Table 5.

Mean RPE by regularization parameter (λ), under three estimation approaches: 1. with no rank constraints, 2. with rank constraint for $𝕏$ but independent models for each entry of $𝕐$, and 3. with low-rank dependence for both $𝕏$ and $𝕐$ (reproduced from Table 2).

1. Unconstrained $𝕏$, unconstrained $𝕐$
RPE (std error)	λ = 0	λ = 0.5	λ = 1	λ = 5	λ = 50
N = 120, SNR = 5	NA	0.64 (0.01)	0.64 (0.01)	0.63 (0.01)	0.64 (0.01)
N = 120, SNR = 1	NA	1.14 (0.01)	1.14 (0.01)	1.11 (0.01)	0.99 (0.01)
N = 30, SNR = 5	NA	0.91 (0.01)	0.91 (0.01)	0.91 (0.01)	0.91 (0.01)
N = 30, SNR = 1	NA	1.00 (0.01)	1.00 (0.01)	1.00 (0.01)	0.99 (0.01)
2. Constrained $𝕏$, unconstrained $𝕐$
RPE (std error)	λ = 0	λ = 0.5	λ = 1	λ = 5	λ = 50
N = 120, SNR = 5	NA	0.30 (0.01)	0.29 (0.01)	0.27 (0.01)	0.38 (0.01)
N = 120, SNR = 1	NA	1.72 (0.01)	1.62 (0.01)	1.30 (0.01)	0.88 (0.01)
N = 30, SNR = 5	NA	0.91 (0.01)	0.90 (0.01)	0.87 (0.01)	0.86 (0.01)
N = 30, SNR = 1	NA	1.20 (0.01)	1.18 (0.01)	1.12 (0.01)	1.00 (0.01)
3. Constrained $𝕏$, Constrained $𝕐$
RPE (std error)	λ = 0	λ = 0.5	λ = 1	λ = 5	λ = 50
N = 120, SNR = 5	0.04 (0.01)	0.04 (0.01)	0.04 (0.01)	0.05 (0.01)	0.20 (0.01)
N = 120, SNR = 1	0.52 (0.01)	0.52 (0.01)	0.52 (0.01)	0.52 (0.01)	0.59 (0.01)
N = 30, SNR = 5	1.64 (0.12)	0.74 (0.05)	0.70 (0.04)	0.63 (0.02)	0.77 (0.01)
N = 30, SNR = 1	1.90 (0.15)	1.07 (0.04)	1.03 (0.04)	0.92 (0.02)	0.91 (0.01)