The main.py works under pytorch v1.9.0 + CUDA 10.2 + cuDNN v7.6.5. Some default settings for Huber and Tukey (biweight) loss functions, where the subscript in $c$ represents asymptotic relative efficiency (ARE) under the Gaussian noise case.

loss	$c_{.85}$	$c_{.90}$	$c_{.95}$	$c_{.98}$	$c_{.99}$
Huber	0.7317	0.9818	1.345	1.7459	2.0102
Tukey (biweight)	3.4437	3.8827	4.685	5.9207	7.0414

We list the exec codes as follows. For more details, check the run.sh, and you can run it by sh run.sh

[linear01]

only

python main.py --func linear01 --data_seed 555 --train_mode sigmas-seeds --epochs 3000 --num_seeds 15 --noise_type Lognormal --bflag 0
python main.py --func linear01 --data_seed 555 --train_mode epsilons-seeds --epochs 3000 --num_seeds 15 --noise_type Lognormal --bflag 0

python main.py --func linear01 --data_seed 555 --train_mode sigmas-seeds --epochs 3000 --num_seeds 15 --noise_type Lognormal --bflag 0 --bmodel Linear
python main.py --func linear01 --data_seed 555 --train_mode epsilons-seeds --epochs 3000 --num_seeds 15 --noise_type Lognormal --bflag 0 --bmodel Linear

BiDA-Huber

- python main.py --func linear01 --data_seed 666 --train_mode regular --epochs 1000 --noise_type Laplace 
- python main.py --func linear01 --data_seed 666 --train_mode sigmas-seeds --epochs 1000 --noise_type Laplace 
- python main.py --func linear01 --data_seed 666 --train_mode epsilons-seeds --epochs 1000 --noise_type Laplace 

• 15mins for a seed with method2+method3
• [500 epochs] 10min for a seed, 5h for 30 seeds with method1+method3
• [800 epochs] 12mins for a seed, 10h for 50 seeds

BiDA-Tukey

- python main.py --func linear01 --data_seed 6 --train_mode regular --epochs 1000 --noise_type Laplace --adap_loss Tukey --hypara 4.685 
- python main.py --func linear01 --data_seed 6 --train_mode sigmas --epochs 1000 --noise_type Laplace --adap_loss Tukey --hypara 4.685
- python main.py --func linear01 --data_seed 6 --train_mode epsilons --epochs 1000 --noise_type Laplace --adap_loss Tukey --hypara 4.685 
- python main.py --func linear01 --data_seed 6 --train_mode sigmas-seeds --epochs 1000 --noise_type Laplace --adap_loss Tukey --hypara 4.685 
- python main.py --func linear01 --data_seed 6 --train_mode epsilons-seeds --epochs 1000 --noise_type Laplace --adap_loss Tukey --hypara 4.685 

- python main.py --func linear01 --data_seed 6 --train_mode sigmas --epochs 1000 --noise_type Lognormal --adap_loss Tukey --hypara 4.685

- python main.py --func linear01 --data_seed 6 --train_mode sigmas-seeds --epochs 2000 --noise_type Lognormal --adap_loss Tukey --hypara 4.685 

- nohup python -u main.py --func linear01 --data_seed 6 --train_mode sigmas-seeds --epochs 2000 --noise_type Lognormal --adap_loss Tukey --hypara 4.685 >> my.log 2>&1 &

- python main.py --func linear01 --data_seed 6 --train_mode epsilons-seeds --epochs 1000 --noise_type Lognormal --adap_loss Tukey --hypara 4.685 

• [1000 epochs] 25mins for a seed with method1+method3,
• [1000 epochs] 17~20h for 50 seeds with method1+method3, 2 exec run simultaneously
• [1000 epochs] 27h for 50 seeds with method1+method3, 4 exec run simultaneously
• 50 seeds are [50, 98, 54, 6, 34, 66, 63, 52, 39, 62, 46, 75, 28, 65, 18, 37, 85, 13, 80, 33, 69, 78, 19, 40, 82, 10, 43, 61, 88, 89, 56, 41, 27, 90, 57, 95, 4, 92, 59, 36, 72, 1, 96, 47, 97, 26, 70, 51, 73, 68]

[sin01]

python main.py --func sin01 --data_seed 555 --train_mode regular --epochs 3000 --noise_type Lognormal
python main.py --func sin01 --data_seed 40 --train_mode sigmas-seeds --epochs 3000
python main.py --func sin01 --data_seed 555 --train_mode sigmas-seeds --epochs 3000 --num_seeds 15 --noise_type Lognormal
python main.py --func sin01 --data_seed 555 --train_mode epsilons-seeds --epochs 3000 --num_seeds 15 --noise_type Lognormal

