In this lab, you will train a model with PyTorch by using the data that we created. The model will have the slope and bias. And we will review how to make a prediction in several different ways by using PyTorch.
Estimated Time Needed: 20 min
We'll need the following libraries:
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# These are the libraries we are going to use in the lab.
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits import mplot3d
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.
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# The class for plot the diagram
class plot_error_surfaces(object):
# Constructor
def __init__(self, w_range, b_range, X, Y, n_samples = 30, go = True):
W = np.linspace(-w_range, w_range, n_samples)
B = np.linspace(-b_range, b_range, n_samples)
w, b = np.meshgrid(W, B)
Z = np.zeros((30,30))
count1 = 0
self.y = Y.numpy()
self.x = X.numpy()
for w1, b1 in zip(w, b):
count2 = 0
for w2, b2 in zip(w1, b1):
Z[count1, count2] = np.mean((self.y - w2 * self.x + b2) ** 2)
count2 += 1
count1 += 1
self.Z = Z
self.w = w
self.b = b
self.W = []
self.B = []
self.LOSS = []
self.n = 0
if go == True:
plt.figure()
plt.figure(figsize = (7.5, 5))
plt.axes(projection='3d').plot_surface(self.w, self.b, self.Z, rstride = 1, cstride = 1,cmap = 'viridis', edgecolor = 'none')
plt.title('Cost/Total Loss Surface')
plt.xlabel('w')
plt.ylabel('b')
plt.show()
plt.figure()
plt.title('Cost/Total Loss Surface Contour')
plt.xlabel('w')
plt.ylabel('b')
plt.contour(self.w, self.b, self.Z)
plt.show()
# Setter
def set_para_loss(self, W, B, loss):
self.n = self.n + 1
self.W.append(W)
self.B.append(B)
self.LOSS.append(loss)
# Plot diagram
def final_plot(self):
ax = plt.axes(projection = '3d')
ax.plot_wireframe(self.w, self.b, self.Z)
ax.scatter(self.W,self.B, self.LOSS, c = 'r', marker = 'x', s = 200, alpha = 1)
plt.figure()
plt.contour(self.w,self.b, self.Z)
plt.scatter(self.W, self.B, c = 'r', marker = 'x')
plt.xlabel('w')
plt.ylabel('b')
plt.show()
# Plot diagram
def plot_ps(self):
plt.subplot(121)
plt.ylim
plt.plot(self.x, self.y, 'ro', label="training points")
plt.plot(self.x, self.W[-1] * self.x + self.B[-1], label = "estimated line")
plt.xlabel('x')
plt.ylabel('y')
plt.ylim((-10, 15))
plt.title('Data Space Iteration: ' + str(self.n))
plt.legend()
plt.show()
plt.subplot(122)
plt.contour(self.w, self.b, self.Z)
plt.scatter(self.W, self.B, c = 'r', marker = 'x')
plt.title('Total Loss Surface Contour Iteration' + str(self.n))
plt.xlabel('w')
plt.ylabel('b')
plt.legend()
Import PyTorch:
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# Import PyTorch library
import torch
Start with generating 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.
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# Create f(X) with a slope of 1 and a bias of -1
X = torch.arange(-3, 3, 0.1).view(-1, 1)
f = 1 * X - 1
Now, add some noise to the data:
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# Add noise
Y = f + 0.1 * torch.randn(X.size())
Plot the line and Y with noise:
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# Plot out the line and the points with noise
plt.plot(X.numpy(), Y.numpy(), 'rx', label = 'y')
plt.plot(X.numpy(), f.numpy(), label = 'f')
plt.xlabel('x')
plt.ylabel('y')
plt.legend()
Define the forward function:
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# Define the forward function
def forward(x):
return w * x + b
Define the cost or criterion function (MSE):
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# 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:
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# Create plot_error_surfaces for viewing the data
get_surface = plot_error_surfaces(15, 15, X, Y, 30)
Create model parameters w, b by setting the argument requires_grad to True because we must learn it using the data.
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# 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.
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# Define learning rate and create an empty list for containing the loss for each iteration.
lr = 0.1
LOSS = []
Define train_model function for train the model.
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# 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())
if epoch % 3 == 0:
get_surface.plot_ps()
# store the loss in the list LOSS
LOSS.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 15 iterations of gradient descent: bug data space is 1 iteration ahead of parameter space
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# Train the model with 15 iterations
train_model(15)
Plot total loss/cost surface with loss values for different parameters in red:
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# Plot out the Loss Result
get_surface.final_plot()
plt.plot(LOSS)
plt.tight_layout()
plt.xlabel("Epoch/Iterations")
plt.ylabel("Cost")
Experiment using s learning rates 0.2 and width the following parameters. Run 15 iterations.
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# Practice: train and plot the result with lr = 0.2 and the following parameters
w = torch.tensor(-15.0, requires_grad = True)
b = torch.tensor(-10.0, requires_grad = True)
lr = 0.2
LOSS2 = []
Double-click here for the solution.
Plot the LOSS and LOSS2
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# Practice: Plot the LOSS and LOSS2 in order to compare the Total Loss
# Type your code here
Double-click here for the solution.
Joseph Santarcangelo has a PhD in Electrical Engineering, his research focused on using machine learning, signal processing, and computer vision to determine how videos impact human cognition. Joseph has been working for IBM since he completed his PhD.
Other contributors: Michelle Carey, Mavis Zhou
Copyright © 2018 cognitiveclass.ai. This notebook and its source code are released under the terms of the MIT License.