%0 Journal Article %1 bravo_estimating_2009 %A Bravo, Héctor Corrada %A Wright, Stephen %A Eng, Kevin H. %A Keles, Sündüz %A Wahba, Grace %D 2009 %J Journal of Machine Learning Research %K Integer Learning, Machine covariance expression, gene matrix, phylogenetics, programming, structure tree %P 41--48 %T Estimating tree-structured covariance matrices via mixed-integer programming %U http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3212858/ %V 5 %X We present a novel method for estimating tree-structured covariance matrices directly from observed continuous data. Specifically, we estimate a covariance matrix from observations of p continuous random variables encoding a stochastic process over a tree with p leaves. A representation of these classes of matrices as linear combinations of rank-one matrices indicating object partitions is used to formulate estimation as instances of well-studied numerical optimization problems., In particular, our estimates are based on projection, where the covariance estimate is the nearest tree-structured covariance matrix to an observed sample covariance matrix. The problem is posed as a linear or quadratic mixed-integer program (MIP) where a setting of the integer variables in the MIP specifies a set of tree topologies of the structured covariance matrix. We solve these problems to optimality using efficient and robust existing MIP solvers., We present a case study in phylogenetic analysis of gene expression and a simulation study comparing our method to distance-based tree estimating procedures.

@article{bravo_estimating_2009, abstract = {We present a novel method for estimating tree-structured covariance matrices directly from observed continuous data. Specifically, we estimate a covariance matrix from observations of p continuous random variables encoding a stochastic process over a tree with p leaves. A representation of these classes of matrices as linear combinations of rank-one matrices indicating object partitions is used to formulate estimation as instances of well-studied numerical optimization problems., In particular, our estimates are based on projection, where the covariance estimate is the nearest tree-structured covariance matrix to an observed sample covariance matrix. The problem is posed as a linear or quadratic mixed-integer program (MIP) where a setting of the integer variables in the MIP specifies a set of tree topologies of the structured covariance matrix. We solve these problems to optimality using efficient and robust existing MIP solvers., We present a case study in phylogenetic analysis of gene expression and a simulation study comparing our method to distance-based tree estimating procedures.}, added-at = {2017-01-09T13:57:26.000+0100}, author = {Bravo, Héctor Corrada and Wright, Stephen and Eng, Kevin H. and Keles, Sündüz and Wahba, Grace}, biburl = {https://www.bibsonomy.org/bibtex/25ecd761ae95c40833411ca65f1422a23/yourwelcome}, interhash = {43665879f7a705a37d3c62c384cf1790}, intrahash = {5ecd761ae95c40833411ca65f1422a23}, issn = {1532-4435}, journal = {Journal of Machine Learning Research}, keywords = {Integer Learning, Machine covariance expression, gene matrix, phylogenetics, programming, structure tree}, pages = {41--48}, pmcid = {PMC3212858}, pmid = {22081761}, timestamp = {2017-01-09T14:01:11.000+0100}, title = {Estimating tree-structured covariance matrices via mixed-integer programming}, url = {http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3212858/}, urldate = {2012-07-28}, volume = 5, year = 2009 }