Debiased Lasso Simulation Visualization
cv error plot for lasso
cv error plot
lambda_lse, lambda_min
hetamap
Sample Size Experiment
Basic Experimental Setup
- n: 100 to 1000, incrementing by 100
- p: Fixed at 1000
- Number of signal variables: 3
- Signal strength: 1
- Intercept: 1
- Error term: N(0,1)
- Design matrix Xij : N(0,1)
only global seed : set.seed(42)
Overall RMSE
## Rows: 10 Columns: 5
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## dbl (5): n, Lasso_min, Debiased_min, Lasso_1se, Debiased_1se
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
## Rows: 10 Columns: 5
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## dbl (5): n, Lasso_min, Debiased_min, Lasso_1se, Debiased_1se
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
## Rows: 10 Columns: 5
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## dbl (5): n, Lasso_min, Debiased_min, Lasso_1se, Debiased_1se
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
## Rows: 10 Columns: 5
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## dbl (5): n, Lasso_min, Debiased_min, Lasso_1se, Debiased_1se
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.## # A tibble: 10 × 5
## n Lasso_min Debiased_min Lasso_1se Debiased_1se
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 100 0.0199 0.0999 0.0291 0.121
## 2 200 0.0109 0.0723 0.0161 0.0808
## 3 300 0.0111 0.0592 0.0139 0.0635
## 4 400 0.0077 0.0511 0.011 0.0528
## 5 500 0.0084 0.0472 0.0115 0.0497
## 6 600 0.0057 0.0415 0.0083 0.0426
## 7 700 0.0047 0.0389 0.0098 0.0406
## 8 800 0.0064 0.0338 0.0085 0.0344
## 9 900 0.0053 0.0334 0.0084 0.0342
## 10 1000 0.0062 0.0299 0.0069 0.0318## # A tibble: 10 × 5
## n Lasso_min Debiased_min Lasso_1se Debiased_1se
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 100 0.357 0.152 0.531 0.16
## 2 200 0.193 0.0756 0.293 0.0692
## 3 300 0.195 0.0954 0.253 0.0871
## 4 400 0.139 0.0245 0.201 0.0268
## 5 500 0.148 0.0387 0.210 0.0393
## 6 600 0.104 0.0324 0.151 0.0337
## 7 700 0.0825 0.0304 0.180 0.0278
## 8 800 0.114 0.0261 0.154 0.0247
## 9 900 0.095 0.021 0.153 0.0224
## 10 1000 0.0825 0.0359 0.125 0.0338## # A tibble: 10 × 5
## n Lasso_min Debiased_min Lasso_1se Debiased_1se
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 100 0.0036 0.0998 0 0.121
## 2 200 0.0027 0.0723 0 0.0809
## 3 300 0.003 0.0591 0.0001 0.0634
## 4 400 0.0009 0.0512 0 0.0528
## 5 500 0.0023 0.0473 0 0.0497
## 6 600 0.0008 0.0415 0 0.0426
## 7 700 0.0013 0.0389 0 0.0407
## 8 800 0.0013 0.0338 0 0.0345
## 9 900 0.0009 0.0334 0 0.0342
## 10 1000 0.0043 0.0299 0.0008 0.0318## # A tibble: 10 × 5
## n Lasso_min Debiased_min Lasso_1se Debiased_1se
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 100 0.0036 0.0998 0 0.121
## 2 200 0.0027 0.0723 0 0.0809
## 3 300 0.003 0.0591 0.0001 0.0634
## 4 400 0.0009 0.0512 0 0.0528
## 5 500 0.0023 0.0473 0 0.0497
## 6 600 0.0008 0.0415 0 0.0426
## 7 700 0.0013 0.0389 0 0.0407
## 8 800 0.0013 0.0338 0 0.0345
## 9 900 0.0009 0.0334 0 0.0342
## 10 1000 0.0043 0.0299 0.0008 0.0318independent seed : set.seed(42)
selected value
