On the inverse association between the number of QTL and the trait-specific genomic relationship of a candidate to the training set.
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Bibliographic record
Abstract
Abstract Background Accuracy of genomic prediction depends on the heritability of the trait, the size of the training set, the relationship of the candidates to the training set, and the $$\text {Min}(N_{\text {QTL}},M_e)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mtext>Min</mml:mtext> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>N</mml:mi> <mml:mtext>QTL</mml:mtext> </mml:msub> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>M</mml:mi> <mml:mi>e</mml:mi> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , where $$N_{\text {QTL}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>N</mml:mi> <mml:mtext>QTL</mml:mtext> </mml:msub> </mml:math> is the number of QTL and $$M_e$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>M</mml:mi> <mml:mi>e</mml:mi> </mml:msub> </mml:math> is the number of independently segregating chromosomal segments. Due to LD, the number $$Q_e$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Q</mml:mi> <mml:mi>e</mml:mi> </mml:msub> </mml:math> of independently segregating QTL (effective QTL) can be lower than $$\text {Min}(N_{\text {QTL}},M_e)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mtext>Min</mml:mtext> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>N</mml:mi> <mml:mtext>QTL</mml:mtext> </mml:msub> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>M</mml:mi> <mml:mi>e</mml:mi> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> . In this paper, we show that $$Q_e$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Q</mml:mi> <mml:mi>e</mml:mi> </mml:msub> </mml:math> is inversely associated with the trait-specific genomic relationship of a candidate to the training set. This provides an explanation for the inverse association between $$Q_e$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Q</mml:mi> <mml:mi>e</mml:mi> </mml:msub> </mml:math> and the accuracy of prediction. Methods To quantify the genomic relationship of a candidate to all members of the training set, we considered the $$k^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>k</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> statistic that has been previously used for this purpose. It quantifies how well the marker covariate vector of a candidate can be represented as a linear combination of the rows of the marker covariate matrix of the training set. In this paper, we used Bayesian regression to make this statistic trait specific and argue that the trait-specific genomic relationship of a candidate to the training set is inversely associated with $$Q_e$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Q</mml:mi> <mml:mi>e</mml:mi> </mml:msub> </mml:math> . Simulation was used to demonstrate the dependence of the trait-specific $$k^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>k</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> statistic on $$Q_e$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Q</mml:mi> <mml:mi>e</mml:mi> </mml:msub> </mml:math> , which is related to $$N_{\text {QTL}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>N</mml:mi> <mml:mtext>QTL</mml:mtext> </mml:msub> </mml:math> . Conclusions The posterior distributions of the trait-specific $$k^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>k</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> statistic showed that the trait-specific genomic relationship between a candidate and the training set is inversely associated to $$Q_e$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Q</mml:mi> <mml:mi>e</mml:mi> </mml:msub> </mml:math> and $$N_{\text {QTL}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>N</mml:mi> <mml:mtext>QTL</mml:mtext> </mml:msub> </mml:math> . Further, we show that trait-specific genomic relationship between a candidate and the training set is directly related to the size of the training set.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it