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