Add lasso-addm example

pycare/examples/addm.py

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+import numpy as np
+import caring
+
+def obj_fun(theta, A, b, lamb, n_samples):
+    # .. the lasso objective function ..
+    loss = (0.5 / n_samples) * np.linalg.norm(A.dot(theta) - b)**2
+    return loss + lamb * np.sum(np.abs(theta))
+
+
+
+def lasso_ADMM(engine: caring.Engine, A, b, max_iter=100, lam=1.):
+    # .. initialize variables ..
+    tau = 1.
+    n_samples, n_features = A.shape
+    rho = np.zeros(n_features)
+    u = np.zeros(n_features)
+
+    # .. to keep track of progress ..
+    obj_fun_history = []
+
+    # .. cache inverse matrix ..
+    AtA_inv = np.linalg.pinv(A.T.dot(A) / n_samples + tau * np.eye(n_features))
+
+    for i in range(max_iter):
+        theta = AtA_inv.dot(A.T.dot(b) / n_samples + tau * (rho - u))
+
+        u0 : list[float] = engine.sum_many(u.tolist())
+        u = np.array(u0) / 2.
+        theta0 = engine.sum_many(theta.tolist())
+        theta = np.array(theta0) / 2.
+        print(f"u = {u}")
+        print(f"theta = {theta}")
+
+        rho = np.fmax(theta + u - lam /tau, 0) - np.fmax(-lam/tau - theta - u, 0)
+        u = u + theta - rho
+        obj_fun_history.append(obj_fun(theta, A, b, lam, n_samples))
+
+    return theta, obj_fun_history

pycare/examples/lasso1.py

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+from addm import lasso_ADMM
+import caring
+import numpy as np
+import matplotlib.pyplot as plt
+
+np.random.seed(0)
+
+n_samples, n_features = 100, 100
+A = np.random.randn(n_samples, n_features)
+w = np.random.randn(n_features)
+b = A.dot(w) + np.random.randn(n_samples)
+
+# .. make b be {-1, 1} since its a classification problem ..
+b = np.sign(A.dot(w) + np.random.randn(n_samples))
+
+
+A_1, A_2 = np.array_split(A, 2)
+b_1, b_2 = np.array_split(b, 2)
+
+
+engine = caring.setup("127.0.0.1:1234", "127.0.0.1:1235")
+theta_1, func_vals = lasso_ADMM(engine, A_1, b_1)
+# lets plot the objective values of the function
+# to make sure it has converged
+plt.plot(func_vals)
+plt.ylabel('function values')
+plt.xlabel('iterations')
+
+plt.grid()
+plt.show()

pycare/examples/lasso2.py

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+from addm import lasso_ADMM
+import caring
+import numpy as np
+import matplotlib.pyplot as plt
+
+np.random.seed(0)
+
+n_samples, n_features = 100, 100
+A = np.random.randn(n_samples, n_features)
+w = np.random.randn(n_features)
+b = A.dot(w) + np.random.randn(n_samples)
+
+# .. make b be {-1, 1} since its a classification problem ..
+b = np.sign(A.dot(w) + np.random.randn(n_samples))
+
+
+A_1, A_2 = np.array_split(A, 2)
+b_1, b_2 = np.array_split(b, 2)
+
+
+engine = caring.setup("127.0.0.1:1235", "127.0.0.1:1234")
+theta_1, func_vals = lasso_ADMM(engine, A_2, b_2)
+# lets plot the objective values of the function
+# to make sure it has converged
+plt.plot(func_vals)
+plt.ylabel('function values')
+plt.xlabel('iterations')
+
+plt.grid()
+plt.show()