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Additional resources for Deep Learning in Python Prerequisites
Since probabilities must be 0 or positive, we can enforce positivity by exponentiating a. How do we ensure these sum to 1? Simply divide by exp(a1) + exp(a0). So now: p(y=1 | x) = exp(a1) / [ exp(a1) + exp(a0) ] p(y=0 | x) = exp(a0) / [ exp(a1) + exp(a0) ] You can see that it would be very easy to extend this to any number of classes. Appropriately, when you hook up a bunch of neurons / logistic units together, you get a neural network. I discuss the similarity between digital neurons and biological neurons more in depth in my next book, Deep Learning in Python: Master Data Science and Machine Learning with Modern Neural Networks written in Python, Theano, and TensorFlow.
It has the same shape as a sigmoid, but a different scale. The output ranges between -1 and 1, thus it cannot be considered a probability. tanh() softmax output What happens when our output is more than 2 classes? Ex. With binary classification, we only needed 1 output node, because P(y=0 | x) = 1 - P(y = 1 | x). The probability of all possibilities must sum to 1. Let’s consider what would happen if we used 2 output nodes. We would have: a1 = w1Tx a0 = w0Tx Recall that a0 and a1 can be either negative or positive.
Use the logistic regression classifier with no hand-crafted features to prove to yourself that this yields a low classification rate. Next, add the features I’ve described in this chapter and show that you can achieve almost-perfect (or perfect in the case of XOR) discrimination. Conclusion I really hope you had as much fun reading this book as I did making it. Do you have any questions? me Do you want to learn more about deep learning? I happen to have a few of them on Udemy. I teach you about ways to accelerate the learning process, including batch gradient descent, momentum, and adaptive learning rates.