Using Dropout in Regression Assignment

in this lab, you will see how adding dropout to your model will decrease overfitting with nn.Sequential.

Create the Model and Cost Function the Pytorch way

Estimated Time Needed: 20 min

Import all the libraries you need for this lab:



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import torch
import matplotlib.pyplot as plt
import torch.nn as nn

import numpy as np

Get Some Data

Create polynomial dataset objects:



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from torch.utils.data import Dataset, DataLoader

class Data(Dataset):
    def __init__(self,N_SAMPLES = 40,noise_std=1,train=True):
      
      
        self.x = torch.linspace(-1, 1, N_SAMPLES).view(-1,1)
        self.f=self.x**2
        
        if train!=True:
            torch.manual_seed(1)
         
            self.y = self.f+noise_std*torch.randn(self.f.size())
            self.y=self.y.view(-1,1)
            torch.manual_seed(0)
        else:
            self.y = self.f+noise_std*torch.randn(self.f.size())
            self.y=self.y.view(-1,1)
    def __getitem__(self,index):    
        return self.x[index],self.y[index]
    def __len__(self):
        return self.len
    def plot(self):
        plt.figure(figsize=(6.1, 10))
        plt.scatter(self.x.numpy(), self.y.numpy(), label="Samples")
        plt.plot(self.x.numpy(), self.f.numpy()  ,label="True function",color='orange')
        plt.xlabel("x")
        plt.ylabel("y")
        plt.xlim((-1, 1))
        plt.ylim((-2, 2.5))
        plt.legend(loc="best")
        plt.show()

Create a dataset object:



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data_set=Data()
data_set.plot()

Get some validation data:



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torch.manual_seed(0) 
validation_set=Data(train=False)

Create the Model, Optimizer, and Total Loss Function (cost)



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torch.manual_seed(4)

Create a three-layer neural network `model` with a ReLU() activation function for regression. All the appropriate layers should be 300 units.



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Double-click here for the solution.

Create a three-layer neural network `model_drop` with a ReLU() activation function for regression. All the appropriate layers should be 300 units. Apply dropout to all but the last layer and make the probability of dropout is 50%.



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Double-click here for the solution.

Train the Model via Mini-Batch Gradient Descent

Set the model using dropout to training mode; this is the default mode, but it's a good practice.



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model_drop.train()

Train the model by using the Adam optimizer. See the unit on other optimizers. Use the mean square loss:



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optimizer_ofit = torch.optim.Adam(model.parameters(), lr=0.01)
optimizer_drop = torch.optim.Adam(model_drop.parameters(), lr=0.01)
criterion = torch.nn.MSELoss()

Initialize a dictionary that stores the training and validation loss for each model:



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LOSS={}
LOSS['training data no dropout']=[]
LOSS['validation data no dropout']=[]
LOSS['training data dropout']=[]
LOSS['validation data dropout']=[]

Run 500 iterations of batch gradient decent:



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epochs=500

for epoch in range(epochs):
    #make a prediction for both models 
    yhat = model(data_set.x)
    yhat_drop = model_drop(data_set.x)
    #calculate the lossf or both models 
    loss = criterion(yhat, data_set.y)
    loss_drop = criterion(yhat_drop, data_set.y)
    
    #store the loss for  both the training and validation  data for both models 
    LOSS['training data no dropout'].append(loss.item())
    LOSS['validation data no dropout'].append(criterion(model(validation_set.x), validation_set.y).item())
    LOSS['training data dropout'].append(loss_drop.item())
    model_drop.eval()
    LOSS['validation data dropout'].append(criterion(model_drop(validation_set.x), validation_set.y).item())
    model_drop.train()
    
    #clear gradient 
    optimizer_ofit.zero_grad()
    optimizer_drop.zero_grad()
    #Backward pass: compute gradient of the loss with respect to all the learnable parameters
    loss.backward()
    loss_drop.backward()
    #the step function on an Optimizer makes an update to its parameters
    optimizer_ofit.step()
    optimizer_drop.step()

Make a prediction by using the test set assign `model` to yhat and `model_drop` to yhat_drop.



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Double-click here for the solution.

Plot predictions of both models. Compare them to the training points and the true function:



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plt.figure(figsize=(6.1, 10))

plt.scatter(data_set.x.numpy(), data_set.y.numpy(), label="Samples")
plt.plot(data_set.x.numpy(), data_set.f.numpy()  ,label="True function",color='orange')
plt.plot(data_set.x.numpy(),yhat.detach().numpy(),label='no dropout',c='r')
plt.plot(data_set.x.numpy(),yhat_drop.detach().numpy(),label="dropout",c='g')


plt.xlabel("x")
plt.ylabel("y")
plt.xlim((-1, 1))
plt.ylim((-2, 2.5))
plt.legend(loc="best")
plt.show()

You can see that the model using dropout does better at tracking the function that generated the data.

Plot out the loss for training and validation data on both models:



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plt.figure(figsize=(6.1, 10))
for key, value in LOSS.items():
    plt.plot(np.log(np.array(value)),label=key)
    plt.legend()
    plt.xlabel("iterations")
    plt.ylabel("Log of cost or total loss")

About the Authors:

Joseph Santarcangelo has a PhD in Electrical Engineering. His research focused on using machine learning, signal processing, and computer vision to determine how videos impact human cognition.

Other contributors: Michelle Carey ,Morvan Youtube channel, Mavis Zhou

Using Dropout in Regression Assignment

Table of Contents

Get Some Data

Create the Model, Optimizer, and Total Loss Function (cost)

Create a three-layer neural network model with a ReLU() activation function for regression. All the appropriate layers should be 300 units.

Create a three-layer neural network model_drop with a ReLU() activation function for regression. All the appropriate layers should be 300 units. Apply dropout to all but the last layer and make the probability of dropout is 50%.

Train the Model via Mini-Batch Gradient Descent

Make a prediction by using the test set assign model to yhat and model_drop to yhat_drop.

About the Authors:

Create a three-layer neural network `model` with a ReLU() activation function for regression. All the appropriate layers should be 300 units.

Create a three-layer neural network `model_drop` with a ReLU() activation function for regression. All the appropriate layers should be 300 units. Apply dropout to all but the last layer and make the probability of dropout is 50%.

Make a prediction by using the test set assign `model` to yhat and `model_drop` to yhat_drop.