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stochastic_gradient_descent/ML_1.py

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+#!/usr/bin/env python
+# coding: utf-8
+
+# In[1]:
+
+
+import numpy as np
+import matplotlib.pyplot as plt
+import random
+import math
+
+
+# In[2]:
+
+
+def gen_data():
+    X = []
+    y = []
+    for i in range(0,100):
+        X.append(np.random.uniform(1,0))
+        epsilon = np.random.uniform(-0.3,0.3)
+        y.append(math.sin(2 * math.pi * X[i]) + epsilon)
+    return(X,y)  
+
+
+# In[3]:
+
+
+def mse_loss(y_cap,y):
+    return (0.5 * ((y_cap - y)**2))
+
+def mse_loss_derv(y_cap,y):
+    return (2 * (y_cap - y))
+
+def gen_thetas(M):
+    poly = np.random.uniform(-0.5,0.5, M)
+    return poly
+
+
+# In[26]:
+
+
+def poly_model(x, thetas):
+    y_cap = np.sum([(thetas[i])*x**i for i in range(len(thetas))])
+    return(y_cap)
+
+def poly_model_derv(x, i):
+    if i == 0:
+        return 1
+    else:
+        return x**i
+
+
+# In[66]:
+
+
+M = 4
+lr = 0.05
+
+X,y = gen_data()
+
+thetas = gen_thetas(M)
+
+# plt.scatter(X,y)
+# plt.show()
+
+
+# In[6]:
+
+
+def prediction(X,thetas):
+    y_predicted = []
+    for i in range(100):
+        y_predicted.append(poly_model(X[i],thetas))
+    return y_predicted
+
+
+# In[67]:
+
+
+# fig = plt.figure()
+# ax = fig.add_subplot(1,1,1)
+# ax.scatter(X,y)
+
+# time = np.arange(0,1,0.01)
+# amplitude = np.sin(2*np.pi*time)
+# ax.plot(time,amplitude)
+
+# plt.scatter(X,prediction(X,thetas))
+# plt.show()
+
+
+# In[35]:
+
+
+def sgd(Xg,yg,lr,epochs=100):
+
+    for k in range(5000):
+        loss = []
+        for i in range(epochs):
+            y_cap = poly_model(Xg[i],thetas)
+            loss.append(mse_loss(y_cap,yg[i]))
+
+            for j in range(M):
+
+                gradient = mse_loss_derv(y_cap,yg[i]) * poly_model_derv(Xg[i],j)
+                thetas[j] = thetas[j] - (lr * gradient)
+
+    return loss,thetas
+
+
+# In[68]:
+
+
+l,t = sgd(X,y,lr)
+
+
+# In[69]:
+
+
+fig = plt.figure()
+ax = fig.add_subplot(1,1,1)
+ax.scatter(X,y, label='data points')
+
+time = np.arange(0,1,0.01)
+amplitude = np.sin(2*np.pi*time)
+ax.plot(time,amplitude, label='ideal model or sin wave')
+
+y_new = prediction(X,t)
+plt.scatter(X,y_new, label='optimized model')
+plt.legend()
+plt.show()
+
+
+# In[52]:
+
+
+# plt.plot(np.arange(100),l)
+# plt.show()
+# print(len(l))
+