Simple linear regression is a statistical method that is used to analyze the relationship between two continuous variables:
x- independent variable also known as explanatory or predictor.
y- dependent variable also known as response or outcome.
Let's say we have the following sets of numbers:
You may notice that the
x value is increasing by 1, and the corresponding
y value is increasing by 2. So relationship is
y = 2 * x + 1.
This tutorial provides example how to create and train a model which predicts the value of
y for the given value of
x using PyTorch.
We define arrays of
y values for training a model. Model contains one layer. It has one input and one output.
We choose the mean squared error (MSE) as loss function and stochastic gradient descent (SGD) as optimizer. A learning rate is 0.01.
During training we perform forward pass to compute predicted
y values by using
x values. The loss function is used to compute error between the predicted and true values of
y. After that, we explicitly set the gradients to zero, perform backward pass and use optimizer to update the network weights. Training is performed 400 epochs.
import torch xs = torch.Tensor([[-2.0], [-1.0], [0.0], [1.0], [2.0], [3.0], [4.0]]) ys = torch.Tensor([[-3.0], [-1.0], [1.0], [3.0], [5.0], [7.0], [9.0]]) model = torch.nn.Sequential( torch.nn.Linear(1, 1) ) loss_fn = torch.nn.MSELoss() optimizer = torch.optim.SGD(model.parameters(), lr=0.01) epochs=400 for epoch in range(epochs): ys_pred = model(xs) loss = loss_fn(ys_pred, ys) optimizer.zero_grad() loss.backward() optimizer.step() x = torch.Tensor([[15.0]]) y = model(x).item() print(y)
When the training is completed, we try to predict value of
y for a previously unknown value of
x. In our case, trained model returns
y equal to 31.001181 when
x is 15.0. We can verify:
y = 2 * x + 1 = 2 * 15 + 1 = 31