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This quickstart tutorial demonstrates how you can use the TensorFlow Core low-level APIs to build and train a multiple linear regression model that predicts fuel efficiency. It uses the Auto MPG dataset which contains fuel efficiency data for late-1970s and early 1980s automobiles.

You will follow the typical stages of a machine learning process:

- Load the dataset.
- Build an input pipeline.
- Build a multiple linear regression model.
- Evaluate the performance of the model.

## Setup

Import TensorFlow and other necessary libraries to get started:

```
import tensorflow as tf
import pandas as pd
import matplotlib
from matplotlib import pyplot as plt
print("TensorFlow version:", tf.__version__)
# Set a random seed for reproducible results
tf.random.set_seed(22)
```

2024-07-19 03:10:58.529724: E external/local_xla/xla/stream_executor/cuda/cuda_fft.cc:485] Unable to register cuFFT factory: Attempting to register factory for plugin cuFFT when one has already been registered 2024-07-19 03:10:58.550668: E external/local_xla/xla/stream_executor/cuda/cuda_dnn.cc:8454] Unable to register cuDNN factory: Attempting to register factory for plugin cuDNN when one has already been registered 2024-07-19 03:10:58.557191: E external/local_xla/xla/stream_executor/cuda/cuda_blas.cc:1452] Unable to register cuBLAS factory: Attempting to register factory for plugin cuBLAS when one has already been registered TensorFlow version: 2.17.0

## Load and preprocess the dataset

Next, you need to load and preprocess the Auto MPG dataset from the UCI Machine Learning Repository. This dataset uses a variety of quantitative and categorical features such as cylinders, displacement, horsepower and weight to predict the fuel efficiencies of automobiles in the late-1970s and early 1980s.

The dataset contains a few unknown values. Make sure to drop any missing values with `pandas.DataFrame.dropna`

, and convert the dataset to a `tf.float32`

tensor type with the `tf.convert_to_tensor`

and `tf.cast`

functions.

```
url = 'http://archive.ics.uci.edu/ml/machine-learning-databases/auto-mpg/auto-mpg.data'
column_names = ['MPG', 'Cylinders', 'Displacement', 'Horsepower', 'Weight',
'Acceleration', 'Model Year', 'Origin']
dataset = pd.read_csv(url, names=column_names, na_values='?', comment='\t',
sep=' ', skipinitialspace=True)
dataset = dataset.dropna()
dataset_tf = tf.convert_to_tensor(dataset, dtype=tf.float32)
dataset.tail()
```

WARNING: All log messages before absl::InitializeLog() is called are written to STDERR I0000 00:00:1721358661.581093 188183 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721358661.584998 188183 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721358661.588229 188183 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721358661.591436 188183 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721358661.602597 188183 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721358661.605610 188183 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721358661.608434 188183 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721358661.611361 188183 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721358661.614314 188183 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721358661.617207 188183 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721358661.620201 188183 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721358661.623143 188183 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721358662.860014 188183 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721358662.862049 188183 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721358662.864099 188183 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721358662.866247 188183 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721358662.868335 188183 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721358662.870190 188183 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721358662.872147 188183 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721358662.874136 188183 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721358662.876124 188183 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721358662.877956 188183 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721358662.879910 188183 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721358662.881921 188183 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721358662.920748 188183 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721358662.922684 188183 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721358662.924672 188183 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721358662.926706 188183 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721358662.928705 188183 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721358662.930574 188183 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721358662.932534 188183 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721358662.934542 188183 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721358662.936548 188183 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721358662.938894 188183 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721358662.941284 188183 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721358662.943710 188183 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355

Next, split the dataset into training and test sets. Make sure to shuffle the dataset with `tf.random.shuffle`

to avoid biased splits.

```
dataset_shuffled = tf.random.shuffle(dataset_tf, seed=22)
train_data, test_data = dataset_shuffled[100:], dataset_shuffled[:100]
x_train, y_train = train_data[:, 1:], train_data[:, 0]
x_test, y_test = test_data[:, 1:], test_data[:, 0]
```

Perform basic feature engineering by one-hot-encoding the `"Origin"`

feature. The `tf.one_hot`

function is useful for transforming this categorical column into 3 separate binary columns.

```
def onehot_origin(x):
origin = tf.cast(x[:, -1], tf.int32)
# Use `origin - 1` to account for 1-indexed feature
origin_oh = tf.one_hot(origin - 1, 3)
x_ohe = tf.concat([x[:, :-1], origin_oh], axis = 1)
return x_ohe
x_train_ohe, x_test_ohe = onehot_origin(x_train), onehot_origin(x_test)
x_train_ohe.numpy()
```

array([[ 4., 140., 72., ..., 1., 0., 0.], [ 4., 120., 74., ..., 0., 0., 1.], [ 4., 122., 88., ..., 0., 1., 0.], ..., [ 8., 318., 150., ..., 1., 0., 0.], [ 4., 156., 105., ..., 1., 0., 0.], [ 6., 232., 100., ..., 1., 0., 0.]], dtype=float32)

