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Ubiquitous linear Gaussian exploratory tools such as principle componentanalysis (PCA) and factor analysis (FA) remain widely used as tools for:exploratory analysis, pre-processing, data visualization and related tasks.However, due to their rigid assumptions including crowding of high dimensionaldata, they have been replaced in many settings by more flexible and stillinterpretable latent feature models. The Feature allocation is usually modelledusing discrete latent variables assumed to follow either parametricBeta-Bernoulli distribution or Bayesian nonparametric prior. In this work wepropose a simple and tractable parametric feature allocation model which canaddress key limitations of current latent feature decomposition techniques. Thenew framework allows for explicit control over the number of features used toexpress each point and enables a more flexible set of allocation distributionsincluding feature allocations with different sparsity levels. This approach isused to derive a novel adaptive Factor analysis (aFA), as well as, an adaptiveprobabilistic principle component analysis (aPPCA) capable of flexiblestructure discovery and dimensionality reduction in a wide case of scenarios.We derive both standard Gibbs sampler, as well as, an expectation-maximizationinference algorithms that converge orders of magnitude faster to a reasonablepoint estimate solution. The utility of the proposed aPPCA model isdemonstrated for standard PCA tasks such as feature learning, datavisualization and data whitening. We show that aPPCA and aFA can inferinterpretable high level features both when applied on raw MNIST and whenapplied for interpreting autoencoder features. We also demonstrate anapplication of the aPPCA to more robust blind source separation for functionalmagnetic resonance imaging (fMRI).

Controlling for sparsity in sparse factor analysis models: adaptive latent feature sharing for piecewise linear dimensionality reduction