Deep-Learning-with-PyTorch

108 CHAPTER 5 The mechanics of learning
# In[2]:
t_c = [0.5, 14.0, 15.0, 28.0, 11.0, 8.0, 3.0, -4.0, 6.0, 13.0, 21.0]
t_u = [35.7, 55.9, 58.2, 81.9, 56.3, 48.9, 33.9, 21.8, 48.4, 60.4, 68.4]
t_c = torch.tensor(t_c)
t_u = torch.tensor(t_u)
Here, the t_c values are temperatures in Celsius, and the t_u values are our unknown
units. We can expect noise in both measurements, coming from the devices themselves
and from our approximate readings. For convenience, we’ve already put the
data into tensors; we’ll use it in a minute.
5.2.3 Visualizing the data
A quick plot of our data in figure 5.3 tells us that it’s noisy, but we think there’s a pattern
here.
25
temperature (°CELSIUS)
20
15
10
5
0
-5
20 30 40 50 60 70 80
measurement
Figure 5.3 Our unknown
data just might follow a
linear model.
NOTE Spoiler alert: we know a linear model is correct because the problem
and data have been fabricated, but please bear with us. It’s a useful motivating
example to build our understanding of what PyTorch is doing under the
hood.
5.2.4 Choosing a linear model as a first try
In the absence of further knowledge, we assume the simplest possible model for converting
between the two sets of measurements, just like Kepler might have done. The
two may be linearly related—that is, multiplying t_u by a factor and adding a constant,
we may get the temperature in Celsius (up to an error that we omit):
t_c = w * t_u + b