Feat: Implement Naive Bayes Classifier for MNIST digits.

 On branch master
 Changes to be committed:
	new file:   naive_bayes.py

Author: dheeraj-coding

naive_bayes.py

@@ -0,0 +1,75 @@
+from mxnet import nd, gluon
+import matplotlib.pyplot as plt
+import random
+
+def show_images(imgs, rows, cols):
+    _, axes = plt.subplots(rows, cols)
+    axes = axes.flatten()
+    for i, (ax, img) in enumerate(zip(axes, imgs)):
+        ax.imshow(img)
+        ax.get_xaxis().set_visible(False)
+        ax.get_yaxis().set_visible(False)
+    plt.show()
+    return axes
+
+def transform(data, label):
+    return (data/128).astype('float32').squeeze(axis=-1), label
+
+def train(train, n_classes):
+    X, Y = train[:]
+    n_y = nd.zeros(n_classes)
+    for y in range(n_classes):
+        n_y[y] = (Y==y).sum()
+    P_y = n_y / n_y.sum()
+
+    n_x = nd.zeros((n_classes, 28, 28))
+    for y in range(n_classes):
+        n_x[y] = nd.array(X.asnumpy()[Y==y].sum(axis=0))
+    P_xy = (n_x+1) / (n_y+1).reshape((10, 1, 1))
+    show_images(P_xy.asnumpy(), 2, 5)
+
+    return P_xy, P_y
+
+def predict(img, P_xy, P_y):
+    img = img.expand_dims(axis=0)
+    log_P_xy = nd.log(P_xy)
+    neg_log_P_xy = nd.log(1-P_xy)
+    pxy = log_P_xy * img + neg_log_P_xy * (1-img)
+    pxy = pxy.reshape((10, -1)).sum(axis=1)
+
+    probs = pxy+nd.log(P_y)
+
+    return probs.argmax(axis=0).asscalar()
+
+def test(test, n_classes, P_xy, P_y):
+    X, Y = test[:]
+    correct = 0
+    for i, img in enumerate(X):
+        result = predict(img, P_xy, P_y)
+        if result == Y[i]:
+            correct += 1
+    acc = (correct/X.shape[0]) * 100
+    print("Accuracy {}%".format(acc))
+    return acc
+
+    
+def main():
+    n_classes = 10
+
+    mnist_train = gluon.data.vision.datasets.MNIST(train=True, transform=transform)
+    mnist_test = gluon.data.vision.datasets.MNIST(train=False, transform=transform)
+
+    P_xy, P_y = train(mnist_train, n_classes)
+    
+    acc = test(mnist_test, n_classes, P_xy, P_y)
+
+    test_X, test_Y = mnist_test[:]
+    index = random.randint(0, test_X.shape[0])
+    result = predict(test_X[index], P_xy, P_y)
+    
+    print("Predicted value {}".format(result))
+    plt.imshow(test_X[index].asnumpy())
+    plt.show()
+   
+if __name__ == "__main__":
+    main()