3 research outputs found
Robust Estimators under the Imprecise Dirichlet Model
Walley's Imprecise Dirichlet Model (IDM) for categorical data overcomes
several fundamental problems which other approaches to uncertainty suffer from.
Yet, to be useful in practice, one needs efficient ways for computing the
imprecise=robust sets or intervals. The main objective of this work is to
derive exact, conservative, and approximate, robust and credible interval
estimates under the IDM for a large class of statistical estimators, including
the entropy and mutual information.Comment: 16 LaTeX page
Robust Inference of Trees
This paper is concerned with the reliable inference of optimal
tree-approximations to the dependency structure of an unknown distribution
generating data. The traditional approach to the problem measures the
dependency strength between random variables by the index called mutual
information. In this paper reliability is achieved by Walley's imprecise
Dirichlet model, which generalizes Bayesian learning with Dirichlet priors.
Adopting the imprecise Dirichlet model results in posterior interval
expectation for mutual information, and in a set of plausible trees consistent
with the data. Reliable inference about the actual tree is achieved by focusing
on the substructure common to all the plausible trees. We develop an exact
algorithm that infers the substructure in time O(m^4), m being the number of
random variables. The new algorithm is applied to a set of data sampled from a
known distribution. The method is shown to reliably infer edges of the actual
tree even when the data are very scarce, unlike the traditional approach.
Finally, we provide lower and upper credibility limits for mutual information
under the imprecise Dirichlet model. These enable the previous developments to
be extended to a full inferential method for trees.Comment: 26 pages, 7 figure