Manifold Relevance Determination

By Andreas C. Damianou, Carl Henrik Ek, Michalis K. Titsias, Neil D. Lawrence. 2012

111 citations recorded by the source corpus.

In this paper we present a fully Bayesian latent variable model which exploits conditional nonlinear (in)-dependence structures to learn an efficient latent representation. The latent space is factorized to represent shared and private information from multiple views of the data. In contrast to previous approaches, we introduce a relaxation to the discrete segmentation and allow for a "softly" shared latent space. Further, Bayesian techniques allow us to automatically estimate the dimensionality of the latent spaces. The model is capable of capturing structure underlying extremely high dimensional spaces. This is illustrated by modelling unprocessed images with tenths of thousands of pixels. This also allows us to directly generate novel images from the trained model by sampling from the discovered latent spaces. We also demonstrate the model by prediction of human pose in an ambiguous setting. Our Bayesian framework allows us to perform disambiguation in a principled manner by including latent space priors which incorporate the dynamic nature of the data.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition

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Citations in the corpus

Deep Gaussian Processes (2012, methodology): “This covariance function assumes a different weight wq for each latent dimension and this can be exploited in a Bayesian training framework in order to “switch off” irrelevant dimensions by driving their corresponding weight to zero, thus helping towards automatically finding the structure of comple”
Bayesian group factor analysis with structured sparsity (2016, methodology): “The complexity of MRD is quadratic in the number of samples n per iteration using a sparse Gaussian process.”
Deep Variational Canonical Correlation Analysis (2016, methodology): “There is also a rich literature in modeling multi-view data using the same or similar graphical models behind VCCA/VCCA-private (Shon et al., 2006; Wang, 2007; Jia et al., 2010; Salzmann et al., 2010; Virtanen et al., 2011; Memisevic et al., 2012; Damianou et al., 2012; Klami et al., 2013).”
Assessment of algorithms for mitosis detection in breast cancer histopathology images (2014, unknown): “However, the classification results were relatively poor, probably because the assumption of independence between the classes does not hold, indicating that a method that jointly models samples and labels can be more promising (e.g. using Manifold Relevance Determination (Damianou et al., 2012)).”
Bayesian Canonical correlation analysis (2013, methodology): “(2012a) and Damianou et al. (2012) discussed the prior in more detail, presenting also extensions to more than two groups.”