[Exercise] Linear Regression
Linear Regression
Data generated from function y = 2*x + 0.5 + noise:
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| def generate_data(n, k, b, low=0.0, high=10.0):
step = (high - low) / n
x, y = [], []
for i in range(n):
x.append(low + step * i)
y.append(x[i] * k + b + np.random.normal(0.0, 0.05 * (high - low)))
return np.array(x), np.array(y)
x_train, y_train = generate_data(100, 2.0, 0.5)
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The linear model:
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| def model(_x, _theta):
return _x * _theta[0] + _theta[1]
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Gradient function:
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| def gradient(_x, _y, _theta, _model):
g = np.array([0.0, 0.0])
for i in range(len(_x)):
g[0] += (model(_x[i], _theta) - _y[i]) * _x[i]
g[1] += (model(_x[i], _theta) - _y[i])
return g
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Training with gradient descent:
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| def train(_x, _y, _theta, _model, lr=1e-5, steps=1000):
for step in range(steps):
_theta -= lr * gradient(_x, _y, _theta, _model)
if step % 100 == 0:
print("step: %d, theta: %f %f, loss: %f" % (step, _theta[0], _theta[1], loss(_x, _y, _theta, _model)))
return _theta
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Result:
