Training Two Parameter Stochastic Gradient Descent

In this Lab, you will practice training a model by using Stochastic Gradient
Author

Juma Shafara

Published

August 7, 2024

Photo by DATAIDEA

Linear regression 1D: Training Two Parameter Stochastic Gradient Descent (SGD)

Objective

Table of Contents

In this Lab, you will practice training a model by using Stochastic Gradient descent.

Estimated Time Needed: 30 min

Preparation

We’ll need the following libraries:

# These are the libraries we are going to use in the lab.

import torch
import matplotlib.pyplot as plt
import numpy as np
from mpl_toolkits import mplot3d
from dataidea_science.plots import plot_error_surfaces

The class plot_error_surfaces is just to help you visualize the data space and the parameter space during training and has nothing to do with PyTorch.

Make Some Data

Set random seed:

# Set random seed

torch.manual_seed(1)
<torch._C.Generator at 0x79c1633e7c10>

Generate values from -3 to 3 that create a line with a slope of 1 and a bias of -1. This is the line that you need to estimate. Add some noise to the data:

# Setup the actual data and simulated data

X = torch.arange(-3, 3, 0.1).view(-1, 1)
f = 1 * X - 1
Y = f + 0.1 * torch.randn(X.size())

Plot the results:

# Plot out the data dots and line
from dataidea.models import *

Create the Model and Cost Function (Total Loss)

Define the forward function:

# Define the forward function

def forward(x):
    return w * x + b

Define the cost or criterion function (MSE):

# Define the MSE Loss function

def criterion(yhat, y):
    return torch.mean((yhat - y) ** 2)

Create a plot_error_surfaces object to visualize the data space and the parameter space during training:

# Create plot_error_surfaces for viewing the data

get_surface = plot_error_surfaces(15, 13, X, Y, 30)
<Figure size 640x480 with 0 Axes>

Train the Model: Batch Gradient Descent

Create model parameters w, b by setting the argument requires_grad to True because the system must learn it.

# Define the parameters w, b for y = wx + b

w = torch.tensor(-15.0, requires_grad = True)
b = torch.tensor(-10.0, requires_grad = True)

Set the learning rate to 0.1 and create an empty list LOSS for storing the loss for each iteration.

# Define learning rate and create an empty list for containing the loss for each iteration.

lr = 0.1
LOSS_BGD = []

Define train_model function for train the model.

# The function for training the model

def train_model(iter):
    
    # Loop
    for epoch in range(iter):
        
        # make a prediction
        Yhat = forward(X)
        
        # calculate the loss 
        loss = criterion(Yhat, Y)

        # Section for plotting
        get_surface.set_para_loss(w.data.tolist(), b.data.tolist(), loss.tolist())
        get_surface.plot_ps()
            
        # store the loss in the list LOSS_BGD
        LOSS_BGD.append(loss)
        
        # backward pass: compute gradient of the loss with respect to all the learnable parameters
        loss.backward()
        
        # update parameters slope and bias
        w.data = w.data - lr * w.grad.data
        b.data = b.data - lr * b.grad.data
        
        # zero the gradients before running the backward pass
        w.grad.data.zero_()
        b.grad.data.zero_()

Run 10 epochs of batch gradient descent: bug data space is 1 iteration ahead of parameter space.

# Train the model with 10 iterations

train_model(10)

Train the Model: Stochastic Gradient Descent

Create a plot_error_surfaces object to visualize the data space and the parameter space during training:

# Create plot_error_surfaces for viewing the data

get_surface = plot_error_surfaces(15, 13, X, Y, 30, go = False)

Define train_model_SGD function for training the model.

# The function for training the model

LOSS_SGD = []
w = torch.tensor(-15.0, requires_grad = True)
b = torch.tensor(-10.0, requires_grad = True)

def train_model_SGD(iter):
    
    # Loop
    for epoch in range(iter):
        
        # SGD is an approximation of out true total loss/cost, in this line of code we calculate our true loss/cost and store it
        Yhat = forward(X)

        # store the loss 
        LOSS_SGD.append(criterion(Yhat, Y).tolist())
        
        for x, y in zip(X, Y):
            
            # make a pridiction
            yhat = forward(x)
        
            # calculate the loss 
            loss = criterion(yhat, y)

            # Section for plotting
            get_surface.set_para_loss(w.data.tolist(), b.data.tolist(), loss.tolist())
        
            # backward pass: compute gradient of the loss with respect to all the learnable parameters
            loss.backward()
        
            # update parameters slope and bias
            w.data = w.data - lr * w.grad.data
            b.data = b.data - lr * b.grad.data

            # zero the gradients before running the backward pass
            w.grad.data.zero_()
            b.grad.data.zero_()
            
        #plot surface and data space after each epoch    
        get_surface.plot_ps()

Run 10 epochs of stochastic gradient descent: bug data space is 1 iteration ahead of parameter space.

