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Instrumental Variable Regression on high-dimensional vector-proxy benchmark

0.1Structural MSEBGM-IV
-0.14281.49613.1354.7739May 7, 2026

Evaluation results

MethodLinks
BGM-IVConfounding level (ρ)=0.75, Sample size (n)=100002026.050.1
BGM-IVConfounding level (ρ)=0.9, Sample size (n)=100002026.050.1
BGM-IVConfounding level (ρ)=0.5, Sample size (n)=100002026.050.17
BGM-IVConfounding level (ρ)=0.25, Sample size (n)=50002026.050.19
BGM-IVConfounding level (ρ)=0.5, Sample size (n)=50002026.050.23
BGM-IVConfounding level (ρ)=0.1, Sample size (n)=100002026.050.25
BGM-IVConfounding level (ρ)=0.25, Sample size (n)=100002026.050.26
BGM-IVConfounding level (ρ)=0.75, Sample size (n)=50002026.050.27
BGM-IVConfounding level (ρ)=0.9, Sample size (n)=50002026.050.3
BGM-IVConfounding level (ρ)=0.1, Sample size (n)=50002026.050.32
BGM-IVConfounding level (ρ)=0.1, Sample size (n)=10002026.050.58
BGM-IVConfounding level (ρ)=0.25, Sample size (n)=10002026.050.61
BGM-IVConfounding level (ρ)=0.75, Sample size (n)=10002026.050.63
DFIVConfounding level (ρ)=0.25, Sample size (n)=100002026.050.65
DFIVConfounding level (ρ)=0.75, Sample size (n)=100002026.050.65
DFIVConfounding level (ρ)=0.5, Sample size (n)=100002026.050.66
BGM-IVConfounding level (ρ)=0.9, Sample size (n)=10002026.050.66
DFIVConfounding level (ρ)=0.9, Sample size (n)=100002026.050.66
BGM-IVConfounding level (ρ)=0.5, Sample size (n)=10002026.050.67
DFIVConfounding level (ρ)=0.1, Sample size (n)=50002026.050.68
DFIVConfounding level (ρ)=0.1, Sample size (n)=100002026.050.68
DFIVConfounding level (ρ)=0.9, Sample size (n)=50002026.050.69
DFIVConfounding level (ρ)=0.25, Sample size (n)=50002026.050.7
DFIVConfounding level (ρ)=0.5, Sample size (n)=50002026.050.7
DFIVConfounding level (ρ)=0.75, Sample size (n)=50002026.050.71
DFIVConfounding level (ρ)=0.75, Sample size (n)=10002026.050.73
DeepIVConfounding level (ρ)=0.9, Sample size (n)=100002026.050.73
DFIVConfounding level (ρ)=0.1, Sample size (n)=10002026.050.74
DFIVConfounding level (ρ)=0.25, Sample size (n)=10002026.050.74
DeepIVConfounding level (ρ)=0.25, Sample size (n)=100002026.050.74
DFIVConfounding level (ρ)=0.5, Sample size (n)=10002026.050.74
DFIVConfounding level (ρ)=0.9, Sample size (n)=10002026.050.74
DeepIVConfounding level (ρ)=0.1, Sample size (n)=100002026.050.75
DeepIVConfounding level (ρ)=0.5, Sample size (n)=100002026.050.75
DeepIVConfounding level (ρ)=0.75, Sample size (n)=100002026.050.75
KIVConfounding level (ρ)=0.1, Sample size (n)=100002026.050.84
KIVConfounding level (ρ)=0.25, Sample size (n)=100002026.050.84
KIVConfounding level (ρ)=0.5, Sample size (n)=100002026.050.84
KIVConfounding level (ρ)=0.75, Sample size (n)=100002026.050.84
KIVConfounding level (ρ)=0.9, Sample size (n)=100002026.050.84
KIVConfounding level (ρ)=0.1, Sample size (n)=50002026.050.9
KIVConfounding level (ρ)=0.25, Sample size (n)=50002026.050.9
KIVConfounding level (ρ)=0.5, Sample size (n)=50002026.050.9
KIVConfounding level (ρ)=0.75, Sample size (n)=50002026.050.9
KIVConfounding level (ρ)=0.9, Sample size (n)=50002026.050.91
KIVConfounding level (ρ)=0.9, Sample size (n)=10002026.051.06
KIVConfounding level (ρ)=0.25, Sample size (n)=10002026.051.07
KIVConfounding level (ρ)=0.5, Sample size (n)=10002026.051.07
KIVConfounding level (ρ)=0.75, Sample size (n)=10002026.051.07
KIVConfounding level (ρ)=0.1, Sample size (n)=10002026.051.08
DeepIVConfounding level (ρ)=0.25, Sample size (n)=50002026.051.1
DeepIVConfounding level (ρ)=0.75, Sample size (n)=50002026.051.1
DeepIVConfounding level (ρ)=0.9, Sample size (n)=50002026.051.1
DeepIVConfounding level (ρ)=0.5, Sample size (n)=50002026.051.11
DeepIVConfounding level (ρ)=0.1, Sample size (n)=50002026.051.12
DeepIVConfounding level (ρ)=0.9, Sample size (n)=10002026.051.37
DeepIVConfounding level (ρ)=0.1, Sample size (n)=10002026.051.38
DeepIVConfounding level (ρ)=0.5, Sample size (n)=10002026.051.38
DeepIVConfounding level (ρ)=0.25, Sample size (n)=10002026.051.39
DeepIVConfounding level (ρ)=0.75, Sample size (n)=10002026.051.39
DeepGMMConfounding level (ρ)=0.75, Sample size (n)=100002026.055.63
DeepGMMConfounding level (ρ)=0.25, Sample size (n)=100002026.055.64
DeepGMMConfounding level (ρ)=0.5, Sample size (n)=100002026.055.68
DeepGMMConfounding level (ρ)=0.9, Sample size (n)=100002026.055.69
DeepGMMConfounding level (ρ)=0.9, Sample size (n)=50002026.055.7
DeepGMMConfounding level (ρ)=0.1, Sample size (n)=100002026.055.74
DeepGMMConfounding level (ρ)=0.25, Sample size (n)=50002026.055.76
DeepGMMConfounding level (ρ)=0.75, Sample size (n)=50002026.055.77
DeepGMMConfounding level (ρ)=0.5, Sample size (n)=50002026.055.78
DeepGMMConfounding level (ρ)=0.1, Sample size (n)=50002026.055.92
DeepGMMConfounding level (ρ)=0.25, Sample size (n)=10002026.056.08
DeepGMMConfounding level (ρ)=0.1, Sample size (n)=10002026.056.12
DeepGMMConfounding level (ρ)=0.5, Sample size (n)=10002026.056.13
DeepGMMConfounding level (ρ)=0.9, Sample size (n)=10002026.056.13
DeepGMMConfounding level (ρ)=0.75, Sample size (n)=10002026.056.17