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Multi-View Oriented GPLVM: Expressiveness and Efficiency
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Proposes NG-MVLVM, a multi-view GPLVM using a universal (non-PSD-constrained) Bochner duality, a bivariate Gaussian mixture spectral density (NG-SM kernel), an unbiased differentiable random Fourier feature approximation with a two-step reparameterization, and sampling-based variational inference.
Problem
MV-GPLVMs have limited kernel expressiveness (stationary kernels) and high computational cost on large multi-view datasets, limiting unified latent representation learning.
Approach
A new universal Bochner duality relaxes the PSD spectral density requirement, allowing a bivariate Gaussian mixture spectral density whose induced kernel admits a closed-form random Fourier feature map, enabling scalable, differentiable variational inference over kernel hyperparameters and latent variables.
Key results
- On multi-view image/text benchmarks, NG-MVLVM reports KNN accuracy 82.72% on MNIST vs 81.85% for MV-ARFLVM and 85.31% on BRIDGES vs 83.42%.
- On NEWSGROUPS, NG-MVLVM and MV-ARFLVM both reach 100% accuracy; on CIFAR SVM accuracy is 32.47% vs MMVAE 34.73% (MMVAE better).
- The method claims lower wall-time than MV-DGPLVM and improved KNN accuracy and lower MSE in wireless channel compression, though exact numbers are shown only in figures.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use NG-SM instead of the MV-ARFLVM kernel | MV-GPLVM · BRIDGES | KNN accuracy: 83.42 $\pm$ 1.53 -> 85.31 $\pm$ 1.47 | Helped |
| Use NG-SM instead of the MV-ARFLVM kernel | MV-GPLVM · BRIDGES | SVM accuracy: 86.21 $\pm$ 7.59 -> 87.49 $\pm$ 1.76 | Helped |
| Use NG-SM instead of the MV-ARFLVM kernel | MV-GPLVM · CIFAR | KNN accuracy: 35.71 $\pm$ 0.59 -> 36.02 $\pm$ 0.34 | Helped |
| Use NG-SM instead of the MMVAE representation | MV-GPLVM · CIFAR | SVM accuracy: 34.73 $\pm$ 1.64 -> 32.47 $\pm$ 0.96 | Hurt |
| Use NG-SM instead of the MV-ARFLVM kernel | MV-GPLVM · MNIST | KNN accuracy: 81.85 $\pm$ 1.58 -> 82.72 $\pm$ 0.61 | Helped |
| Use NG-SM instead of the MV-ARFLVM kernel | MV-GPLVM · MNIST | SVM accuracy: 59.51 $\pm$ 2.43 -> 60.14 $\pm$ 1.11 | Helped |
| Use NG-SM instead of the MV-ARFLVM kernel | MV-GPLVM · NEWSGROUPS | KNN accuracy: 100.0 $\pm$ 0.00 -> 100.0 $\pm$ 0.00 | No clear effect |
| Use NG-SM instead of the MV-ARFLVM kernel | MV-GPLVM · NEWSGROUPS | SVM accuracy: 100.0 $\pm$ 0.00 -> 100.0 $\pm$ 0.00 | No clear effect |
| Use NG-SM instead of the MV-ARFLVM kernel | MV-GPLVM · YALE | KNN accuracy: 78.86 $\pm$ 2.23 -> 83.87 $\pm$ 1.44 | Helped |
| Use NG-SM instead of the MVAE representation | MV-GPLVM · YALE | SVM accuracy: 65.13 $\pm$ 2.34 -> 64.81 $\pm$ 2.50 | Hurt |
Surprising findings
- On CIFAR SVM accuracy, MMVAE (34.73%) outperforms the proposed method (32.47%).
- MV-DGPLVM shows large variance and instability across datasets despite its deep architecture.
Limitations
- Kernel hyperparameter and mixture-component choices (Q, L) affect performance; sensitivity not fully characterized in main text.
- Gains are not uniform: several baselines win on individual metrics (e.g., MMVAE on CIFAR SVM, MVAE on YALE SVM).
Experimental setup
Datasets: MNIST CIFAR YALE NEWSGROUPS BRIDGES QuaDRiGa wireless channel simulation (synthetic)
Benchmarks: MNIST CIFAR YALE NEWSGROUPS BRIDGES QuaDRiGa channel compression
Metrics: KNN accuracy SVM accuracy logistic regression accuracy mean squared error wall-time
Baselines: MV-ARFLVM MV-DGPLVM MVAE MMVAE MV-NGPLVM
Builds on: spectral mixture kernel bivariate spectral mixture kernel random Fourier features ARFLVM MV-GPLVM
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