In this tutorial, you will learn how to perform regression using Keras and Deep Learning. You will learn how to train a Keras neural network for regression and continuous value prediction, specifically in the context of house price prediction.

Today’s post kicks off a 3-part series on **deep learning, regression, and continuous value prediction.**

We’ll be studying Keras regression prediction in the context of house price prediction:

**Part 1:**Today we’ll be training a Keras neural network to**predict house prices based on categorical and numerical attributes**such as the number of bedrooms/bathrooms, square footage, zip code, etc.**Part 2:**Next week we’ll train a Keras**Convolutional Neural Network to predict house prices based on input images of the houses themselves**(i.e., frontal view of the house, bedroom, bathroom, and kitchen).**Part 3:**In two weeks we’ll define and train a neural network thatleading to better, more accurate house price prediction than the attributes or images alone.*combines*our categorical/numerical attributes with our images,

Unlike classification (which predicts * labels*), regression enables us to predict

*.*

**continuous values**For example, classification may be able to predict one of the following values: *{cheap, affordable, expensive}*.

Regression, on the other hand, will be able to predict an exact dollar amount, such as *“The estimated price of this house is $489,121”*.

In many real-world situations, such as house price prediction or stock market forecasting, applying regression rather than classification is *critical* to obtaining good predictions.

**To learn how to perform regression with Keras, just keep reading!**

#### Looking for the source code to this post?

Jump Right To The Downloads Section## Regression with Keras

**2020-06-12 Update:** This blog post is now TensorFlow 2+ compatible!

In the first part of this tutorial, we’ll briefly discuss the difference between classification and regression.

We’ll then explore the house prices dataset we’re using for this series of Keras regression tutorials.

From there, we’ll configure our development environment and review our project structure.

Along the way, we will learn how to use Pandas to load our house price dataset and define a neural network that for Keras regression prediction.

Finally, we’ll train our Keras network and then evaluate the regression results.

### Classification vs. Regression

Typically on the PyImageSearch blog, we discuss Keras and deep learning in the context of classification — predicting a label to characterize the contents of an image or an input set of data.

**Regression**, on the other hand, enables us to predict continuous values. Let’s again consider the task of house price prediction.

As we know, classification is used to predict a class label.

For house price prediction we may define our categorical labels as:

labels = {very cheap, cheap, affordable, expensive, very expensive}

If we performed classification, our model could then learn to predict one of those five values based on a set of input features.

However, those labels are just that — categories that represent a potential range of prices for the house but do *nothing* to represent the *actual cost* of the home.

**In order to predict the actual cost of a home, we need to perform regression.**

Using regression we can train a model to predict a continuous value.

For example, while classification may only be able to predict a label, regression could say:

*“Based on my input data, I estimate the cost of this house to be $781,993.”*

**Figure 1** above provides a visualization of performing both classification and regression.

In the rest of this tutorial, you’ll learn how to train a neural network for regression using Keras.

### The House Prices Dataset

The dataset we’ll be using today is from 2016 paper, *House price estimation from visual and textual features*, by Ahmed and Moustafa.

**The dataset includes both numerical/categorical attributes along with images for 535 data points,** making it an excellent dataset to study for regression and mixed data prediction.

The house dataset includes **four numerical and categorical attributes:**

- Number of bedrooms
- Number of bathrooms
- Area (i.e., square footage)
- Zip code

These attributes are stored on disk in CSV format.

We’ll be loading these attributes from disk later in this tutorial using `pandas`

, a popular Python package used for data analysis.

**A total of four images are also provided for each house:**

- Bedroom
- Bathroom
- Kitchen
- Frontal view of the house

**The end goal of the houses dataset is to predict the price of the home itself.**

In today’s tutorial, we’ll be working with *just* the numerical and categorical data.

Next week’s blog post will discuss working with the image data.

And finally, two weeks from now we’ll *combine* the numerical/categorical data with the images to obtain our best performing model.

But before we can train our Keras model for regression, we first need to configure our development environment and grab the data.

