Research map / Learning theory and algorithms / Matrix and tensor methods
A Completely Tuning-Free and Robust Approach to Sparse Precision Matrix Estimation
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use completely tuning-free rank-Lasso (gRankLasso) instead of TIGER with fixed lambda for column-wise precision estimation | gRankLasso vs TIGER · Random graph, Gaussian, n=100 | spectral norm error | Helped |
| Increase column-wise heterogeneity of precision scale (tau from 1 to 3) and compare gRankLasso to TIGER (ablation) | gRankLasso vs TIGER · Random graph, n=100, d in {50,100,200} | Frobenius error ratio (gRankLasso/TIGER) | Helped |
| Add second-stage MCP non-convex penalty on top of gRankLasso (HBIC light tuning) (ablation) | gRankLasso · Decay graph Omega_ij=0.6^|i-j|, n=100, d in {25..400} | spectral norm error | Helped |
| Add second-stage MCP non-convex penalty on top of gRankLasso (ablation) | gRankLasso · Random/band/cluster graphs, Gaussian, n=100 | spectral norm error | No clear effect |
| Use rank loss (gRankLasso) instead of likelihood-based or CV-based methods under heavy-tailed data | gRankLasso / gRankMCP · Random graph, t-distribution nu=3, d=400 | Frobenius norm error | Helped |
| Use rank loss under heavy-tailed data with nu=10 | gRankLasso / gRankMCP · Random graph, t-distribution nu=10 | Frobenius norm error | No clear effect |
| Second-stage MCP penalty on gRankLasso (ablation) | Human gene network precision · Human gene network (n=60, d=100) | precision: 0.456 -> 0.518 | Helped |
| Use gRankLasso instead of GLasso on human gene network | gRankLasso · Human gene network (n=60, d=100) | precision: 0.255 (GLasso) -> 0.456 | Helped |
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