*Learn logistic regression with TensorFlow and Keras in this article by Armando Fandango, an inventor of AI empowered products by leveraging expertise in deep learning, machine learning, distributed computing, and computational methods. He has also provided thought leadership roles as Chief Data Scientist and Director at startups and large enterprises.*

This article will show you how to implement a classification algorithm, known as multinomial logistic regression, to identify the handwritten digits dataset. You’ll use both TensorFlow core and Keras to implement this logistic regression algorithm.

### Logistic regression with TensorFlow

One of the most popular examples regarding multiclass classification is to label the images of handwritten digits. The classes, or labels, in this example are ** {0,1,2,3,4,5,6,7,8,9}**. The dataset that you’ll use is popularly known as MNIST and is available from the following link: http://yann.lecun.com/exdb/mnist/. The MNIST dataset has 60,000 images for training and 10,000 images for testing. The images in the dataset appear as follows:

1. First, import `datasetslib`

, a library from https://github.com/PacktPublishing/TensorFlow-Machine-Learning-Projects:

`DSLIB_HOME = '../datasetslib'`

`import sys`

`if not DSLIB_HOME in sys.path:`

`sys.path.append(DSLIB_HOME)`

`%reload_ext autoreload`

`%autoreload 2`

`import datasetslib as dslib`

`from datasetslib.utils import imutil`

`from datasetslib.utils import nputil`

`from datasetslib.mnist import MNIST`

2. Set the path to the `datasets`

folder in your home directory, which is where you want all of the `datasets`

to be stored:

`import os`

`datasets_root = os.path.join(os.path.expanduser('~'),'datasets')`

3. Get the MNIST data using your `datasetslib`

and print the shapes to ensure that the data is loaded properly:

`mnist=MNIST()`

`x_train,y_train,x_test,y_test=mnist.load_data()`

`mnist.y_onehot = True`

`mnist.x_layout = imutil.LAYOUT_NP`

`x_test = mnist.load_images(x_test)`

`y_test = nputil.onehot(y_test)`

`print('Loaded x and y')`

`print('Train: x:{}, y:{}'.format(len(x_train),y_train.shape))`

`print('Test: x:{}, y:{}'.format(x_test.shape,y_test.shape))`

4. Define the hyperparameters for training the model:

`learning_rate = 0.001`

`n_epochs = 5`

`mnist.batch_size = 100`

5. Define the placeholders and parameters for your simple model:

`# define input images`

`x = tf.placeholder(dtype=tf.float32, shape=[None, mnist.n_features])`

`# define output labels`

`y = tf.placeholder(dtype=tf.float32, shape=[None, mnist.n_classes])`

`# model parameters`

`w = tf.Variable(tf.zeros([mnist.n_features, mnist.n_classes]))`

`b = tf.Variable(tf.zeros([mnist.n_classes]))`

6. Define the model with `logits`

and `y_hat`

:

`logits = tf.add(tf.matmul(x, w), b)`

`y_hat = tf.nn.softmax(logits)`

7. Define the `loss`

function:

`epsilon = tf.keras.backend.epsilon()`

`y_hat_clipped = tf.clip_by_value(y_hat, epsilon, 1 - epsilon)`

`y_hat_log = tf.log(y_hat_clipped)`

`cross_entropy = -tf.reduce_sum(y * y_hat_log, axis=1)`

`loss_f = tf.reduce_mean(cross_entropy)`

8. Define the `optimizer`

function:

`optimizer = tf.train.GradientDescentOptimizer`

`optimizer_f = optimizer(learning_rate=learning_rate).minimize(loss_f)`

9. Define the function to check the accuracy of the trained model:

`predictions_check = tf.equal(tf.argmax(y_hat, 1), tf.argmax(y, 1))`

`accuracy_f = tf.reduce_mean(tf.cast(predictions_check, tf.float32))`

10. Run the `training`

loop for each epoch in a TensorFlow session:

`n_batches = int(60000/mnist.batch_size)`

`with tf.Session() as tfs:`

`tf.global_variables_initializer().run()`

`for epoch in range(n_epochs):`

`mnist.reset_index()`

`for batch in range(n_batches):`

`x_batch, y_batch = mnist.next_batch()`

`feed_dict={x: x_batch, y: y_batch}`

`batch_loss,_ = tfs.run([loss_f, optimizer_f],feed_dict=feed_dict )`

`#print('Batch loss:{}'.format(batch_loss))`

11. Run the evaluation function for each epoch with the test data in the same TensorFlow session that was created previously:

`feed_dict = {x: x_test, y: y_test}`

`accuracy_score = tfs.run(accuracy_f, feed_dict=feed_dict)`

`print('epoch {0:04d} accuracy={1:.8f}'`

`.format(epoch, accuracy_score))`

You’ll get the following output:

`epoch 0000 accuracy=0.73280001 epoch 0001 accuracy=0.72869998 epoch 0002 accuracy=0.74550003 epoch 0003 accuracy=0.75260001 epoch 0004 accuracy=0.74299997`

There you go. You just trained your very first logistic regression model using TensorFlow for classifying handwritten digit images and got 74.3% accuracy. Now, see how writing the same model in Keras makes this process even easier.

### Logistic regression with Keras

**Keras** is a high-level library that is available as part of TensorFlow. In this section, you will rebuild the same model built earlier with TensorFlow core with Keras:

1. Keras takes data in a different format and so, you must first reformat the data using `datasetslib`

:

`x_train_im = mnist.load_images(x_train)`

`x_train_im, x_test_im = x_train_im / 255.0, x_test / 255.0`

In the preceding code, you are loading the training images in memory before both the training and test images are scaled, which you do by dividing them by `255`

.

2. Then, you build the model:

`model = tf.keras.models.Sequential([`

`tf.keras.layers.Flatten(),`

`tf.keras.layers.Dense(10, activation=tf.nn.softmax)`

`])`

3. Compile the model with the `sgd`

optimizer. Set the categorical entropy as the `loss`

function and the accuracy as a metric to test the model:

`model.compile(optimizer='sgd',`

`loss='sparse_categorical_crossentropy',`

`metrics=['accuracy'])`

4. Train the model for `5`

epochs with the training set of images and labels:

`model.fit(x_train_im, y_train, epochs=5)`

`Epoch 1/5`

`60000/60000 [==============================] - 3s 45us/step - loss: 0.7874 - acc: 0.8095`

`Epoch 2/5`

`60000/60000 [==============================] - 3s 42us/step - loss: 0.4585 - acc: 0.8792`

`Epoch 3/5`

`60000/60000 [==============================] - 2s 42us/step - loss: 0.4049 - acc: 0.8909`

`Epoch 4/5`

`60000/60000 [==============================] - 3s 42us/step - loss: 0.3780 - acc: 0.8965`

`Epoch 5/5`

`60000/60000 [==============================] - 3s 42us/step - loss: 0.3610 - acc: 0.9012`

`10000/10000 [==============================] - 0s 24us/step`

5. Evaluate the model with the test data:

`model.evaluate(x_test_im, nputil.argmax(y_test))`

You’ll get the following evaluation scores as output:

`[0.33530342621803283, 0.9097]`

Wow! Using Keras, you can achieve higher accuracy. Here, you achieved approximately 90% accuracy. This is because Keras internally sets many optimal values so that you can quickly start building models.

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