### Configuring Your Development Environment

For this 3-part series of blog posts, you’ll need to have the following packages installed:

**NumPy****scikit-learn****pandas****Keras**with the**TensorFlow**backend (CPU or GPU)**OpenCV**(for the next two blog posts in the series)

To configure your system for this series of tutorials, I recommend following either of these tutorials:

Either tutorial will help you configure you system with all the necessary software for this blog post in a convenient Python virtual environment.

Please note that PyImageSearch does not recommend or support Windows for CV/DL projects.

### Downloading the House Prices Dataset

Before you download the dataset, go ahead and grab the source code to this post by using * “Downloads” *section.

From there, unzip the file and navigate into the directory:

$ cd path/to/downloaded/zip $ unzip keras-regression.zip $ cd keras-regression

From there, you can download the House Prices Dataset using the following command:

$ git clone https://github.com/emanhamed/Houses-dataset

When we are ready to train our Keras regression network you’ll then need to supply the path to the `Houses-dataset`

directory via command line argument.

### Project structure

Now that you have the dataset, go ahead and use the `tree`

command with the same arguments shown below to print a directory + file listing for the project:

$ tree --dirsfirst --filelimit 10 . ├── Houses-dataset │ ├── Houses Dataset [2141 entries] │ └── README.md ├── pyimagesearch │ ├── __init__.py │ ├── datasets.py │ └── models.py └── mlp_regression.py 3 directories, 5 files

The dataset downloaded from GitHub now resides in the `Houses-dataset/`

folder.

The `pyimagesearch/`

directory is actually a module included with the code * “Downloads”* where inside, you’ll find:

`datasets.py`

: Our script for loading the numerical/categorical data from the dataset`models.py`

: Our Multi-Layer Perceptron architecture implementation

These two scripts will be reviewed today. Additionally, we’ll be reusing both `datasets.py`

and `models.py`

(with modifications) in the next two tutorials to keep our code organized and reusable.

The regression + Keras script is contained in `mlp_regression.py`

which we’ll be reviewing it as well.

### Loading the House Prices Dataset

Before we can train our Keras regression model we first need to load the numerical and categorical data for the houses dataset.

Open up the `datasets.py`

file and insert the following code:

# import the necessary packages from sklearn.preprocessing import LabelBinarizer from sklearn.preprocessing import MinMaxScaler import pandas as pd import numpy as np import glob import cv2 import os def load_house_attributes(inputPath): # initialize the list of column names in the CSV file and then # load it using Pandas cols = ["bedrooms", "bathrooms", "area", "zipcode", "price"] df = pd.read_csv(inputPath, sep=" ", header=None, names=cols)

We begin by importing libraries and modules from scikit-learn, pandas, NumPy and OpenCV. OpenCV will be used next week as we’ll be adding the ability to load images to this script.

On **Line 10**, we define the `load_house_attributes`

function which accepts the path to the input dataset.

Inside the function we start off by defining the names of the columns in the CSV file (**Line 13**). From there, we use pandas’ function, `read_csv`

to load the CSV file into memory as a date frame ( `df`

) on **Line 14**.

Below you can see an example of our input data, including the number of bedrooms, number of bathrooms, area (i.e., square footage), zip code, code, and finally the target price our model should be trained to predict:

bedrooms bathrooms area zipcode price 0 4 4.0 4053 85255 869500.0 1 4 3.0 3343 36372 865200.0 2 3 4.0 3923 85266 889000.0 3 5 5.0 4022 85262 910000.0 4 3 4.0 4116 85266 971226.0

Let’s finish up the rest of the `load_house_attributes`

function:

# determine (1) the unique zip codes and (2) the number of data # points with each zip code zipcodes = df["zipcode"].value_counts().keys().tolist() counts = df["zipcode"].value_counts().tolist() # loop over each of the unique zip codes and their corresponding # count for (zipcode, count) in zip(zipcodes, counts): # the zip code counts for our housing dataset is *extremely* # unbalanced (some only having 1 or 2 houses per zip code) # so let's sanitize our data by removing any houses with less # than 25 houses per zip code if count < 25: idxs = df[df["zipcode"] == zipcode].index df.drop(idxs, inplace=True) # return the data frame return df

In the remaining lines, we:

- Determine the unique set of zip codes and then count the number of data points with each unique zip code (
**Lines 18 and 19**). - Filter out zip codes with low counts (
**Line 28**). For some zip codes we only have one or two data points, making it extremely challenging, if not impossible, to obtain accurate house price estimates. - Return the data frame to the calling function (
**Line 33**).

