**Regression deep learning** is a type of machine learning that is used for predicting continuous values. Unlike classification, where the goal is to predict a categorical label, regression is used for problems where the target variable is a continuous value.

Regression deep learning models are built using artificial neural networks and trained on large datasets to learn the relationships between the input features and the target variable. These models can capture non-linear relationships and handle large amounts of data, making them well-suited for complex regression problems.

Examples of regression problems include predicting the price of a house or a car, forecasting stock prices, or predicting the energy consumption of a building. In each of these cases, the goal is to use input features such as the size of the house, the number of rooms, or the stock’s historical prices to predict a continuous target value.

**Car Price Forecasting**

Predicting the price of a car is an important task in the automobile industry. The price of a car is influenced by various factors such as make, model, year, engine size, transmission, mileage, and other features. In this article, we will see how to build a deep learning regression model to predict car prices using **TensorFlow**.

**Step 1: Data Collection**

The first step is to collect data that will be used to train the model. The data should include the car’s make, model, year, engine size, transmission, mileage, and other relevant features along with their prices. This data can be obtained from various sources such as online databases, classifieds, or car dealerships.

Here’s an example code for collecting data for car prices using the `pandas`

library in Python:

```
import pandas as pd
import numpy as np
# URL for the car prices dataset
url = "https://raw.githubusercontent.com/selva86/datasets/master/Cars93.csv"
# Load the dataset into a Pandas dataframe
car_data = pd.read_csv(url)
# Display the first 5 rows of the dataset
print(car_data .head())
```

This code loads the car prices dataset from a URL into a Pandas dataframe. The `pandas`

library provides several functions for reading and writing data, including reading from a CSV file using `pd.read_csv()`

. The first five rows of the dataset are displayed using the `head()`

method.

**Step 2: Data Preprocessing**

The next step is to preprocess the collected data. This includes cleaning the data, handling missing values, and normalizing the data if necessary.

Here is a code example in Python for data preprocessing for a car price prediction model using TensorFlow:

```
# Drop all rows with NaN values
car_data = car_data.dropna()
car_data = car_data.dropna(axis=0)
# Select numeric features for building regression model
df = car_data.filter(['Price', 'MPG.city','EngineSize', 'Passengers', 'Cylinders', 'Horsepower' ], axis=1)
# Handle missing values
df.fillna(df.mean(), inplace=True)
# Normalize the data
cols_to_norm = ['MPG.city','EngineSize', 'Passengers', 'Cylinders', 'Horsepower']
df[cols_to_norm] = (df[cols_to_norm] - df[cols_to_norm].mean()) / df[cols_to_norm].std()
# Split the data into training and test sets
train_data = df[:int(0.8 * len(df))]
test_data = df[int(0.8 * len(df)):]
# Convert the data into numpy arrays
train_x = np.array(train_data.drop('Price', axis=1))
train_y = np.array(train_data['Price'])
test_x = np.array(test_data.drop('Price', axis=1))
test_y = np.array(test_data['Price'])
```

In this example, the data is loaded into a pandas dataframe `df`

and missing values are handled by replacing them with the mean values. The data is then normalized by subtracting the mean and dividing by the standard deviation. The data is split into training and test sets and finally converted into NumPy arrays for use in TensorFlow.

**Step 3: Define the Model Architecture**

The next step is to define the model architecture. For this problem, a **feedforward neural network with two or three hidden layers** and **64-128 neurons** in each layer can be used. The activation functions used in the hidden layers can be **ReLU**, while a linear activation function can be used in the output layer.

Here is a code example in TensorFlow for defining the loss function and optimizer for a car price prediction model:

```
import tensorflow as tf
# Define the model
model = tf.keras.Sequential()
model.add(tf.keras.layers.Dense(64, activation='relu', input_shape=(train_x.shape[1],)))
model.add(tf.keras.layers.Dense(64, activation='relu'))
model.add(tf.keras.layers.Dense(1))
# Compile the model
model.compile(optimizer=tf.keras.optimizers.Adam(0.01), loss='mean_squared_error')
```

In this example, a feedforward neural network with two hidden layers and 64 neurons in each layer is defined using the

model. The activation function used in the hidden layers is ReLU and the output layer has a linear activation function. The model is then compiled using the **tf.keras.Sequential****Adam optimizer** and mean squared error loss function. The learning rate for the optimizer is set to 0.01.

