Controlling for sparsity in sparse factor analysis models: adaptive latent feature sharing for piecewise linear dimensionality reduction
This work addresses the problem of flexible and interpretable dimensionality reduction for researchers in machine learning and data analysis, though it appears incremental as it builds on existing latent feature models.
The authors tackled the limitations of linear Gaussian exploratory tools like PCA and factor analysis by proposing adaptive latent feature sharing models (aFA and aPPCA) that allow explicit control over feature sparsity, resulting in faster inference algorithms and applications in tasks such as feature learning and fMRI analysis.
Ubiquitous linear Gaussian exploratory tools such as principle component analysis (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 dimensional data, they have been replaced in many settings by more flexible and still interpretable latent feature models. The Feature allocation is usually modelled using discrete latent variables assumed to follow either parametric Beta-Bernoulli distribution or Bayesian nonparametric prior. In this work we propose a simple and tractable parametric feature allocation model which can address key limitations of current latent feature decomposition techniques. The new framework allows for explicit control over the number of features used to express each point and enables a more flexible set of allocation distributions including feature allocations with different sparsity levels. This approach is used to derive a novel adaptive Factor analysis (aFA), as well as, an adaptive probabilistic principle component analysis (aPPCA) capable of flexible structure discovery and dimensionality reduction in a wide case of scenarios. We derive both standard Gibbs sampler, as well as, an expectation-maximization inference algorithms that converge orders of magnitude faster to a reasonable point estimate solution. The utility of the proposed aPPCA model is demonstrated for standard PCA tasks such as feature learning, data visualization and data whitening. We show that aPPCA and aFA can infer interpretable high level features both when applied on raw MNIST and when applied for interpreting autoencoder features. We also demonstrate an application of the aPPCA to more robust blind source separation for functional magnetic resonance imaging (fMRI).