A Bayesian Multiresolution Independence Test for Continuous Variables

In this paper we present a method of computing the posterior probability of conditional independence of two or more continuous variables from data, examined at several resolutions. Our approach is motivated by the observation that the appearance of continuous data varies widely at various resolutions, producing very different independence estimates between the variables involved. Therefore, it is difficult to ascertain independence without examining data at several carefully selected resolutions. In our paper, we accomplish this using the exact computation of the posterior probability of independence, calculated analytically given a resolution. At each examined resolution, we assume a multinomial distribution with Dirichlet priors for the discretized table parameters, and compute the posterior using Bayesian integration. Across resolutions, we use a search procedure to approximate the Bayesian integral of probability over an exponential number of possible histograms. Our method genera...

• Type: Conference
• Year: 2001
• Where: UAI
• Authors: Dimitris Margaritis, Sebastian Thrun
• Keywords: Conditional Independence, Continuous Variables, Posterior Probability, UAI 2001, UAI 2008