Now let’s create the `process_house_attributes`

function used to preprocess our data:

def process_house_attributes(df, train, test): # initialize the column names of the continuous data continuous = ["bedrooms", "bathrooms", "area"] # performin min-max scaling each continuous feature column to # the range [0, 1] cs = MinMaxScaler() trainContinuous = cs.fit_transform(train[continuous]) testContinuous = cs.transform(test[continuous])

We define the function on **Line 35**. The `process_house_attributes`

function accepts three parameters:

`df`

: Our data frame generated by pandas (the previous function helps us to drop some records from the data frame)`train`

: Our training data for the House Prices Dataset`test`

: Our testing data.

Then on **Line 37**, we define the columns of our continuous data, including bedrooms, bathrooms, and size of the home.

We’ll take these values and use scikit-learn’s `MinMaxScaler`

to scale the continuous features to the range *[0, 1]* (**Lines 41-43**).

Now we need to pre-process our categorical features, namely the zip code:

# one-hot encode the zip code categorical data (by definition of # one-hot encoing, all output features are now in the range [0, 1]) zipBinarizer = LabelBinarizer().fit(df["zipcode"]) trainCategorical = zipBinarizer.transform(train["zipcode"]) testCategorical = zipBinarizer.transform(test["zipcode"]) # construct our training and testing data points by concatenating # the categorical features with the continuous features trainX = np.hstack([trainCategorical, trainContinuous]) testX = np.hstack([testCategorical, testContinuous]) # return the concatenated training and testing data return (trainX, testX)

First, we’ll one-hot encode the zip codes (**Lines 47-49**).

Then we’ll concatenate the *categorical features* with the *continuous features* using NumPy’s `hstack`

function (**Lines 53 and 54**), returning the resulting training and testing sets as a tuple (**Line 57**).

Keep in mind that now *both* our categorical features and continuous features are *all* in the range *[0, 1].*

### Implementing a Neural Network for Regression

Before we can train a Keras network for regression, we first need to define the architecture itself.

Today we’ll be using a simple Multilayer Perceptron (MLP) as shown in **Figure 5**.

Open up the `models.py`

file and insert the following code:

# import the necessary packages from tensorflow.keras.models import Sequential from tensorflow.keras.layers import BatchNormalization from tensorflow.keras.layers import Conv2D from tensorflow.keras.layers import MaxPooling2D from tensorflow.keras.layers import Activation from tensorflow.keras.layers import Dropout from tensorflow.keras.layers import Dense from tensorflow.keras.layers import Flatten from tensorflow.keras.layers import Input from tensorflow.keras.models import Model def create_mlp(dim, regress=False): # define our MLP network model = Sequential() model.add(Dense(8, input_dim=dim, activation="relu")) model.add(Dense(4, activation="relu")) # check to see if the regression node should be added if regress: model.add(Dense(1, activation="linear")) # return our model return model

First, we’ll import all of the necessary modules from Keras (**Lines 2-11**). We’ll be adding a Convolutional Neural Network to this file in *next week’s tutorial*, hence the additional imports that aren’t utilized here today.

Let’s define the MLP architecture by writing a function to generate it called `create_mlp`

.

The function accepts two parameters:

`dim`

: Defines our input dimensions`regress`

: A boolean defining whether or not our regression neuron should be added

We’ll go ahead and start construction our MLP with a `dim-8-4`

architecture (**Lines 15-17**).

If we are performing regression, we add a `Dense`

layer containing a single neuron with a linear activation function (**Lines 20 and 21**). Typically we use ReLU-based activations, but since we are performing regression we need a linear activation.

Finally, our `model`

is returned on **Line 24**.

### Implementing our Keras Regression Script

It’s now time to put all the pieces together!

Open up the `mlp_regression.py`

file and insert the following code:

# import the necessary packages from tensorflow.keras.optimizers import Adam from sklearn.model_selection import train_test_split from pyimagesearch import datasets from pyimagesearch import models import numpy as np import argparse import locale import os # construct the argument parser and parse the arguments ap = argparse.ArgumentParser() ap.add_argument("-d", "--dataset", type=str, required=True, help="path to input dataset of house images") args = vars(ap.parse_args())

We begin by importing necessary packages, modules, and libraries.

