Z)
• Sample Complexity Characterization for Linear Contextual MDPs [67.79455646673762]
  Contextual decision processes (CMDPs) describe a class of reinforcement learning problems in which the transition kernels and reward functions can change over time with different MDPs indexed by a context variable. CMDPs serve as an important framework to model many real-world applications with time-varying environments. We study CMDPs under two linear function approximation models: Model I with context-varying representations and common linear weights for all contexts; and Model II with common representations for all contexts and context-varying linear weights.
  arXiv  Detail & Related papers  (2024-02-05T03:25:04Z)
• Gaussian Mixture Solvers for Diffusion Models [84.83349474361204]
  We introduce a novel class of SDE-based solvers called GMS for diffusion models. Our solver outperforms numerous SDE-based solvers in terms of sample quality in image generation and stroke-based synthesis.
  arXiv  Detail & Related papers  (2023-11-02T02:05:38Z)
• Heterogeneous Multi-Task Gaussian Cox Processes [61.67344039414193]
  We present a novel extension of multi-task Gaussian Cox processes for modeling heterogeneous correlated tasks jointly. A MOGP prior over the parameters of the dedicated likelihoods for classification, regression and point process tasks can facilitate sharing of information between heterogeneous tasks. We derive a mean-field approximation to realize closed-form iterative updates for estimating model parameters.
  arXiv  Detail & Related papers  (2023-08-29T15:01:01Z)
• GFlowNet-EM for learning compositional latent variable models [115.96660869630227]
  A key tradeoff in modeling the posteriors over latents is between expressivity and tractable optimization. We propose the use of GFlowNets, algorithms for sampling from an unnormalized density. By training GFlowNets to sample from the posterior over latents, we take advantage of their strengths as amortized variational algorithms.
  arXiv  Detail & Related papers  (2023-02-13T18:24:21Z)
• Tensor-based Multi-view Spectral Clustering via Shared Latent Space [14.470859959783995]
  Multi-view Spectral Clustering (MvSC) attracts increasing attention due to diverse data sources. New method for MvSC is proposed via a shared latent space from the Restricted Kernel Machine framework.
  arXiv  Detail & Related papers  (2022-07-23T17:30:54Z)
• Generalised Gaussian Process Latent Variable Models (GPLVM) with Stochastic Variational Inference [9.468270453795409]
  We study the doubly formulation of the BayesianVM model amenable with minibatch training. We show how this framework is compatible with different latent variable formulations and perform experiments to compare a suite of models. We demonstrate how we can train in the presence of massively missing data and obtain high-fidelity reconstructions.
  arXiv  Detail & Related papers  (2022-02-25T21:21:51Z)
• Scalable Variational Gaussian Processes via Harmonic Kernel Decomposition [54.07797071198249]
  We introduce a new scalable variational Gaussian process approximation which provides a high fidelity approximation while retaining general applicability. We demonstrate that, on a range of regression and classification problems, our approach can exploit input space symmetries such as translations and reflections. Notably, our approach achieves state-of-the-art results on CIFAR-10 among pure GP models.
  arXiv  Detail & Related papers  (2021-06-10T18:17:57Z)
• Sampling in Combinatorial Spaces with SurVAE Flow Augmented MCMC [83.48593305367523]
  Hybrid Monte Carlo is a powerful Markov Chain Monte Carlo method for sampling from complex continuous distributions. We introduce a new approach based on augmenting Monte Carlo methods with SurVAE Flows to sample from discrete distributions. We demonstrate the efficacy of our algorithm on a range of examples from statistics, computational physics and machine learning, and observe improvements compared to alternative algorithms.
  arXiv  Detail & Related papers  (2021-02-04T02:21:08Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.