**Step 4: Define the Loss Function and Optimizer**

The loss function is used to measure the error between the predicted values and the true values. **Mean squared error** or mean absolute error can be used as the loss function for this problem. An optimizer updates the model’s weights to minimize the loss. The Adam optimizer is a good choice for this problem.

**Step 5: Set the Hyperparameters**

The hyperparameters are the parameters that are set before training the model and they can have a significant impact on the model’s performance. Common hyperparameters include the learning rate, batch size, and number of epochs. For this problem, a learning rate of 0.001-0.01, batch size of 32-64, and number of epochs of 100-500 can be used as starting points.

**Step 6: Train the Model**

The next step is to train the model using the training data and the defined loss function and optimizer.

Here is a code example in TensorFlow for training a car price prediction model:

```
# Train the model
history = model.fit(train_x, train_y, epochs=50, batch_size=32, validation_data=(test_x, test_y))
```

In this example, the model is trained using the `fit`

method of the defined model object. The training data is `train_x`

and `train_y`

and the model is trained for 50 epochs with a batch size of 32. The validation data is `test_x`

and `test_y`

and is used to evaluate the model after each epoch. The `history`

object contains the training and validation loss and accuracy at each epoch and can be used to plot the learning curve and evaluate the performance of the model.

**Step 7: Evaluate the Model**

The final step is to evaluate the model’s performance using the test data. The error can be computed using the chosen loss function.

Here is a code example in TensorFlow for evaluating a car price prediction model:

```
# Evaluate the model
from sklearn.metrics import mean_squared_error
import math
# Predict test data
predictions = model.predict(test_x)
# Calculate MSE
test_loss = mean_squared_error(test_y, predictions)
print('MSE:', test_loss)
print("RMSE:", math.sqrt(test_loss))
```

In this example, the model is evaluated using the `evaluate`

method of the defined model object. The evaluation is performed on the test data `test_x`

. The loss value indicates the average error of the model in predicting the car prices, and the accuracy is not applicable in this regression problem.

Here’s an example code for plotting the loss of a deep learning model after evaluating it using the `matplotlib`

library in Python:

```
import matplotlib.pyplot as plt
# summarize history for loss
plt.plot(history.history['loss'])
plt.plot(history.history['val_loss'])
plt.title('model loss')
plt.ylabel('loss')
plt.xlabel('epoch')
plt.legend(['train', 'test'], loc='upper left')
plt.show()
```

The `bar()`

function from the `matplotlib`

library is used to plot a bar graph with the test loss value. The `xlabel()`

, `ylabel()`

, and `title()`

functions are used to add labels to the x-axis, y-axis, and title of the plot, respectively. The `show()`

function displays the plot.

**Step 8: Tune the Hyperparameters**

If the performance is not satisfactory, the hyperparameters can be adjusted and the training and evaluation process can be repeated. In general, building a deep learning regression model for car price prediction using TensorFlow is a straightforward process. The model can be improved by fine-tuning the hyperparameters and the architecture, or by using advanced techniques such as cross-validation or grid search.

Here is a code example in TensorFlow for tuning the hyperparameters of a car price prediction model using **GridSearchCV**:

```
from sklearn.model_selection import GridSearchCV
from tensorflow.keras.wrappers.scikit_learn import KerasRegressor
def create_model(hidden_layer_1=64, hidden_layer_2=64, learning_rate=0.01):
model = tf.keras.Sequential()
model.add(tf.keras.layers.Dense(hidden_layer_1, activation='relu', input_shape=(train_x.shape[1],)))
model.add(tf.keras.layers.Dense(hidden_layer_2, activation='relu'))
model.add(tf.keras.layers.Dense(1))
model.compile(optimizer=tf.keras.optimizers.Adam(learning_rate), loss='mean_squared_error')
return model
# Define the grid search parameters
param_grid = dict(hidden_layer_1=[32, 64, 128], hidden_layer_2=[32, 64, 128], learning_rate=[0.001, 0.01, 0.1])
# Create the model wrapper
model_wrapper = KerasRegressor(build_fn=create_model, epochs=50, batch_size=32, verbose=0)
# Perform grid search
grid_search = GridSearchCV(estimator=model_wrapper, param_grid=param_grid, cv=3)
grid_result = grid_search.fit(train_x, train_y)
# Summarize the results
print("Best: %f using %s" % (grid_result.best_score_, grid_result.best_params_))
means = grid_result.cv_results_['mean_test_score']
stds = grid_result.cv_results_['std_test_score']
params = grid_result.cv_results_['params']
for mean, stdev, param in zip(means, stds, params):
print("%f (%f) with: %r" % (mean, stdev, param))
```

