  The commonly used latent space embedding techniques, such as Principal
Component Analysis, Factor Analysis, and manifold learning techniques, are
typically used for learning effective representations of homogeneous data.
However, they do not readily extend to heterogeneous data that are a
combination of numerical and categorical variables, e.g., arising from linked
GPS and text data. In this paper, we are interested in learning probabilistic
generative models from high-dimensional heterogeneous data in an unsupervised
fashion. The learned generative model provides latent unified representations
that capture the factors common to the multiple dimensions of the data, and
thus enable fusing multimodal data for various machine learning tasks.
Following a Bayesian approach, we propose a general framework that combines
disparate data types through the natural parameterization of the exponential
family of distributions. To scale the model inference to millions of instances
with thousands of features, we use the Laplace-Bernstein approximation for
posterior computations involving nonlinear link functions. The proposed
algorithm is presented in detail for the commonly encountered heterogeneous
datasets with real-valued (Gaussian) and categorical (multinomial) features.
Experiments on two high-dimensional and heterogeneous datasets (NYC Taxi and
MovieLens-10M) demonstrate the scalability and competitive performance of the
proposed algorithm on different machine learning tasks such as anomaly
detection, data imputation, and recommender systems.