# Train the model with 10 iterations

train_model_SGD(10)

Compare the loss of both batch gradient descent as SGD.

LOSS_BGD_ = [loss.item() for loss in LOSS_BGD]
# Plot out the LOSS_BGD and LOSS_SGD

plt.plot(LOSS_BGD_,label = "Batch Gradient Descent")
plt.plot(LOSS_SGD,label = "Stochastic Gradient Descent")
plt.xlabel('epoch')
plt.ylabel('Cost/ total loss')
plt.legend()
plt.show()

SGD with Dataset DataLoader

Import the module for building a dataset class:

# Import the library for DataLoader

from torch.utils.data import Dataset, DataLoader

Create a dataset class:

# Dataset Class

class Data(Dataset):
    
    # Constructor
    def __init__(self):
        self.x = torch.arange(-3, 3, 0.1).view(-1, 1)
        self.y = 1 * self.x - 1
        self.len = self.x.shape[0]
        
    # Getter
    def __getitem__(self,index):    
        return self.x[index], self.y[index]
    
    # Return the length
    def __len__(self):
        return self.len

Create a dataset object and check the length of the dataset.

# Create the dataset and check the length

dataset = Data()
print("The length of dataset: ", len(dataset))
The length of dataset:  60

Obtain the first training point:

# Print the first point

x, y = dataset[0]
print("(", x, ", ", y, ")")
( tensor([-3.]) ,  tensor([-4.]) )

Similarly, obtain the first three training points:

# Print the first 3 point

x, y = dataset[0:3]
print("The first 3 x: ", x)
print("The first 3 y: ", y)
The first 3 x:  tensor([[-3.0000],
        [-2.9000],
        [-2.8000]])
The first 3 y:  tensor([[-4.0000],
        [-3.9000],
        [-3.8000]])

Create a plot_error_surfaces object to visualize the data space and the parameter space during training:

# Create plot_error_surfaces for viewing the data

get_surface = plot_error_surfaces(15, 13, X, Y, 30, go = False)

Create a DataLoader object by using the constructor:

# Create DataLoader

trainloader = DataLoader(dataset = dataset, batch_size = 1)

Define train_model_DataLoader function for training the model.

# The function for training the model

w = torch.tensor(-15.0,requires_grad=True)
b = torch.tensor(-10.0,requires_grad=True)
LOSS_Loader = []

def train_model_DataLoader(epochs):
    
    # Loop
    for epoch in range(epochs):
        
        # SGD is an approximation of out true total loss/cost, in this line of code we calculate our true loss/cost and store it
        Yhat = forward(X)
        
        # store the loss 
        LOSS_Loader.append(criterion(Yhat, Y).tolist())
        
        for x, y in trainloader:
            
            # make a prediction
            yhat = forward(x)
            
            # calculate the loss
            loss = criterion(yhat, y)
            
            # Section for plotting
            get_surface.set_para_loss(w.data.tolist(), b.data.tolist(), loss.tolist())
            
            # Backward pass: compute gradient of the loss with respect to all the learnable parameters
            loss.backward()
            
            # Updata parameters slope
            w.data = w.data - lr * w.grad.data
            b.data = b.data - lr* b.grad.data
            
            # Clear gradients 
            w.grad.data.zero_()
            b.grad.data.zero_()
            
        #plot surface and data space after each epoch    
        get_surface.plot_ps()

Run 10 epochs of stochastic gradient descent: bug data space is 1 iteration ahead of parameter space.

# Run 10 iterations

train_model_DataLoader(10)

Compare the loss of both batch gradient decent as SGD. Note that SGD converges to a minimum faster, that is, it decreases faster.

# Plot the LOSS_BGD and LOSS_Loader

plt.plot(LOSS_BGD_,label="Batch Gradient Descent")
plt.plot(LOSS_Loader,label="Stochastic Gradient Descent with DataLoader")
plt.xlabel('epoch')
plt.ylabel('Cost/ total loss')
plt.legend()
plt.show()

Practice

For practice, try to use SGD with DataLoader to train model with 10 iterations. Store the total loss in LOSS. We are going to use it in the next question.

# Practice: Use SGD with trainloader to train model and store the total loss in LOSS

LOSS = []
w = torch.tensor(-12.0, requires_grad = True)
b = torch.tensor(-10.0, requires_grad = True)

Double-click here for the solution.

Plot the total loss

# Practice: Plot the total loss using LOSS

# Type your code here

Double-click here for the solution.

About the Author:

Hi, My name is Juma Shafara. Am a Data Scientist and Instructor at DATAIDEA. I have taught hundreds of peope Programming, Data Analysis and Machine Learning.

I also enjoy developing innovative algorithms and models that can drive insights and value.

I regularly share some content that I find useful throughout my learning/teaching journey to simplify concepts in Machine Learning, Mathematics, Programming, and related topics on my website jumashafara.dataidea.org.

Besides these technical stuff, I enjoy watching soccer, movies and reading mystery books.

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