Fitting

MultilayerFitting(model_fit,device_fit,train_loader_fit, test_loader_fit,epochs_fit, criterion_fit, optimizer_fit, terminate_fit=100, print_fit=100,printchoice=True)

Description: The procedure for estimation and inference.

Parameters:

  • model_fit : chosen network structure (see module “Structure”)

  • device_fit : char, device to use, “cpu” or “cuda”

  • train_loader_fit : dataloader, training data

  • test_loader_fit : dataloader, testing data

  • epochs_fit : int, maximum epoch number

  • criterion_fit : chosen criterion

  • optimizer_fit : chosen optimizer

  • terminate_fit : int, terminate parameter, terminate if the loss has no significant improvement over T consecutive epochs, default=100

  • print_fit : int, print parameter for outputting results, print the results after every T epochs, default=100

  • printchoice : bool, choice of print or not, default=True

Methods:

  • fitting(train_x,train_y,test_x,test_y) The procedure for model training and testing.
    • Parameters:

      • train_x, test_x : DataFrame, predictors

      • train_y, test_y : Series, responses

    • Returns:

      • trainloss : list, trainning loss

      • testloss : list, testing loss

      • prediction : list, model prediction for testing data

  • Bootstrap(time_boot,bootbase,train_x,train_y,test_x,test_y, batch,init_weights) 95% Bootstrap confidence band.
    • Parameters:

      • time_boot : int, Boostrap times

      • bootbase : list, the original prediction for testing data (see returns of module “fitting”)

      • train_x, test_x : DataFrame, predictors

      • train_y, test_y : Series, responses

      • batch : int, batch size

      • init_weights : function, initialization method

    • Returns:

      • length : float, interval length

      • coverage : %, 95% coverage probability

  • HomoConformalBand(train_x,train_y,test_x,test_y,calibration_x,calibration_y) 95% Conformal confidence band
    • Parameters:

      • train_x, test_x, calibration_x : DataFrame, predictors

      • train_y, test_y, calibration_y : Series, responses

    • Returns:

      • length : float, interval length

      • coverage : %, 95% coverage probability

    • References:

      [1] Lei, Jing, et al. “Distribution-free predictive inference for regression.” Journal of the American Statistical Association 113.523 (2018): 1094-1111.

  • HeteConformalBand(loss,train_x,train_y,test_x,test_y,calibration_x,calibration_y) Our proposed 95% MLKM conformal confidence band.
    • Parameters:

      • loss : list, training loss (used for RSS)

      • train_x, test_x, calibration_x : DataFrame, predictors

      • train_y, test_y, calibration_y : Series, responses

    • Returns:

      • length : float, interval length

      • coverage : %, 95% coverage probability

Example:

 1from Multi_Layer_Kernel_Machine.Structure import KernelNet
 2from Multi_Layer_Kernel_Machine.Fitting import MultilayerFitting
 3def init_weights(m):
 4   if type(m) == nn.Conv2d:
 5      torch.nn.init.normal_(m.weight,mean=0,std=0.5)
 6   if type(m) == nn.Linear:
 7      torch.nn.init.uniform_(m.weight,a=0,b=1)
 8      m.bias.data.fill_(0.01)
 9device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
10net = KernelNet([90,32,8,1],["C","G"],[0.01,0.1],device)
11torch.manual_seed(1)
12net.apply(init_weights)
13criterion=nn.MSELoss()
14optimizer=optim.SGD(net.parameters(),lr=1e-3,momentum=0.9,weight_decay=1e-4)
15## Model Fitting
16mlmodel=MultilayerFitting(net,device,train_loader, test_loader, 2000, criterion, optimizer,100,100,printchoice=False)
17kernelnn_trainloss,kernelnn_testloss,kernelnn_bootbase=mlmodel.fitting(train_x,train_y,test_x,test_y)
18## Confidence Bands
19mlmodel.HomoConformalBand(train_x,train_y,test_x,test_y, calibration_x,calibration_y)
20mlmodel.HeteConformalBand(kernelnn_trainloss,train_x,train_y,test_x,test_y, calibration_x,calibration_y)