Group 3: linear_regression.py

snippets/linear_regression.py

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+import numpy as np
+
+def compCostFunction(estim_y, true_y):
+    E = estim_y - true_y
+    C = (1 / 2 * m) * np.sum(E ** 2)
+    return C
+
+def test_dimensions(x, y):
+    # this checks whether the x and y have the same number of samples
+    assert isinstance(x, np.ndarray), "Only works for arrays"
+    assert isinstance(y, np.ndarray), "Only works for arrays"
+    return x.shape[0] == y.shape[0]
+
+# To be deleted later
+# feature_1 = np.linspace(0, 2, num=100)
+
+X = np.random.randn(100,3)  # feature matrix
+y = 1 + np.dot(X, [3.5, 4., -4])  # target vector
+
+m = np.shape(X)[0]  # nr of samples
+n = np.shape(X)[1]  # nr of features
+
+def iterativeLinearRegression(X, y, alpha=0.01):
+    """
+    This makes iterative LR via gradient descent and returns estimated parameters and history list.
+    """
+    steps=500
+    X = np.concatenate((np.ones((m, 1)), X), axis=1)
+
+    W = np.random.randn(n + 1, )
+
+    # stores the updates on the cost function
+    cost_history = []
+    # iterate until the maximum number of steps
+    for i in np.arange(steps):  # begin the process
+
+        y_estimated = X.dot(W)
+
+        cost = compCostFunction(y_estimated, y)
+        # Update gradient descent
+        E = y_estimated - y
+        gradient = (1 / m) * X.T.dot(E)
+
+        W = W - alpha * gradient
+        if i % 10 == 0:
+            print(f"step: {i}\tcost: {cost}")
+
+        cost_history.append(cost)
+
+    return W, cost_history
+
+params, history = iterativeLinearRegression(X, y)
+
+# test 1
+print(params)
+print(history)
+
+import matplotlib.pyplot as plt
+plt.plot(history)
+plt.xlabel("steps")
+plt.show()
+
+# test 2
+
+X = np.random.randn(500,2)  # feature matrix
+y = np.dot(X, [5, -1])  # target vector
+
+m = np.shape(X)[0]  # nr of samples
+n = np.shape(X)[1]  # nr of features
+
+params, history = iterativeLinearRegression(X, y)
+print(params)
+
+import matplotlib.pyplot as plt
+plt.plot(history)
+plt.xlabel("steps")
+plt.show()