Integrating Exponential Dispersion Models to Latent Structures

Jan 10, 2017, 1:00 pm2:30 pm
Event Description

Latent variable models have two basic components: a latent structure encoding a hypothesized complex pattern and an observation model capturing the data distribution. With the advancements in machine learning and increasing availability of resources, we are able to perform inference in deeper and more sophisticated latent variable models. In most cases, these models are designed with a particular application in mind; hence, they tend to have restrictive observation models. The challenge, surfaced with the increasing diversity of data sets, is to generalize these latent models to work with different data types. We aim to address this problem by utilizing exponential dispersion models (EDMs) and proposing mechanisms for incorporating them into latent structures.
First, we show that the common EDM families can be expressed as a divergence from its mean in the dual domain. In particular, we argue that each EDM family induces a unique topology. For example, the Gaussian family relates to the Euclidean topology. We parametrize classes of EDM families in terms of the induced topology. We then propose an adaptive algorithm (AdaCluster) for clustering heterogeneous data sets. AdaCluster can, for instance, identify if the underlying distribution of a multi-modal positive continuous attribute is gamma, Gaussian or inverse-Gaussian.
Next, we generalize a Bayesian non-negative matrix factorization model (Poisson factorization) to various data types using EDMs. Poisson factorization has been successfully used to uncover the activity patterns in large scale problems like the Netflix recommendation problem. We extend the original model to other domains such as genomics and finance. Furthermore, our model decouples the preference and activity patterns–effectively distinguishing how much someone is interested in seeing a given movie and what rating she would give to the movie.
Lastly, we use the Poisson factorization and EDMs within the context of missing data. We show that an arbitrary data-generating model with EDM output–such as Gaussian mixture model, probabilistic matrix factorization, Poisson mixture model or linear regression model–can be coupled with a Poisson factorization encoding the missing-data pattern. In particular, we argue that the heteroscedastic impact of missing-data pattern on the dispersion of observation variable can be captured with the proposed model