Namely, we’ll need the `Adam`

optimizer from Keras, `train_test_split`

from scikit-learn, and our `datasets`

+ `models`

functions from the `pyimagesearch`

module.

Additionally, we’ll use math features from NumPy for collecting statistics when we evaluate our model.

The `argparse`

module is for parsing command line arguments.

Our script requires just one command line argument `--dataset`

(**Lines 12-15**). You’ll need to provide the `--dataset`

switch and the actual path to the dataset when you go to run the training script in your terminal.

Let’s load the house dataset attributes and construct our training and testing splits:

# construct the path to the input .txt file that contains information # on each house in the dataset and then load the dataset print("[INFO] loading house attributes...") inputPath = os.path.sep.join([args["dataset"], "HousesInfo.txt"]) df = datasets.load_house_attributes(inputPath) # construct a training and testing split with 75% of the data used # for training and the remaining 25% for evaluation print("[INFO] constructing training/testing split...") (train, test) = train_test_split(df, test_size=0.25, random_state=42)

Using our handy `load_house_attributes`

function, and by passing the `inputPath`

to the dataset itself, our data is loaded into memory (**Lines 20 and 21**).

Our training (75%) and testing (25%) data is constructed via **Line 26** and scikit-learn’s `train_test_split`

method.

Let’s scale our house pricing data:

# find the largest house price in the training set and use it to # scale our house prices to the range [0, 1] (this will lead to # better training and convergence) maxPrice = train["price"].max() trainY = train["price"] / maxPrice testY = test["price"] / maxPrice

As stated in the comment, scaling our house prices to the range *[0, 1]* will allow our model to more easily train and converge. Scaling the output targets to *[0, 1]* will reduce the range of our output predictions (versus *[0, maxPrice ]*) and make it not only

*but enable our model to*

**easier and faster to train our network**

**obtain better results as well.**Thus, we grab the maximum price in the training set (**Line 31**), and proceed to scale our training and testing data accordingly (**Lines 32 and 33**).

Let’s process the house attributes now:

# process the house attributes data by performing min-max scaling # on continuous features, one-hot encoding on categorical features, # and then finally concatenating them together print("[INFO] processing data...") (trainX, testX) = datasets.process_house_attributes(df, train, test)

Recall from the `datasets.py`

script that the `process_house_attributes`

function:

- Pre-processes our categorical and continuous features.
- Scales our continuous features to the range
*[0, 1]*via min-max scaling. - One-hot encodes our categorical features.
- Concatenates the categorical and continuous features to form the final feature vector.

Now let’s go ahead and fit our MLP model to the data:

# create our MLP and then compile the model using mean absolute # percentage error as our loss, implying that we seek to minimize # the absolute percentage difference between our price *predictions* # and the *actual prices* model = models.create_mlp(trainX.shape[1], regress=True) opt = Adam(lr=1e-3, decay=1e-3 / 200) model.compile(loss="mean_absolute_percentage_error", optimizer=opt) # train the model print("[INFO] training model...") model.fit(x=trainX, y=trainY, validation_data=(testX, testY), epochs=200, batch_size=8)

Our `model`

is initialized with the `Adam`

optimizer (**Lines 45 and 46**) and then compiled (**Line 47**). Notice that we’re using *mean absolute percentage error* as our loss function, indicating that we seek to minimize the *mean percentage difference* between the predicted price and the actual price.