## Rows: 4 Columns: 13
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (1): Method
## dbl (12): Overall_Mean, Overall_SD, Overall_Min, Overall_Max, Signal_Mean, S...
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.## # A tibble: 4 × 13
## Method Overall_Mean Overall_SD Overall_Min Overall_Max Signal_Mean Signal_SD
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Debiase… 0.0547 0.0263 0.0327 0.113 0.0432 0.0285
## 2 Debiase… 0.0478 0.0164 0.0316 0.0790 0.0412 0.0282
## 3 Lasso_1… 0.0110 0.00338 0.00633 0.0165 0.199 0.0600
## 4 Lasso_m… 0.00755 0.00344 0.00438 0.0155 0.120 0.0408
## # ℹ 6 more variables: Signal_Min <dbl>, Signal_Max <dbl>, Null_Mean <dbl>,
## # Null_SD <dbl>, Null_Min <dbl>, Null_Max <dbl>monte_carlo : avg of 50 seeds
overall RMSE
signal RMSE
null RMSE
selected value
## Rows: 4 Columns: 13
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (1): Method
## dbl (12): Overall_Mean, Overall_SD, Overall_Min, Overall_Max, Signal_Mean, S...
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.## # A tibble: 4 × 13
## Method Overall_Mean Overall_SD Overall_Min Overall_Max Signal_Mean Signal_SD
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Debiase… 0.0547 0.0263 0.0327 0.113 0.0432 0.0285
## 2 Debiase… 0.0478 0.0164 0.0316 0.079 0.0412 0.0282
## 3 Lasso_1… 0.011 0.0034 0.0063 0.0165 0.199 0.06
## 4 Lasso_m… 0.0075 0.0034 0.0044 0.0155 0.120 0.0408
## # ℹ 6 more variables: Signal_Min <dbl>, Signal_Max <dbl>, Null_Mean <dbl>,
## # Null_SD <dbl>, Null_Min <dbl>, Null_Max <dbl>Sparsity Experiment
Basic Experimental Setup
- n: Fixed at 1000
- p: Fixed at 1000
- Number of signal variables: (3, 5, 10, 15, 20, 30, 40, 50)
- Signal strength: 1
- Intercept: 1
- Error term: N(0,1)
- Design matrix Xij : N(0,1)
only global seed : set.seed(42)
null RMSE
selected value
## Rows: 4 Columns: 13
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (1): Method
## dbl (12): Overall_Mean, Overall_SD, Overall_Min, Overall_Max, Signal_Mean, S...
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.## # A tibble: 4 × 13
## Method Overall_Mean Overall_SD Overall_Min Overall_Max Signal_Mean Signal_SD
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Debiase… 0.0333 0.0009 0.0321 0.0348 0.0286 0.0099
## 2 Debiase… 0.0312 0.0012 0.03 0.0333 0.0291 0.0097
## 3 Lasso_1… 0.0132 0.0041 0.007 0.0196 0.103 0.0205
## 4 Lasso_m… 0.0107 0.0047 0.0041 0.0183 0.0728 0.0098
## # ℹ 6 more variables: Signal_Min <dbl>, Signal_Max <dbl>, Null_Mean <dbl>,
## # Null_SD <dbl>, Null_Min <dbl>, Null_Max <dbl>monte_carlo : avg of 50 seeds
overall RMSE
signal RMSE
null RMSE
selected value
Signal Strength experiment
Basic Experimental Setup
- n: Fixed at 1000
- p: Fixed at 1000
- Number of signal variables: 3
- Signal strength: (0.3, 0.5, 1, 2, 3, 4, 5)
- Intercept: 1
- Error term: N(0,1)
- Design matrix Xij : N(0,1)
only global seed : set.seed(42)
