Automatic Bayesian Density Analysis

Making sense of a dataset in an automatic and unsupervised fashion is a challenging problem in statistics and AI. Classical approaches for density estimation are usually not flexible enough to deal with the uncertainty inherent to real-world data: they are often restricted to fixed latent interaction models and homogeneous likelihoods; they are sensitive to missing, corrupt and anomalous data; moreover, their expressiveness generally comes at the price of intractable inference. As a result, supervision from statisticians is usually needed to find the right model for the data. However, as domain experts do not necessarily have to be experts in statistics, we propose Automatic Bayesian Density Analysis (ABDA) to make density estimation accessible at large. ABDA automates the selection of adequate likelihood models from arbitrarily rich dictionaries while modeling their interactions via a deep latent structure adaptively learned from data as a sum-product network. ABDA casts uncertainty estimation at these local and global levels into a joint Bayesian inference problem, providing robust and yet tractable inference. Extensive empirical evidence shows that ABDA is a suitable tool for automatic exploratory analysis of heterogeneous tabular data, allowing for missing value estimation, statistical data type and likelihood discovery, anomaly detection and dependency structure mining, on top of providing accurate density estimation.