The actual training process is kicked off on **Lines 51-53.**

After training is complete we can evaluate our model and summarize our results:

# make predictions on the testing data print("[INFO] predicting house prices...") preds = model.predict(testX) # compute the difference between the *predicted* house prices and the # *actual* house prices, then compute the percentage difference and # the absolute percentage difference diff = preds.flatten() - testY percentDiff = (diff / testY) * 100 absPercentDiff = np.abs(percentDiff) # compute the mean and standard deviation of the absolute percentage # difference mean = np.mean(absPercentDiff) std = np.std(absPercentDiff) # finally, show some statistics on our model locale.setlocale(locale.LC_ALL, "en_US.UTF-8") print("[INFO] avg. house price: {}, std house price: {}".format( locale.currency(df["price"].mean(), grouping=True), locale.currency(df["price"].std(), grouping=True))) print("[INFO] mean: {:.2f}%, std: {:.2f}%".format(mean, std))

**Line 57** instructs Keras to make predictions on our testing set.

Using the predictions, we compute the:

- Difference between
*predicted*house prices and the*actual*house prices (**Line 62**). - Percentage difference (
**Line 63**). - Absolute percentage difference (
**Line 64**).

From there, on **Lines 68 and 69**, we calculate the mean and standard deviation of the absolute percentage difference.

The results are printed via **Lines 73-76**.

Regression with Keras wasn’t so tough, now was it?

Let’s train the model and analyze the results!

### Keras Regression Results

To train our own Keras network for regression and house price prediction make sure you have:

- Configured your development environment according to the guidance above.
- Used the
section of this tutorial to download the source code.**“Downloads”** - Downloaded the house prices dataset based on the instructions in the
*“The House Prices Dataset”*section above.

From there, open up a terminal and supply the following command (making sure the `--dataset`

command line argument points to where you downloaded the house prices dataset):

$ python mlp_regression.py --dataset Houses-dataset/Houses\ Dataset/ [INFO] loading house attributes... [INFO] constructing training/testing split... [INFO] processing data... [INFO] training model... Epoch 1/200 34/34 [==============================] - 0s 4ms/step - loss: 73.0898 - val_loss: 63.0478 Epoch 2/200 34/34 [==============================] - 0s 2ms/step - loss: 58.0629 - val_loss: 56.4558 Epoch 3/200 34/34 [==============================] - 0s 1ms/step - loss: 51.0134 - val_loss: 50.1950 Epoch 4/200 34/34 [==============================] - 0s 1ms/step - loss: 47.3431 - val_loss: 47.6673 Epoch 5/200 34/34 [==============================] - 0s 1ms/step - loss: 45.5581 - val_loss: 44.9802 Epoch 6/200 34/34 [==============================] - 0s 1ms/step - loss: 42.4403 - val_loss: 41.0660 Epoch 7/200 34/34 [==============================] - 0s 1ms/step - loss: 39.5451 - val_loss: 34.4310 Epoch 8/200 34/34 [==============================] - 0s 2ms/step - loss: 34.5027 - val_loss: 27.2138 Epoch 9/200 34/34 [==============================] - 0s 2ms/step - loss: 28.4326 - val_loss: 25.1955 Epoch 10/200 34/34 [==============================] - 0s 2ms/step - loss: 28.3634 - val_loss: 25.7194 ... Epoch 195/200 34/34 [==============================] - 0s 2ms/step - loss: 20.3496 - val_loss: 22.2558 Epoch 196/200 34/34 [==============================] - 0s 2ms/step - loss: 20.4404 - val_loss: 22.3071 Epoch 197/200 34/34 [==============================] - 0s 2ms/step - loss: 20.0506 - val_loss: 21.8648 Epoch 198/200 34/34 [==============================] - 0s 2ms/step - loss: 20.6169 - val_loss: 21.5130 Epoch 199/200 34/34 [==============================] - 0s 2ms/step - loss: 19.9067 - val_loss: 21.5018 Epoch 200/200 34/34 [==============================] - 0s 2ms/step - loss: 19.9570 - val_loss: 22.7063 [INFO] predicting house prices... [INFO] avg. house price: $533,388.27, std house price: $493,403.08 [INFO] mean: 22.71%, std: 18.26%

As you can see from our output, our initial mean absolute percentage error starts off as high as 73% and then quickly drops to under 30%.

By the time we finish training we can see our network starting to overfit a bit. Our training loss is as low as ~20%; however, our validation loss is at ~23%.

Computing our final mean absolute percentage error we obtain a final value of **22.71%.**

**What does this value mean?**

Our final mean absolute percentage error implies, that on average, our network will be ~23% off in its house price predictions with a standard deviation of ~18%.

### Limitations of the House Price Dataset

Being 22% off in a house price prediction is a good start but is certainly *not* the type of accuracy we are looking for.

