Title: Automatic Bayesian Density Analysis,
Abstract: 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.