This example shows a multiple regression problem with predictors or features on vastly different scales. Therefore, it is beneficial to standardize the data so that each feature has zero mean and unit variance. Use the `tf.reduce_mean`

and `tf.math.reduce_std`

functions for standardization. The regression model's prediction can then be unstandardized to obtain its value in terms of the original units.

```
class Normalize(tf.Module):
def __init__(self, x):
# Initialize the mean and standard deviation for normalization
self.mean = tf.math.reduce_mean(x, axis=0)
self.std = tf.math.reduce_std(x, axis=0)
def norm(self, x):
# Normalize the input
return (x - self.mean)/self.std
def unnorm(self, x):
# Unnormalize the input
return (x * self.std) + self.mean
```

```
norm_x = Normalize(x_train_ohe)
norm_y = Normalize(y_train)
x_train_norm, y_train_norm = norm_x.norm(x_train_ohe), norm_y.norm(y_train)
x_test_norm, y_test_norm = norm_x.norm(x_test_ohe), norm_y.norm(y_test)
```

## Build a machine learning model

Build a linear regression model with the TensorFlow Core APIs. The equation for multiple linear regression is as follows:

\[{\mathrm{Y} } = {\mathrm{X} }w + b\]

where

- \(\underset{m\times 1}{\mathrm{Y} }\): target vector
- \(\underset{m\times n}{\mathrm{X} }\): feature matrix
- \(\underset{n\times 1}w\): weight vector
- \(b\): bias

By using the `@tf.function`

decorator, the corresponding Python code is traced to generate a callable TensorFlow graph. This approach is beneficial for saving and loading the model after training. It can also provide a performance boost for models with many layers and complex operations.

```
class LinearRegression(tf.Module):
def __init__(self):
self.built = False
@tf.function
def __call__(self, x):
# Initialize the model parameters on the first call
if not self.built:
# Randomly generate the weight vector and bias term
rand_w = tf.random.uniform(shape=[x.shape[-1], 1])
rand_b = tf.random.uniform(shape=[])
self.w = tf.Variable(rand_w)
self.b = tf.Variable(rand_b)
self.built = True
y = tf.add(tf.matmul(x, self.w), self.b)
return tf.squeeze(y, axis=1)
```

For each example, the model returns a prediction for the input automobile's MPG by computing the weighted sum of its features plus a bias term. This prediction can then be unstandardized to obtain its value in terms of the original units.

```
lin_reg = LinearRegression()
prediction = lin_reg(x_train_norm[:1])
prediction_unnorm = norm_y.unnorm(prediction)
prediction_unnorm.numpy()
```

array([6.8007355], dtype=float32)

## Define a loss function

Now, define a loss function to evaluate the model's performance during the training process.

Since regression problems deal with continuous outputs, the mean squared error (MSE) is an ideal choice for the loss function. The MSE is defined by the following equation:

\[MSE = \frac{1}{m}\sum_{i=1}^{m}(\hat{y}_i -y_i)^2\]

where

- \(\hat{y}\): vector of predictions
- \(y\): vector of true targets

The goal of this regression problem is to find the optimal weight vector, \(w\), and bias, \(b\), that minimizes the MSE loss function.

```
def mse_loss(y_pred, y):
return tf.reduce_mean(tf.square(y_pred - y))
```

## Train and evaluate your model

Using mini-batches for training provides both memory efficiency and faster convergence. The `tf.data.Dataset`

API has useful functions for batching and shuffling. The API enables you to build complex input pipelines from simple, reusable pieces. Learn more about building TensorFlow input pipelines in this guide.

```
batch_size = 64
train_dataset = tf.data.Dataset.from_tensor_slices((x_train_norm, y_train_norm))
train_dataset = train_dataset.shuffle(buffer_size=x_train.shape[0]).batch(batch_size)
test_dataset = tf.data.Dataset.from_tensor_slices((x_test_norm, y_test_norm))
test_dataset = test_dataset.shuffle(buffer_size=x_test.shape[0]).batch(batch_size)
```

Next, write a training loop to iteratively update your model's parameters by making use of the MSE loss function and its gradients with respect to the input parameters.

