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A MINE alternative to D-optimal designs for the linear model.

Bouffier AM, Arnold J, Schüttler HB - PLoS ONE (2014)

Bottom Line: Doing large-scale genomics experiments can be expensive, and so experimenters want to get the most information out of each experiment.Here we explore this idea in a simplified context, the linear model.We also establish in simulations with n<100, p=1000, σ=0.01 and 1000 replicates that these two variations of MINE also display a lower false positive rate than the MINE-like method and additionally, for a majority of the experiments, for the MINE method.

View Article: PubMed Central - PubMed

Affiliation: Institute of Bioinformatics, University of Georgia, Athens, Georgia, United States of America.

ABSTRACT
Doing large-scale genomics experiments can be expensive, and so experimenters want to get the most information out of each experiment. To this end the Maximally Informative Next Experiment (MINE) criterion for experimental design was developed. Here we explore this idea in a simplified context, the linear model. Four variations of the MINE method for the linear model were created: MINE-like, MINE, MINE with random orthonormal basis, and MINE with random rotation. Each method varies in how it maximizes the MINE criterion. Theorem 1 establishes sufficient conditions for the maximization of the MINE criterion under the linear model. Theorem 2 establishes when the MINE criterion is equivalent to the classic design criterion of D-optimality. By simulation under the linear model, we establish that the MINE with random orthonormal basis and MINE with random rotation are faster to discover the true linear relation with p regression coefficients and n observations when p>n. We also establish in simulations with n<100, p=1000, σ=0.01 and 1000 replicates that these two variations of MINE also display a lower false positive rate than the MINE-like method and additionally, for a majority of the experiments, for the MINE method.

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Graph of the number of significant nonzero regression coefficients averaged over 1000 replicates for: (A) the MINE-like method; (B) MINE method; (C) MINE method with random orthonormal basis; (D) MINE method with random rotation.Each graph identifies the number of replicates (y-axis) with a varying number of the nonzero  components as significant as a function of the number of experiments (x-axis). Blue corresponds to 70% correctly identified, red to 80%, green to 90% and purple to 100%.
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pone-0110234-g003: Graph of the number of significant nonzero regression coefficients averaged over 1000 replicates for: (A) the MINE-like method; (B) MINE method; (C) MINE method with random orthonormal basis; (D) MINE method with random rotation.Each graph identifies the number of replicates (y-axis) with a varying number of the nonzero components as significant as a function of the number of experiments (x-axis). Blue corresponds to 70% correctly identified, red to 80%, green to 90% and purple to 100%.

Mentions: The first criterion discerns if the methods correctly identify the nonzero values of as being significant or successful discovery as given by the test described above. A method is considered better or more successful the fewer experiments are needed to discover the truly nonzero regression coefficients. In Figure 3 there are four graphs provided (A–D) to display this criterion, and all iterations performed are shown.


A MINE alternative to D-optimal designs for the linear model.

Bouffier AM, Arnold J, Schüttler HB - PLoS ONE (2014)

Graph of the number of significant nonzero regression coefficients averaged over 1000 replicates for: (A) the MINE-like method; (B) MINE method; (C) MINE method with random orthonormal basis; (D) MINE method with random rotation.Each graph identifies the number of replicates (y-axis) with a varying number of the nonzero  components as significant as a function of the number of experiments (x-axis). Blue corresponds to 70% correctly identified, red to 80%, green to 90% and purple to 100%.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4214713&req=5

pone-0110234-g003: Graph of the number of significant nonzero regression coefficients averaged over 1000 replicates for: (A) the MINE-like method; (B) MINE method; (C) MINE method with random orthonormal basis; (D) MINE method with random rotation.Each graph identifies the number of replicates (y-axis) with a varying number of the nonzero components as significant as a function of the number of experiments (x-axis). Blue corresponds to 70% correctly identified, red to 80%, green to 90% and purple to 100%.
Mentions: The first criterion discerns if the methods correctly identify the nonzero values of as being significant or successful discovery as given by the test described above. A method is considered better or more successful the fewer experiments are needed to discover the truly nonzero regression coefficients. In Figure 3 there are four graphs provided (A–D) to display this criterion, and all iterations performed are shown.

Bottom Line: Doing large-scale genomics experiments can be expensive, and so experimenters want to get the most information out of each experiment.Here we explore this idea in a simplified context, the linear model.We also establish in simulations with n<100, p=1000, σ=0.01 and 1000 replicates that these two variations of MINE also display a lower false positive rate than the MINE-like method and additionally, for a majority of the experiments, for the MINE method.

View Article: PubMed Central - PubMed

Affiliation: Institute of Bioinformatics, University of Georgia, Athens, Georgia, United States of America.

ABSTRACT
Doing large-scale genomics experiments can be expensive, and so experimenters want to get the most information out of each experiment. To this end the Maximally Informative Next Experiment (MINE) criterion for experimental design was developed. Here we explore this idea in a simplified context, the linear model. Four variations of the MINE method for the linear model were created: MINE-like, MINE, MINE with random orthonormal basis, and MINE with random rotation. Each method varies in how it maximizes the MINE criterion. Theorem 1 establishes sufficient conditions for the maximization of the MINE criterion under the linear model. Theorem 2 establishes when the MINE criterion is equivalent to the classic design criterion of D-optimality. By simulation under the linear model, we establish that the MINE with random orthonormal basis and MINE with random rotation are faster to discover the true linear relation with p regression coefficients and n observations when p>n. We also establish in simulations with n<100, p=1000, σ=0.01 and 1000 replicates that these two variations of MINE also display a lower false positive rate than the MINE-like method and additionally, for a majority of the experiments, for the MINE method.

Show MeSH
Related in: MedlinePlus