• [500 epochs] 8mins for a seed, 4h for 30 seeds with method3=meta+meta2,
• [750 epochs] 20mins for one seed with 5 sigmas and method2+method3,
• [1500 epochs] 12 mins for a seed in a sigma and 5 methods,
• [2000 epochs] almost 45mins for a seed, 8h for 10 seeds with method2+method3
• [2000 epochs] 9h for 10 seeds with method2+method3, [59, 75, 68, 5, 32, 37, 86, 82, 27, 17]
• [3000 epochs] 52h for 15 seeds with method2+method3, 7Huber+3others [50, 98, 54, 6, 34, 66, 63, 52, 39, 62, 46, 75, 28, 65, 18]
• [3000 epochs] 50h for 50 seeds with [25, 36, 21, 17, 72, 91, 14, 20, 33, 53, 99, 71, 37, 77, 58, 3, 96, 75, 5, 63, 57, 6, 93, 16, 11, 42, 54, 94, 74, 19]

[poly5]

• [360 epochs] 11mins for one seeds, 6h for 30 seeds, method2+method3

[tan01]

python train.py --func tan01 --data_seed 666 --mode normal --epochs 1000 --noise_type Lognormal


python main.py --func tan01 --data_seed 6666 --train_mode regular --epochs 2000 --noise_type Lognormal

python main.py --func tan01 --data_seed 6666 --train_mode regular --epochs 2000 --noise_type Lognormal --outer_loss Huber

python main.py --func tan01 --data_seed 666 --train_mode regular --epochs 2000 --noise_type Lognormal --noisy_val 1 --outer_loss Huber

python main.py --func tan01 --data_seed 666 --train_mode regular --epochs 2000 --noise_type Lognormal --noisy_val 1 --outer_loss MAE


python main.py --func tan01 --data_seed 66 --train_mode sigmas-seeds --epochs 1500 --num_seeds 15 --noise_type Lognormal
python main.py --func tan01 --data_seed 66 --train_mode epsilons-seeds --epochs 1500 --num_seeds 15 --noise_type Lognormal


- 28h for 15 seeds [50, 98, 54, 6, 34, 66, 63, 52, 39, 62, 46, 75, 28, 65, 18]

[log01]

python main.py --func log01 --data_seed 66 --train_mode regular --epochs 1500 --noise_type Lognormal


--

python main.py --func log01 --data_seed 66 --train_mode sigmas-seeds --epochs 1500 --num_seeds 15 --noise_type Lognormal
python main.py --func log01 --data_seed 66 --train_mode epsilons-seeds --epochs 1500 --num_seeds 15 --noise_type Lognormal

python main.py --func log01 --data_seed 6 --train_mode sigmas-seeds --epochs 1500 --num_seeds 15 --noise_type Lognormal --noisy_val 1 --outer_loss Huber

- 28h for 15 seeds [50, 98, 54, 6, 34, 66, 63, 52, 39, 62, 46, 75, 28, 65, 18]

some new baseline settings

Level 1: use linear model as the backbone for BiDA-M

python main.py --func linear01 --data_seed 666 --train_mode sigmas-seeds --epochs 1000 --noise_type Laplace  --adap_loss Huber --model Linear 
python main.py --func linear01 --data_seed 666 --train_mode sigmas-seeds --epochs 1000 --noise_type Lognormal --adap_loss Huber --model Linear 

python main.py --func linear01 --data_seed 6 --train_mode sigmas-seeds --epochs 1000 --noise_type Laplace --adap_loss Tukey --hypara 4.685 --model Linear 
python main.py --func linear01 --data_seed 6 --train_mode sigmas-seeds --epochs 1000 --noise_type Lognormal --adap_loss Tukey --hypara 4.685 --model Linear 

Level 2: add validation data to the training data for the baseline methods

python main.py --func linear01 --data_seed 666 --train_mode sigmas-seeds --epochs 1000 --noise_type Laplace  --adap_loss Huber --model NN --train_add_val 1
python main.py --func linear01 --data_seed 666 --train_mode sigmas-seeds --epochs 1000 --noise_type Lognormal --adap_loss Huber --model NN --train_add_val 1

python main.py --func linear01 --data_seed 6 --train_mode sigmas-seeds --epochs 1000 --noise_type Laplace --adap_loss Tukey --hypara 4.685 --model NN --train_add_val 1
python main.py --func linear01 --data_seed 6 --train_mode sigmas-seeds --epochs 1000 --noise_type Lognormal --adap_loss Tukey --hypara 4.685 --model NN --train_add_val 1

Level 3: the validation data also contains the noise`