That said, this prediction accuracy can also be seen as a *limitation* of the house price dataset itself.

Keep in mind that the dataset only includes four attributes:

- Number of bedrooms
- Number of bathrooms
- Area (i.e., square footage)
- Zip code

Most other house price datasets include *many* more attributes.

For example, the Boston House Prices Dataset includes a total of *fourteen attributes* which can be leveraged for house price prediction (although that dataset does have some racial discrimination).

The Ames House Dataset *includes over 79 different attributes* which can be used to train regression models.

When you think about it, the fact that we are able to even obtain 26% mean absolute percentage error without the knowledge of an expert real estate agent is fairly reasonable given:

- There are only 535 total houses in the dataset (we only used
**362 total houses**for the purpose of this guide). - We only have
**four attributes**to train our regression model on. - The attributes themselves, while important in describing the home itself,
**do little to characterize the area surrounding the house.** **The house prices are incredibly varied**with a mean of $533K and a standard deviation of $493K (based on our filtered dataset of 362 homes).

**With all that said, learning how to perform regression with Keras is an important skill!**

In the next two posts in this series I’ll be showing you how to:

- Leverage the images provided with the house price dataset to train a CNN on them.
- Combine our numerical/categorical data with the house images, leading to a model that outperforms all of our previous Keras regression experiments.

### What's next? We recommend PyImageSearch University.

**Course information:**

84 total classes • 114+ hours of on-demand code walkthrough videos • Last updated: February 2024

★★★★★ 4.84 (128 Ratings) • 16,000+ Students Enrolled

**I strongly believe that if you had the right teacher you could master computer vision and deep learning.**

Do you think learning computer vision and deep learning has to be time-consuming, overwhelming, and complicated? Or has to involve complex mathematics and equations? Or requires a degree in computer science?

That’s *not* the case.

All you need to master computer vision and deep learning is for someone to explain things to you in *simple, intuitive* terms. *And that’s exactly what I do*. My mission is to change education and how complex Artificial Intelligence topics are taught.

If you're serious about learning computer vision, your next stop should be PyImageSearch University, the most comprehensive computer vision, deep learning, and OpenCV course online today. Here you’ll learn how to *successfully* and *confidently* apply computer vision to your work, research, and projects. Join me in computer vision mastery.

**Inside PyImageSearch University you'll find:**

- ✓
**86 courses**on essential computer vision, deep learning, and OpenCV topics - ✓
**86 Certificates**of Completion - ✓
**115+ hours**of on-demand video - ✓
**Brand new courses released**, ensuring you can keep up with state-of-the-art techniques*regularly* - ✓
**Pre-configured Jupyter Notebooks in Google Colab** - ✓ Run all code examples in your web browser — works on Windows, macOS, and Linux (no dev environment configuration required!)
- ✓ Access to
**centralized code repos for**on PyImageSearch*all*540+ tutorials - ✓
**Easy one-click downloads**for code, datasets, pre-trained models, etc. - ✓
**Access**on mobile, laptop, desktop, etc.

## Summary

In this tutorial, you learned how to use the Keras deep learning library for regression.

Specifically, we used Keras and regression to predict the price of houses based on four numerical and categorical attributes:

- Number of bedrooms
- Number of bathrooms
- Area (i.e., square footage)
- Zip code

Overall our neural network obtained a mean absolute percentage error of 22.71%, implying that, on average, our house price predictions will be off by 22.71%.

That raises the questions:

- How can we
*better*our house price prediction accuracy? - What if we
*leveraged images*for each house? Would that improve accuracy? - Is there some way to
*combine*both our categorical/numerical attributes with our image data?

To answer these questions you’ll need to stay tuned for the remaining to tutorials in this Keras regression series.

**To download the source code to this post (and be notified when the next tutorial is published here on PyImageSearch), just enter your email address in the form below.**

#### Download the Source Code and FREE 17-page Resource Guide

Enter your email address below to get a .zip of the code and a **FREE 17-page Resource Guide on Computer Vision, OpenCV, and Deep Learning.** Inside you'll find my hand-picked tutorials, books, courses, and libraries to help you master CV and DL!