Bayesian Sparse Latent Factor Model (work in pregress)

Currently, this code runs using the fixed number of latent factors, utilizing an IBP prior only for imposing sparseness on factor loadings.

Bayesian Sparse Latent Factor Model using an IBP prior with a nonparametric modeling of the latent factor distribution.

This code tries to implement a sparse multivriate latent factor model, with an extension for regression components based on covariates. It follows the model specifications in Lucas et al.(2006) and Carvalho et al. (2008) but I attempted to use an IBP prior for a posterior inference on the number of latent factors instead of using a spike-slab prior used in the papers.

This model imposes explicit sparseness on the factor loading matrix. A simple linear-gaussian model imposing sparseness on latent factors (factor scores) rather than on factor loadings is available in IBP_Linear_Gaussian_Latent_Factor_Model.

The IBP-based factor model components were constructed based on Knowles and Ghahrmani (2011) and its MATLAB code.

The nonparametric extension on latent factors (factor scores) for adaptating non-Gaussianity in data was coded following the specifications in Carvalho et al. (2008) (utilize a Dirichlet Process Mixture Model on latent factors) but I was not sure I did the math correctly and this python code runs a little slow. It needs to be updated and validated.

For example usage, run

python demo.py

This demo is based on a simulated data set consisting of 6x6 images in Griffiths and Ghahramani (2011). The default setting assumes Gaussian latent factors.

The demo output will be saved as figures using David Andrzejewski's code (scaledimage.py) that mimics MATLAB imagesc().