Bayesian Sparse Factor Analysis with Kernelized Observations
- URL: http://arxiv.org/abs/2006.00968v3
- Date: Wed, 27 Jan 2021 12:57:35 GMT
- Title: Bayesian Sparse Factor Analysis with Kernelized Observations
- Authors: Carlos Sevilla-Salcedo, Alejandro Guerrero-L\'opez, Pablo M. Olmos and
Vanessa G\'omez-Verdejo
- Abstract summary: Multi-view problems can be faced with latent variable models.
High-dimensionality and non-linear issues are traditionally handled by kernel methods.
We propose merging both approaches into single model.
- Score: 67.60224656603823
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Multi-view problems can be faced with latent variable models since they are
able to find low-dimensional projections that fairly capture the correlations
among the multiple views that characterise each datum. On the other hand,
high-dimensionality and non-linear issues are traditionally handled by kernel
methods, inducing a (non)-linear function between the latent projection and the
data itself. However, they usually come with scalability issues and exposition
to overfitting. Here, we propose merging both approaches into single model so
that we can exploit the best features of multi-view latent models and kernel
methods and, moreover, overcome their limitations.
In particular, we combine probabilistic factor analysis with what we refer to
as kernelized observations, in which the model focuses on reconstructing not
the data itself, but its relationship with other data points measured by a
kernel function. This model can combine several types of views (kernelized or
not), and it can handle heterogeneous data and work in semi-supervised
settings. Additionally, by including adequate priors, it can provide compact
solutions for the kernelized observations -- based in a automatic selection of
Bayesian Relevance Vectors (RVs) -- and can include feature selection
capabilities. Using several public databases, we demonstrate the potential of
our approach (and its extensions) w.r.t. common multi-view learning models such
as kernel canonical correlation analysis or manifold relevance determination.
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