This iterative method is referred to as gradient descent. At each iteration, the model's parameters are updated by taking a step in the opposite direction of their computed gradients. The size of this step is determined by the learning rate, which is a configurable hyperparameter. Recall that the gradient of a function indicates the direction of its steepest ascent; therefore, taking a step in the opposite direction indicates the direction of steepest descent, which ultimately helps to minimize the MSE loss function.

```
# Set training parameters
epochs = 100
learning_rate = 0.01
train_losses, test_losses = [], []
# Format training loop
for epoch in range(epochs):
batch_losses_train, batch_losses_test = [], []
# Iterate through the training data
for x_batch, y_batch in train_dataset:
with tf.GradientTape() as tape:
y_pred_batch = lin_reg(x_batch)
batch_loss = mse_loss(y_pred_batch, y_batch)
# Update parameters with respect to the gradient calculations
grads = tape.gradient(batch_loss, lin_reg.variables)
for g,v in zip(grads, lin_reg.variables):
v.assign_sub(learning_rate * g)
# Keep track of batch-level training performance
batch_losses_train.append(batch_loss)
# Iterate through the testing data
for x_batch, y_batch in test_dataset:
y_pred_batch = lin_reg(x_batch)
batch_loss = mse_loss(y_pred_batch, y_batch)
# Keep track of batch-level testing performance
batch_losses_test.append(batch_loss)
# Keep track of epoch-level model performance
train_loss = tf.reduce_mean(batch_losses_train)
test_loss = tf.reduce_mean(batch_losses_test)
train_losses.append(train_loss)
test_losses.append(test_loss)
if epoch % 10 == 0:
print(f'Mean squared error for step {epoch}: {train_loss.numpy():0.3f}')
# Output final losses
print(f"\nFinal train loss: {train_loss:0.3f}")
print(f"Final test loss: {test_loss:0.3f}")
```

Mean squared error for step 0: 2.866 Mean squared error for step 10: 0.453 Mean squared error for step 20: 0.285 Mean squared error for step 30: 0.231 Mean squared error for step 40: 0.209 Mean squared error for step 50: 0.203 Mean squared error for step 60: 0.194 Mean squared error for step 70: 0.184 Mean squared error for step 80: 0.186 Mean squared error for step 90: 0.176 Final train loss: 0.177 Final test loss: 0.157

Plot the changes in MSE loss over time. Calculating performance metrics on a designated validation set or test set ensures the model does not overfit to the training dataset and can generalize well to unseen data.

```
matplotlib.rcParams['figure.figsize'] = [9, 6]
plt.plot(range(epochs), train_losses, label = "Training loss")
plt.plot(range(epochs), test_losses, label = "Testing loss")
plt.xlabel("Epoch")
plt.ylabel("Mean squared error loss")
plt.legend()
plt.title("MSE loss vs training iterations");
```

It seems like the model does a good job of fitting the training data while also generalizing well to the unseen test data.

## Save and load the model

Start by making an export module that takes in raw data and performs the following operations:

- Feature extraction
- Normalization
- Prediction
- Unnormalization

```
class ExportModule(tf.Module):
def __init__(self, model, extract_features, norm_x, norm_y):
# Initialize pre and postprocessing functions
self.model = model
self.extract_features = extract_features
self.norm_x = norm_x
self.norm_y = norm_y
@tf.function(input_signature=[tf.TensorSpec(shape=[None, None], dtype=tf.float32)])
def __call__(self, x):
# Run the ExportModule for new data points
x = self.extract_features(x)
x = self.norm_x.norm(x)
y = self.model(x)
y = self.norm_y.unnorm(y)
return y
```

```
lin_reg_export = ExportModule(model=lin_reg,
extract_features=onehot_origin,
norm_x=norm_x,
norm_y=norm_y)
```

If you want to save the model at its current state, use the `tf.saved_model.save`

function. To load a saved model for making predictions, use the `tf.saved_model.load`

function.

```
import tempfile
import os
models = tempfile.mkdtemp()
save_path = os.path.join(models, 'lin_reg_export')
tf.saved_model.save(lin_reg_export, save_path)
```

INFO:tensorflow:Assets written to: /tmpfs/tmp/tmp82n361w_/lin_reg_export/assets INFO:tensorflow:Assets written to: /tmpfs/tmp/tmp82n361w_/lin_reg_export/assets

```
lin_reg_loaded = tf.saved_model.load(save_path)
test_preds = lin_reg_loaded(x_test)
test_preds[:10].numpy()
```

array([28.097498, 26.193336, 33.564373, 27.719315, 31.787922, 24.014559, 24.421043, 13.459579, 28.562454, 27.368692], dtype=float32)

## Conclusion

Congratulations! You have trained a regression model using the TensorFlow Core low-level APIs.

For more examples of using TensorFlow Core APIs, check out the following guides:

- Logistic regression for binary classification
- Multi-layer perceptrons for hand-written digit recognition