removing invalid character on windows

python/Supervised Learning/Linear Regression/16 Quiz Mini-Batch Gradient Descent/batch_graddesc.py

@@ -0,0 +1,92 @@
+import numpy as np
+# Setting a random seed, feel free to change it and see different solutions.
+np.random.seed(42)
+
+
+# TODO: Fill in code in the function below to implement a gradient descent
+# step for linear regression, following a squared error rule. See the docstring
+# for parameters and returned variables.
+def MSEStep(X, y, W, b, learn_rate=0.005):
+    """
+    This function implements the gradient descent step for squared error as a
+    performance metric.
+
+    Parameters
+    X : array of predictor features
+    y : array of outcome values
+    W : predictor feature coefficients
+    b : regression function intercept
+    learn_rate : learning rate
+
+    Returns
+    W_new : predictor feature coefficients following gradient descent step
+    b_new : intercept following gradient descent step
+    """
+
+    # compute errors
+    y_pred = np.matmul(X, W) + b
+    error = y - y_pred
+
+    # compute steps
+    W_new = W + learn_rate * np.matmul(error, X)
+    b_new = b + learn_rate * error.sum()
+    return W_new, b_new
+
+    return W_new, b_new
+
+
+# The parts of the script below will be run when you press the "Test Run"
+# button. The gradient descent step will be performed multiple times on
+# the provided dataset, and the returned list of regression coefficients
+# will be plotted.
+def miniBatchGD(X, y, batch_size=20, learn_rate=0.005, num_iter=25):
+    """
+    This function performs mini-batch gradient descent on a given dataset.
+
+    Parameters
+    X : array of predictor features
+    y : array of outcome values
+    batch_size : how many data points will be sampled for each iteration
+    learn_rate : learning rate
+    num_iter : number of batches used
+
+    Returns
+    regression_coef : array of slopes and intercepts generated by gradient
+      descent procedure
+    """
+    n_points = X.shape[0]
+    W = np.zeros(X.shape[1])  # coefficients
+    b = 0  # intercept
+
+    # run iterations
+    regression_coef = [np.hstack((W, b))]
+    for _ in range(num_iter):
+        batch = np.random.choice(range(n_points), batch_size)
+        X_batch = X[batch, :]
+        y_batch = y[batch]
+        W, b = MSEStep(X_batch, y_batch, W, b, learn_rate)
+        regression_coef.append(np.hstack((W, b)))
+
+    return regression_coef
+
+
+if __name__ == "__main__":
+    # perform gradient descent
+    data = np.loadtxt('data.csv', delimiter=',')
+    X = data[:, :-1]
+    y = data[:, -1]
+    regression_coef = miniBatchGD(X, y)
+
+    # plot the results
+    import matplotlib.pyplot as plt
+
+    plt.figure()
+    X_min = X.min()
+    X_max = X.max()
+    counter = len(regression_coef)
+    for W, b in regression_coef:
+        counter -= 1
+        color = [1 - 0.92 ** counter for _ in range(3)]
+        plt.plot([X_min, X_max], [X_min * W + b, X_max * W + b], color=color)
+    plt.scatter(X, y, zorder=3)
+    plt.show()

python/Supervised Learning/Linear Regression/16 Quiz Mini-Batch Gradient Descent/data.csv

@@ -0,0 +1,100 @@
+-0.72407,2.23863
+-2.40724,-0.00156
+2.64837,3.01665
+0.36092,2.31019
+0.67312,2.05950
+-0.45460,1.24736
+2.20168,2.82497
+1.15605,2.21802
+0.50694,1.43644
+-0.85952,1.74980
+-0.59970,1.63259
+1.46804,2.43461
+-1.05659,1.02226
+1.29177,3.11769
+-0.74565,0.81194
+0.15033,2.81910
+-1.49627,0.53105
+-0.72071,1.64845
+0.32924,1.91416
+-0.28053,2.11376
+-1.36115,1.70969
+0.74678,2.92253
+0.10621,3.29827
+0.03256,1.58565
+-0.98290,2.30455
+-1.15661,1.79169
+0.09024,1.54723
+-1.03816,1.06893
+-0.00604,1.78802
+0.16278,1.84746
+-0.69869,1.58732
+1.03857,1.94799
+-0.11783,3.09324
+-0.95409,1.86155
+-0.81839,1.88817
+-1.28802,1.39474
+0.62822,1.71526
+-2.29674,1.75695
+-0.85601,1.12981
+-1.75223,1.67000
+-1.19662,0.66711
+0.97781,3.11987
+-1.17110,0.56924
+0.15835,2.28231
+-0.58918,1.23798
+-1.79678,1.35803
+-0.95727,1.75579
+0.64556,1.91470
+0.24625,2.33029
+0.45917,3.25263
+1.21036,2.07602
+-0.60116,1.54254
+0.26851,2.79202
+0.49594,1.96178
+-2.67877,0.95898
+0.49402,1.96690
+1.18643,3.06144
+-0.17741,1.85984
+0.57938,1.82967
+-2.14926,0.62285
+2.27700,3.63838
+-1.05695,1.11807
+1.68288,2.91735
+-1.53513,1.99668
+0.00099,1.76149
+0.45520,2.31938
+-0.37855,0.90172
+1.35638,3.49432
+0.01763,1.87838
+2.21725,2.61171
+-0.44442,2.06623
+0.89583,3.04041
+1.30499,2.42824
+0.10883,0.63190
+1.79466,2.95265
+-0.00733,1.87546
+0.79862,3.44953
+-0.12353,1.53740
+-1.34999,1.59958
+-0.67825,1.57832
+-0.17901,1.73312
+0.12577,2.00244
+1.11943,2.08990
+-3.02296,1.09255
+0.64965,1.28183
+1.05994,2.32358
+0.53360,1.75136
+-0.73591,1.43076
+-0.09569,2.81376
+1.04694,2.56597
+0.46511,2.36401
+-0.75463,2.30161
+-0.94159,1.94500
+-0.09314,1.87619
+-0.98641,1.46602
+-0.92159,1.21538
+0.76953,2.39377
+0.03283,1.55730
+-1.07619,0.70874
+0.20174,1.76894

python/Supervised Learning/Linear Regression/16 Quiz Mini-Batch Gradient Descent/solution.py

@@ -0,0 +1,25 @@
+def MSEStep(X, y, W, b, learn_rate = 0.001):
+    """
+    This function implements the gradient descent step for squared error as a
+    performance metric.
+
+    Parameters
+    X : array of predictor features
+    y : array of outcome values
+    W : predictor feature coefficients
+    b : regression function intercept
+    learn_rate : learning rate
+
+    Returns
+    W_new : predictor feature coefficients following gradient descent step
+    b_new : intercept following gradient descent step
+    """
+
+    # compute errors
+    y_pred = np.matmul(X, W) + b
+    error = y - y_pred
+
+    # compute steps
+    W_new = W + learn_rate * np.matmul(error, X)
+    b_new = b + learn_rate * error.sum()
+    return W_new, b_new