In this tutorial, we'll discuss one of the foundational algorithms in machine learning: Linear regression. We'll create a model that predicts crop yields for apples and oranges (target variables) by looking at the average temperature, rainfall, and humidity (input variables or features) in a region. Here's the training data:
linear-regression-training-data
In a linear regression model, each target variable is estimated to be a weighted sum of the input variables, offset by some constant, known as a bias :
yield_apple = w11 * temp + w12 * rainfall + w13 * humidity + b1
yield_orange = w21 * temp + w22 * rainfall + w23 * humidity + b2
Visually, it means that the yield of apples is a linear or planar function of temperature, rainfall and humidity
The learning part of linear regression is to figure out a set of weights w11, w12,... w23, b1 & b2 using the training data, to make accurate predictions for new data. The learned weights will be used to predict the yields for apples and oranges in a new region using the average temperature, rainfall, and humidity for that region.
We'll train our model by adjusting the weights slightly many times to make better predictions, using an optimization technique called gradient descent. Let's begin by importing Numpy and PyTorch
import numpy as np
import torchTraining data
We can represent the training data using two matrices: inputs and targets, each with one row per observation, and one column per variable
# Input (temp, rainfall, humidity)
inputs = np.array([[73, 67, 43],
[91, 88, 64],
[87, 134, 58],
[102, 43, 37],
[69, 96, 70]], dtype='float32')# Targets (apples, oranges)
targets = np.array([[56, 70],
[81, 101],
[119, 133],
[22, 37],
[103,119]], dtype='float32')