Abstract-The problem of composite binary hypothesis testing of Markov forest (or tree) distributions is considered. The worstcase type-II error exponent is derived under the Neyman-Pearson formulation. Under simple null hypothesis, the error exponent is derived in closed-form and is characterized in terms of the so-called bottleneck edge of the forest distribution. The least favorable distribution for detection is shown to be Markov on the second-best max-weight spanning tree with mutual information edge weights. A necessary and sufficient condition to have positive error exponent is derived.
In addition, we posed the structure learning problem for trees as a composite hypothesis testing problem REF and derived a closed-form expression for the ChernoffStein exponent in terms of the mutual information on the bottleneck edge.
Error exponents for composite hypothesis testing of Markov forest distributions
2010 IEEE International Symposium on Information Theory
2010 IEEE International Symposium on Information Theory
Mathematics Computer Science