overall RMSE
signal RMSE
null RMSE
selected value
## Rows: 4 Columns: 13
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (1): Method
## dbl (12): Overall_Mean, Overall_SD, Overall_Min, Overall_Max, Signal_Mean, S...
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.## # A tibble: 4 × 13
## Method Overall_Mean Overall_SD Overall_Min Overall_Max Signal_Mean Signal_SD
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Debiase… 0.0327 0.00160 0.0308 0.0350 0.0298 0.0115
## 2 Debiase… 0.0315 0.00165 0.0295 0.0342 0.0289 0.0114
## 3 Lasso_1… 0.00747 0.00152 0.00539 0.00978 0.135 0.0292
## 4 Lasso_m… 0.00508 0.00110 0.00352 0.00641 0.0778 0.0169
## # ℹ 6 more variables: Signal_Min <dbl>, Signal_Max <dbl>, Null_Mean <dbl>,
## # Null_SD <dbl>, Null_Min <dbl>, Null_Max <dbl>monte_carlo : avg of 50 seeds
overall RMSE
signal RMSE
null RMSE
selected value
## Rows: 7 Columns: 5
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## dbl (5): SignalStrength, Debiased_1se, Debiased_min, Lasso_1se, Lasso_min
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.## # A tibble: 7 × 5
## SignalStrength Debiased_1se Debiased_min Lasso_1se Lasso_min
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0.3 3.22 18.5 3.22 18.5
## 2 0.5 3.12 16.3 3.12 16.3
## 3 1 3 14.3 3 14.3
## 4 2 3.24 21.2 3.24 21.2
## 5 3 3.06 15.8 3.06 15.8
## 6 4 3.18 19.1 3.18 19.1
## 7 5 3.24 16.2 3.24 16.2Compound symmetry experiment
Basic Experimental Setup
- n: Fixed at 1000
- p: Fixed at 1000
- Number of signal variables: 3
- Signal strength: 1
- Intercept: 1
- Error term: N(0,1)
- Design matrix Xij : Compound symmetry
only global seed : set.seed(42)
null RMSE
## Rows: 36 Columns: 5
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (1): Method
## dbl (4): Overall_RMSE, Signal_RMSE, Null_RMSE, rho
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.## # A tibble: 36 × 5
## Method Overall_RMSE Signal_RMSE Null_RMSE rho
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 Lasso_min 0.00508 0.0827 0.00231 0.1
## 2 Debiased_min 0.0311 0.0302 0.0311 0.1
## 3 Lasso_1se 0.00905 0.165 0 0.1
## 4 Debiased_1se 0.0377 0.0348 0.0377 0.1
## 5 Lasso_min 0.00335 0.0567 0.00126 0.2
## 6 Debiased_min 0.0324 0.0515 0.0323 0.2
## 7 Lasso_1se 0.00766 0.140 0 0.2
## 8 Debiased_1se 0.0478 0.0726 0.0477 0.2
## 9 Lasso_min 0.00499 0.0822 0.00216 0.3
## 10 Debiased_min 0.0338 0.0280 0.0338 0.3
## # ℹ 26 more rowsmonte_carlo : avg of 50 seeds
null RMSE
## Rows: 36 Columns: 8
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (1): Method
## dbl (7): rho, Overall_RMSE.mean, Overall_RMSE.sd, Signal_RMSE.mean, Signal_R...
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.## # A tibble: 36 × 8
## Method rho Overall_RMSE.mean Overall_RMSE.sd Signal_RMSE.mean
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 Debiased_1se 0.1 0.0421 0.00465 0.0330
## 2 Debiased_min 0.1 0.0322 0.00149 0.0294
## 3 Lasso_1se 0.1 0.00728 0.00117 0.133
## 4 Lasso_min 0.1 0.00483 0.00102 0.0799
## 5 Debiased_1se 0.2 0.0464 0.00461 0.0362
## 6 Debiased_min 0.2 0.0331 0.00124 0.0311
## 7 Lasso_1se 0.2 0.00683 0.00107 0.124
## 8 Lasso_min 0.2 0.00502 0.00108 0.0820
## 9 Debiased_1se 0.3 0.0498 0.00502 0.0391
## 10 Debiased_min 0.3 0.0343 0.00119 0.0335
## # ℹ 26 more rows
## # ℹ 3 more variables: Signal_RMSE.sd <dbl>, Null_RMSE.mean <dbl>,
## # Null_RMSE.sd <dbl>