notesum.ai

Published at November 29

Another look at inference after prediction

stat.ML

cs.LG

Released Date: November 29, 2024

Authors: Jessica Gronsbell¹, Jianhui Gao¹, Yaqi Shi¹, Zachary R. McCaw², David Cheng³

Aff.: ¹Department of Statistical Sciences, University of Toronto; ²Department of Biostatistics, UNC Chapel Hill; ³Biostatistics Center, Massachusetts General Hospital

Arxiv: http://arxiv.org/pdf/2411.19908v1

Scenario 1a
	Labeled set size
Method	1000	2000	3000	4000	5000
$\hat{\bm{\gamma}}^{\text{\tiny{all}}}$	-0.181	0.124	0.650	0.430	0.165
$\hat{\bm{\beta}}^{\text{\tiny{lab}}}$	0.035	-0.042	0.015	0.005	-0.005
$\hat{\bm{\beta}}^{\text{\tiny{PPI}}}$	0.004	0.010	-0.004	-0.018	-0.001
$\hat{\bm{\beta}}^{\text{\tiny{PPI}}_{a}}$	0.007	0.000	0.002	-0.009	-0.003
$\hat{\bm{\beta}}^{\text{\tiny{CC}}}$	0.007	0.000	0.002	-0.009	-0.003
Scenario 1b
$\hat{\bm{\gamma}}^{\text{\tiny{all}}}$	-1.070	0.181	0.426	-0.423	-1.205
$\hat{\bm{\beta}}^{\text{\tiny{lab}}}$	0.008	0.002	-0.016	-0.001	0.004
$\hat{\bm{\beta}}^{\text{\tiny{PPI}}}$	0.007	-0.001	-0.003	-0.008	-0.010
$\hat{\bm{\beta}}^{\text{\tiny{PPI}}_{a}}$	0.007	0.000	-0.007	-0.006	-0.003
$\hat{\bm{\beta}}^{\text{\tiny{CC}}}$	0.006	0.000	-0.007	-0.006	-0.003
Scenario 2a
$\hat{\bm{\gamma}}^{\text{\tiny{all}}}$	-46.980	-47.523	-45.946	-46.725	-47.695
$\hat{\bm{\beta}}^{\text{\tiny{lab}}}$	-0.033	-0.023	0.027	0.004	0.005
$\hat{\bm{\beta}}^{\text{\tiny{PPI}}}$	-0.023	-0.009	-0.003	-0.032	-0.003
$\hat{\bm{\beta}}^{\text{\tiny{PPI}}_{a}}$	-0.024	-0.012	0.006	-0.018	0.001
$\hat{\bm{\beta}}^{\text{\tiny{CC}}}$	-0.030	-0.016	0.016	-0.007	0.003
Scenario 2b
$\hat{\bm{\gamma}}^{\text{\tiny{all}}}$	-64.272	-64.115	-63.307	-63.759	-64.627
$\hat{\bm{\beta}}^{\text{\tiny{lab}}}$	-0.012	-0.003	0.002	0.012	0.013
$\hat{\bm{\beta}}^{\text{\tiny{PPI}}}$	0.000	0.001	-0.006	0.012	0.009
$\hat{\bm{\beta}}^{\text{\tiny{PPI}}_{a}}$	-0.001	0.000	-0.004	0.012	0.010
$\hat{\bm{\beta}}^{\text{\tiny{CC}}}$	-0.014	-0.006	-0.003	0.011	0.010