Multiple Linear Regression

In this lab, you will review how to make a prediction in several different ways by using PyTorch.

Keywords

Multiple Linear Regression, How to make the prediction for multiple inputs, How to use linear class to build more complex models, How to build a custom module

Photo by DATAIDEA

Objective

• How to make the prediction for multiple inputs.
• How to use linear class to build more complex models.
• How to build a custom module.

Table of Contents

In this lab, you will review how to make a prediction in several different ways by using PyTorch.

• Prediction
• Class Linear
• Build Custom Modules

Estimated Time Needed: 15 min

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Preparation

Import the libraries and set the random seed.

# Import the libraries and set the random seed

from torch import nn
import torch
torch.manual_seed(1)

<torch._C.Generator at 0x70efcb47eef0>

Prediction

Set weight and bias.

# Set the weight and bias

w = torch.tensor([[2.0], [3.0]], requires_grad=True)
b = torch.tensor([[1.0]], requires_grad=True)

Define the parameters. torch.mm uses matrix multiplication instead of scaler multiplication.

# Define Prediction Function

def forward(x):
    yhat = torch.mm(x, w) + b
    return yhat

The function forward implements the following equation:

If we input a 1x2 tensor, because we have a 2x1 tensor as w, we will get a 1x1 tensor:

# Calculate yhat

x = torch.tensor([[1.0, 2.0]])
yhat = forward(x)
print("The result: ", yhat)

The result:  tensor([[9.]], grad_fn=<AddBackward0>)

Each row of the following tensor represents a sample:

# Sample tensor X

X = torch.tensor([[1.0, 1.0], [1.0, 2.0], [1.0, 3.0]])

# Make the prediction of X 

yhat = forward(X)
print("The result: ", yhat)

The result:  tensor([[ 6.],
        [ 9.],
        [12.]], grad_fn=<AddBackward0>)

Class Linear

We can use the linear class to make a prediction. You’ll also use the linear class to build more complex models.

Let us create a model.

# Make a linear regression model using build-in function

model = nn.Linear(2, 1)

Make a prediction with the first sample:

# Make a prediction of x

yhat = model(x)
print("The result: ", yhat)

The result:  tensor([[-0.3969]], grad_fn=<AddmmBackward0>)

Predict with multiple samples X:

# Make a prediction of X

yhat = model(X)
print("The result: ", yhat)

The result:  tensor([[-0.0848],
        [-0.3969],
        [-0.7090]], grad_fn=<AddmmBackward0>)

The function performs matrix multiplication as shown in this image:

Build Custom Modules

Now, you’ll build a custom module. You can make more complex models by using this method later.

# Create LinearRegression Class

class LinearRegression(nn.Module):
    
    # Constructor
    def __init__(self, input_size, output_size):
        super(LinearRegression, self).__init__()
        self.linear = nn.Linear(input_size, output_size)
    
    # Prediction function
    def forward(self, x):
        yhat = self.linear(x)
        return yhat

Build a linear regression object. The input feature size is two.

model = LinearRegression(2, 1)

This will input the following equation:

You can see the randomly initialized parameters by using the parameters() method:

# Print model parameters

print("The parameters: ", list(model.parameters()))

The parameters:  [Parameter containing:
tensor([[ 0.3319, -0.6657]], requires_grad=True), Parameter containing:
tensor([0.4241], requires_grad=True)]

You can also see the parameters by using the state_dict() method:

# Print model parameters

print("The parameters: ", model.state_dict())

The parameters:  OrderedDict({'linear.weight': tensor([[ 0.3319, -0.6657]]), 'linear.bias': tensor([0.4241])})

Now we input a 1x2 tensor, and we will get a 1x1 tensor.

# Make a prediction of x

yhat = model(x)
print("The result: ", yhat)

The result:  tensor([[-0.5754]], grad_fn=<AddmmBackward0>)

The shape of the output is shown in the following image:

Make a prediction for multiple samples:

# Make a prediction of X

yhat = model(X)
print("The result: ", yhat)

The result:  tensor([[ 0.0903],
        [-0.5754],
        [-1.2411]], grad_fn=<AddmmBackward0>)

The shape is shown in the following image:

Practice

Build a model or object of type linear_regression. Using the linear_regression object will predict the following tensor:

# Practice: Build a model to predict the follow tensor.

X = torch.tensor([[11.0, 12.0, 13, 14], [11, 12, 13, 14]])

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.

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