Morten Hjorth-Jensen
34 lines
1.1 KiB
Python
34 lines
1.1 KiB
Python
import autograd.numpy as np
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from autograd import grad
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def sigmoid(x):
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return 0.5 * (np.tanh(x / 2.) + 1)
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def logistic_predictions(weights, inputs):
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# Outputs probability of a label being true according to logistic model.
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return sigmoid(np.dot(inputs, weights))
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def training_loss(weights):
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# Training loss is the negative log-likelihood of the training labels.
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preds = logistic_predictions(weights, inputs)
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label_probabilities = preds * targets + (1 - preds) * (1 - targets)
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return -np.sum(np.log(label_probabilities))
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# Build a toy dataset.
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inputs = np.array([[0.52, 1.12, 0.77],
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[0.88, -1.08, 0.15],
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[0.52, 0.06, -1.30],
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[0.74, -2.49, 1.39]])
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targets = np.array([True, True, False, True])
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# Define a function that returns gradients of training loss using Autograd.
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training_gradient_fun = grad(training_loss)
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# Optimize weights using gradient descent.
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weights = np.array([0.0, 0.0, 0.0])
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print("Initial loss:", training_loss(weights))
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for i in range(100):
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weights -= training_gradient_fun(weights) * 0.01
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print("Trained loss:", training_loss(weights))
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