  The ability to estimate joint, conditional and marginal probability
distributions over some set of variables is of great utility for many common
machine learning tasks. However, estimating these distributions can be
challenging, particularly in the case of data containing a mix of discrete and
continuous variables. This paper presents a non-parametric method for
estimating these distributions directly from a dataset. The data are first
represented as a graph consisting of object nodes and attribute value nodes.
Depending on the distribution to be estimated, an appropriate eigenvector
equation is then constructed. This equation is then solved to find the
corresponding stationary distribution of the graph, from which the required
distributions can then be estimated and sampled from. The paper demonstrates
how the method can be applied to many common machine learning tasks including
classification, regression, missing value imputation, outlier detection, random
vector generation, and clustering.
