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The ability to estimate joint, conditional and marginal probabilitydistributions over some set of variables is of great utility for many commonmachine learning tasks. However, estimating these distributions can bechallenging, particularly in the case of data containing a mix of discrete andcontinuous variables. This paper presents a non-parametric method forestimating these distributions directly from a dataset. The data are firstrepresented as a graph consisting of object nodes and attribute value nodes.Depending on the distribution to be estimated, an appropriate eigenvectorequation is then constructed. This equation is then solved to find thecorresponding stationary distribution of the graph, from which the requireddistributions can then be estimated and sampled from. The paper demonstrateshow the method can be applied to many common machine learning tasks includingclassification, regression, missing value imputation, outlier detection, randomvector generation, and clustering.

Using Eigencentrality to Estimate Joint, Conditional and Marginal Probabilities from Mixed-Variable Data: Method and Applications