Adaptive probabilistic principal component analysis
This work provides an incremental improvement for passive health monitoring using sensor data by making probabilistic PCA more flexible and interpretable.
The authors tackled the problem of rigid dimensionality reduction in linear Gaussian latent variable models by developing a nonparametric latent feature Gaussian variable model that adapts complexity with data, resulting in a locally adaptive probabilistic PCA (A-PPCA) that projects data onto varying subspaces.
Using the linear Gaussian latent variable model as a starting point we relax some of the constraints it imposes by deriving a nonparametric latent feature Gaussian variable model. This model introduces additional discrete latent variables to the original structure. The Bayesian nonparametric nature of this new model allows it to adapt complexity as more data is observed and project each data point onto a varying number of subspaces. The linear relationship between the continuous latent and observed variables make the proposed model straightforward to interpret, resembling a locally adaptive probabilistic PCA (A-PPCA). We propose two alternative Gibbs sampling procedures for inference in the new model and demonstrate its applicability on sensor data for passive health monitoring.