Deep-Learning-with-PyTorch

Predicting malignancy
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Here, we also call out two specific threshold values: diameters of 5.42 mm and 10.55
mm. We chose those two values because they give us somewhat reasonable endpoints
for the range of thresholds we might consider, were we to need to pick a single threshold.
Anything smaller than 5.42 mm, and we’d only be dropping our TPR. Larger
than 10.55 mm, and we’d just be flagging malignant nodules as benign for no gain.
The best threshold for this classifier will probably be in the middle somewhere.
How do we actually compute the values shown here? We first grab the candidate
info list, filter out the annotated nodules, and get the malignancy label and diameter.
For convenience, we also get the number of benign and malignant nodules.
Listing 14.8
p2ch14_malben_baseline.ipynb
Takes the regular dataset and in particular
the list of benign and malignant nodules
# In[2]:
ds = p2ch14.dsets.MalignantLunaDataset(val_stride=10, isValSet_bool=True)
nodules = ds.ben_list + ds.mal_list
is_mal = torch.tensor([n.isMal_bool for n in nodules])
diam = torch.tensor([n.diameter_mm for n in nodules])
num_mal = is_mal.sum()
num_ben = len(is_mal) - num_mal For normalization of the TPR and
FPR , we take the number of
malignant and benign nodules.
To compute the ROC curve, we need an array of the possible thresholds. We get this
from torch.linspace, which takes the two boundary elements. We wish to start at
zero predicted positives, so we go from maximal threshold to minimal. This is the 3.25
to 22.78 we already mentioned:
# In[3]:
threshold = torch.linspace(diam.max(), diam.min())
Gets lists of
malignancy status
and diameter
We then build a two-dimensional tensor in which the rows are per threshold, the columns
are per-sample information, and the value is whether this sample is predicted as
positive. This Boolean tensor is then filtered by whether the label of the sample is
malignant or benign. We sum the rows to count the number of True entries. Dividing
by the number of malignant or benign nodules gives us the TPR and FPR—the two
coordinates for the ROC curve:
Indexing by None adds a dimension of size 1, just like
.unsqueeze(ndx). This gets us a 2D tensor of whether a
given nodule (in a column) is classified as malignant for
# In[4]:
a given diameter (in the row).
predictions = (diam[None] >= threshold[:, None])
tp_diam = (predictions & is_mal[None]).sum(1).float() / num_mal
fp_diam = (predictions & ~is_mal[None]).sum(1).float() / num_ben
With the predictions matrix, we can
compute the TPRs and FPRs for each
diameter by summing over the columns.