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Multiple LR Prediction

title: Multiple Linear Regression author: Juma Shafara date: "2024-08-08" date-modified: "2024-08-21" 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, ] description: In this lab, you will review how to make a prediction in several different ways by using PyTorch.

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.

Estimated Time Needed: 15 min

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:

Matrix Linear Regression

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>)

Linear Regression Matrix Sample One

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:

Linear Regression Matrix Sample One

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:

Matrix Linear Regression

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:

Matrix Linear Regression

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:

Multiple Samples Linear Regression

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.

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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