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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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Related in: MedlinePlus

Posterior means of the first 20 regression coefficients as a function of the number of experiments for: (A) the MINE-like method; (B) MINE method; (C) MINE method with random orthonormal basis; (D) MINE method with random rotation.Each panel is averaged over all 1000 simulations with 10 zero (in blue) and 10 nonzero (in red). The first ten (red) are truly nonzero.
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pone-0110234-g004: Posterior means of the first 20 regression coefficients as a function of the number of experiments for: (A) the MINE-like method; (B) MINE method; (C) MINE method with random orthonormal basis; (D) MINE method with random rotation.Each panel is averaged over all 1000 simulations with 10 zero (in blue) and 10 nonzero (in red). The first ten (red) are truly nonzero.

Mentions: The second criterion involved identifying the correct sign and value for the nonzero beta values. This is evaluated by methods described earlier. Figures 4A–4D depict an average value for the first 20 values where the first ten are the nonzero coefficients and the second ten are zero and are shown as a comparison. As previously discussed, early detection is important.


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

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

Posterior means of the first 20 regression coefficients as a function of the number of experiments for: (A) the MINE-like method; (B) MINE method; (C) MINE method with random orthonormal basis; (D) MINE method with random rotation.Each panel is averaged over all 1000 simulations with 10 zero (in blue) and 10 nonzero (in red). The first ten (red) are truly nonzero.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0110234-g004: Posterior means of the first 20 regression coefficients as a function of the number of experiments for: (A) the MINE-like method; (B) MINE method; (C) MINE method with random orthonormal basis; (D) MINE method with random rotation.Each panel is averaged over all 1000 simulations with 10 zero (in blue) and 10 nonzero (in red). The first ten (red) are truly nonzero.
Mentions: The second criterion involved identifying the correct sign and value for the nonzero beta values. This is evaluated by methods described earlier. Figures 4A–4D depict an average value for the first 20 values where the first ten are the nonzero coefficients and the second ten are zero and are shown as a comparison. As previously discussed, early detection is important.

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