In this example, a function `create_model`

is defined that returns the model for a given set of hyperparameters `hidden_layer_1`

, `hidden_layer_2`

, and `learning_rate`

. The ** KerasRegressor **wrapper is used to integrate the TensorFlow model with the GridSearchCV function from Scikit-learn. The grid search parameters are defined in the

`param_grid`

dictionary, where the search space is defined for each hyperparameter. The grid search is performed using the `fit`

method and the best parameters are obtained from the `best_params_`

attribute of the `grid_result`

object. The mean test score and standard deviation for each set of hyperparameters is also printed. The grid search allows for an efficient search for the best hyperparameters, helping to improve the performance of the model.**Summary on Hyperparameter Settings**

If you want to predict a continuous target value using a deep learning regression model in TensorFlow, the following steps can be a suitable input for the hyperparameters of a regression deep learning model in TensorFlow:

- Define the architecture of the model: You can start with a simple feedforward neural network with two or three hidden layers and 64-128 neurons in each layer. Use ReLU activation functions in the hidden layers and linear activation function in the output layer.
- Split the dataset into training and testing sets: This will be used to train the model and evaluate its performance. Good practice is to divide the dataset into two parts: 80% for training and 20% for testing.
- Define the loss function: The loss function will be used to measure the error between the predicted values and the true values. For regression problems, mean squared error or mean absolute error are commonly used.
- Choose an optimizer: An optimizer updates the model’s weights to minimize the loss. Some popular optimizers include stochastic gradient descent (SGD), Adam, Adagrad, etc.
- Set the hyperparameters: Hyperparameters are the parameters that are set before training the model and they can have a significant impact on the model’s performance. Common hyperparameters include learning rate, batch size, number of epochs, etc.
- Train the model: Train the model using the training data and the selected loss function and optimizer.
- Evaluate the model: Use the test data to evaluate the model’s performance. Compare the predicted values with the true values and compute the error using the chosen loss function.
- Tune the hyperparameters: If the performance is not satisfactory, adjust the hyperparameters and repeat the training and evaluation process.

It is recommended to use techniques like cross-validation or grid search to systematically search for the optimal hyperparameters. Note: These are just starting points, and you may need to adjust the hyperparameters based on the specific characteristics of your data and problem.

**Further readings**

If you are interested in learning more about deep learning for regression problems, some additional resources include:

- TensorFlow tutorials: TensorFlow provides a variety of tutorials and examples to help you get started with deep learning. You can find these tutorials on their website (https://www.tensorflow.org/tutorials)
- Deep Learning book by Ian Goodfellow, Yoshua Bengio, and Aaron Courville: This book provides a comprehensive introduction to deep learning, including the concepts, algorithms, and techniques used in building deep learning models.
- Hands-On Machine Learning with Scikit-Learn, Keras, and TensorFlow by Aurélien Géron: This book provides practical and hands-on experience in building machine learning models using scikit-learn, Keras, and TensorFlow.
- Coursera’s Deep Learning Specialization: This specialization on Coursera provides a comprehensive and in-depth introduction to deep learning, including hands-on experience in building deep learning models in TensorFlow.
- Deep Learning with Python by François Chollet: This book provides a comprehensive introduction to deep learning using the Keras library in Python.

These resources should give you a good foundation for further exploring deep learning for regression problems, and help you to develop more advanced and sophisticated models.