Answered: def weighted_mse_grad(w, X, y, V): """…

Computer Networking: A Top-Down Approach (7th Edition)

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

Section: Chapter Questions

Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

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def weighted_mse_grad(w, X, y, V):
"""
Calculate gradient of the weight MSE loss in the given point w

Parameters
----------
w: array_like
Current point, in which we want to evaluate gradient (vector with k+1 elements)
X: array_like
Design matrix with N rows and k+1 columns
y: array_like
Vector with N observations of the target variable
V: array_like
Diagonal matrix N x N, with the weights

Returns
----------
out: ndarray
vector of gradient, k+1
"""
# your code here

# TEST weighted_mse_grad()
w = np.zeros(5)
X = np.random.randn(10, 5)
y = np.ones(10)
V = np.diag(np.ones(10))

L_grad = weighted_mse_grad(w, X, y, V)
assert(L_grad.shape == (5,))

w = np.zeros(5)
X = np.eye(5)
y = np.ones(5)
V = np.diag(np.ones(5))
L_grad = weighted_mse_grad(w, X, y, V)
assert(L_grad.shape == (5,)), 'The shape of the output on the test case is wrong'
assert(np.allclose(5 * L_grad,- y * 2)), 'The values of the output on the test case is wrong'