Answer:
In[7] def pegasos(feature_matrix, labels, T, L):
"""
.
let learning rate = 1/sqrt(t),
where t is a counter for the number of updates performed so far (between 1 and nT inclusive).
Args:
feature_matrix - A numpy matrix describing the given data. Each row
represents a single data point.
labels - A numpy array where the kth element of the array is the
correct classification of the kth row of the feature matrix.
T - the maximum number of times that you should iterate through the feature matrix before terminating the algorithm.
L - The lamba valueto update the pegasos
Returns: Is defined as a tuple in which the first element is the final value of θ and the second element is the value of θ0
"""
(nsamples, nfeatures) = feature_matrix.shape
theta = np.zeros(nfeatures)
theta_0 = 0
count = 0
for t in range(T):
for i in get_order(nsamples):
count += 1
eta = 1.0 / np.sqrt(count)
(theta, theta_0) = pegasos_single_step_update(
feature_matrix[i], labels[i], L, eta, theta, theta_0)
return (theta, theta_0)
In[7] (np.array([1-1/np.sqrt(2), 1-1/np.sqrt(2)]), 1)
Out[7] (array([0.29289322, 0.29289322]), 1)
In[8] feature_matrix = np.array([[1, 1], [1, 1]])
labels = np.array([1, 1])
T = 1
L = 1
exp_res = (np.array([1-1/np.sqrt(2), 1-1/np.sqrt(2)]), 1)
pegasos(feature_matrix, labels, T, L)
Out[8] (array([0.29289322, 0.29289322]), 1.0)
Explanation:
In[7] def pegasos(feature_matrix, labels, T, L):
"""
.
let learning rate = 1/sqrt(t),
where t is a counter for the number of updates performed so far (between 1 and nT inclusive).
Args:
feature_matrix - A numpy matrix describing the given data. Each row
represents a single data point.
labels - A numpy array where the kth element of the array is the
correct classification of the kth row of the feature matrix.
T - the maximum number of times that you should iterate through the feature matrix before terminating the algorithm.
L - The lamba valueto update the pegasos
Returns: Is defined as a tuple in which the first element is the final value of θ and the second element is the value of θ0
"""
(nsamples, nfeatures) = feature_matrix.shape
theta = np.zeros(nfeatures)
theta_0 = 0
count = 0
for t in range(T):
for i in get_order(nsamples):
count += 1
eta = 1.0 / np.sqrt(count)
(theta, theta_0) = pegasos_single_step_update(
feature_matrix[i], labels[i], L, eta, theta, theta_0)
return (theta, theta_0)
In[7] (np.array([1-1/np.sqrt(2), 1-1/np.sqrt(2)]), 1)
Out[7] (array([0.29289322, 0.29289322]), 1)
In[8] feature_matrix = np.array([[1, 1], [1, 1]])
labels = np.array([1, 1])
T = 1
L = 1
exp_res = (np.array([1-1/np.sqrt(2), 1-1/np.sqrt(2)]), 1)
pegasos(feature_matrix, labels, T, L)
Out[8] (array([0.29289322, 0.29289322]), 1.0)
