Daniel Voigt Godoy - Deep Learning with PyTorch Step-by-Step A Beginner’s Guide-leanpub
Outputarray([[0.5504593 ],[0.94999564],[0.9757515 ],[0.22519748]], dtype=float32)Now we’re talking! These are the probabilities, given our model, of those fourpoints being positive examples.Lastly, we need to go from probabilities to classes. If the probability is greater thanor equal to a threshold, it is a positive example. If it is less than the threshold, it is anegative example. Simple enough. The trivial choice of a threshold is 0.5:Equation 3.19 - From probabilities to classesBut the probability itself is just the sigmoid function applied to the logit (z):Equation 3.20 - From logits to classes, via sigmoid functionBut the sigmoid function has a value of 0.5 only when the logit (z) has a value ofzero:Equation 3.21 - From logits to classes, directlyThus, if we don’t care about the probabilities, we could use the predictions (logits)directly to get the predicted classes for the data points:Model Training | 235
Making Predictions (Classes)classes = (predictions >= 0).astype(np.int)classesOutputarray([[1],[1],[1],[0]])Clearly, the points where the logits (z) equal zero determine the boundarybetween positive and negative examples."Why 0.5? Can I choose a different threshold?"Sure, you can! Different thresholds will give you different confusion matrices and,therefore, different metrics, like accuracy, precision, and recall. We’ll get back tothat in the "Decision Boundary" section.By the way, are you still holding that thought about the "glorified linear regression?"Good!Decision BoundaryWe have just figured out that whenever z equals zero, we are in the decisionboundary. But z is given by a linear combination of features x 1 and x 2 . If we workout some basic operations, we arrive at:Equation 3.22 - Decision boundary for logistic regression with two featuresGiven our model (b, w 1 , and w 2 ), for any value of the first feature (x 1 ), we cancompute the corresponding value of the second feature (x 2 ) that sits exactly at the236 | Chapter 3: A Simple Classification Problem
- Page 210 and 211: setattrThe setattr function sets th
- Page 212 and 213: See? We effectively modified the un
- Page 214 and 215: the random seed as arguments.This s
- Page 216 and 217: The current state of development of
- Page 218 and 219: Lossesdef plot_losses(self):fig = p
- Page 220 and 221: Run - Data Preparation V21 # %load
- Page 222 and 223: Model TrainingWe start by instantia
- Page 224 and 225: Making PredictionsLet’s make up s
- Page 226 and 227: OutputOrderedDict([('0.weight', ten
- Page 228 and 229: Run - Data Preparation V21 # %load
- Page 230 and 231: • defining our StepByStep class
- Page 232 and 233: import numpy as npimport torchimpor
- Page 234 and 235: Next, we’ll standardize the featu
- Page 236 and 237: Equation 3.1 - A linear regression
- Page 238 and 239: The odds ratio is given by the rati
- Page 240 and 241: As expected, probabilities that add
- Page 242 and 243: Sigmoid Functiondef sigmoid(z):retu
- Page 244 and 245: A picture is worth a thousand words
- Page 246 and 247: OutputOrderedDict([('linear.weight'
- Page 248 and 249: The first summation adds up the err
- Page 250 and 251: IMPORTANT: Make sure to pass the pr
- Page 252 and 253: To make it clear: In this chapter,
- Page 254 and 255: argument of nn.BCEWithLogitsLoss().
- Page 256 and 257: It is not that hard, to be honest.
- Page 258 and 259: Figure 3.6 - Training and validatio
- Page 262 and 263: decision boundary.Look at the expre
- Page 264 and 265: Are my data points separable?That
- Page 266 and 267: model = nn.Sequential()model.add_mo
- Page 268 and 269: It looks like this:Figure 3.10 - Sp
- Page 270 and 271: True and False Positives and Negati
- Page 272 and 273: tpr_fpr(cm_thresh50)Output(0.909090
- Page 274 and 275: The trade-off between precision and
- Page 276 and 277: Figure 3.13 - Using a low threshold
- Page 278 and 279: Figure 3.16 - Trade-offs for two di
- Page 280 and 281: thresholds do not necessarily inclu
- Page 282 and 283: actual data, it is as bad as it can
- Page 284 and 285: If you want to learn more about bot
- Page 286 and 287: Model Training1 n_epochs = 10023 sb
- Page 288 and 289: step in your journey! What’s next
- Page 290 and 291: Chapter 4Classifying ImagesSpoilers
- Page 292 and 293: Data GenerationOur images are quite
- Page 294 and 295: Images and ChannelsIn case you’re
- Page 296 and 297: image_rgb = np.stack([image_r, imag
- Page 298 and 299: That’s fairly straightforward; we
- Page 300 and 301: • Transformations based on Tensor
- Page 302 and 303: position of an object in a picture
- Page 304 and 305: Outputtensor([[[0., 0., 0., 1., 0.]
- Page 306 and 307: Outputtensor([[[-1., -1., -1., 1.,
- Page 308 and 309: We can convert the former into the
Output
array([[0.5504593 ],
[0.94999564],
[0.9757515 ],
[0.22519748]], dtype=float32)
Now we’re talking! These are the probabilities, given our model, of those four
points being positive examples.
Lastly, we need to go from probabilities to classes. If the probability is greater than
or equal to a threshold, it is a positive example. If it is less than the threshold, it is a
negative example. Simple enough. The trivial choice of a threshold is 0.5:
Equation 3.19 - From probabilities to classes
But the probability itself is just the sigmoid function applied to the logit (z):
Equation 3.20 - From logits to classes, via sigmoid function
But the sigmoid function has a value of 0.5 only when the logit (z) has a value of
zero:
Equation 3.21 - From logits to classes, directly
Thus, if we don’t care about the probabilities, we could use the predictions (logits)
directly to get the predicted classes for the data points:
Model Training | 235
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