The Data Science Lab
Regression Using a scikit MLPRegressor Neural Network
Dr. James McCaffrey of Microsoft Research uses a full-code, step-by-step demo to show how to predict the annual income of a person based on their sex, age, state where they live and political leaning.
A regression problem is one where the goal is to predict a single numeric value. For example, you might want to predict the annual income of a person based on their sex, age, state where they live and political leaning. Note that the common "logistic regression" machine learning technique is actually a binary classification system in spite of its name.
Arguably the most powerful regression technique is a neural network model. There are several tools and code libraries that you can use to create a neural network regression model. The scikit-learn library (also called scikit or sklearn) is based on the Python language and is one of the more popular.
A good way to see where this article is headed is to take a look at the screenshot in Figure 1. The demo program loads a 200-item set of training data and a 40-item set of test data into memory. Next, the demo creates and trains a neural network regression model using the MLPRegressor module ("multi-layer perceptron," an old term for a neural network) from the scikit library.
[Click on image for larger view.] Figure 1: Regression Using a scikit Neural Network
After training, the model is applied to the training data and the test data. The model scores 91.50 percent accuracy (183 out of 200 correct) on the training data, and 90.00 percent accuracy (36 out of 40 correct) on the test data. The demo program defines a correct income prediction as one that's within 10 percent of the true income.
The demo concludes by predicting the income of a new, previously unseen person who is male, age 34, from Oklahoma, and who is a political moderate. The predicted income is $44,355.38.
This article assumes you have intermediate or better skill with a C-family programming language, but doesn't assume you know much about neural networks or the scikit library. The complete source code for the demo program is presented in this article and in the accompanying file download. The source code and data are also available online.
Installing the scikit Library
There are several ways to install the scikit library. I recommend installing the Anaconda Python distribution. Anaconda contains a core Python engine plus over 500 libraries that are (mostly) compatible with one another. I used Anaconda3-2020.02, which contains Python 3.7.6 and the scikit 0.22.1 version. The demo code runs on Windows 10 or 11.
Briefly, Anaconda is installed using a Windows self-extracting executable file. The setup process is mostly straightforward and takes about 15 minutes. You can follow these step-by-step instructions to help.
There are more up-to-date versions of Anaconda / Python / scikit library available. But because the Python ecosystem has hundreds of libraries, if you install the most recent versions of these libraries, you run a greater risk of library incompatibilities -- a major headache when working with Python.
The Data
The data is artificial. There are 200 training items and 40 test items. The structure of data looks like:
1 0.24 1 0 0 0.2950 0 0 1
-1 0.39 0 0 1 0.5120 0 1 0
1 0.63 0 1 0 0.7580 1 0 0
-1 0.36 1 0 0 0.4450 0 1 0
1 0.27 0 1 0 0.2860 0 0 1
. . .
The tab-delimited fields are sex (-1 = male, 1 = female), age (divided by 100), state (Michigan = 100, Nebraska = 010, Oklahoma = 001), income (divided by $100,000) and political leaning (conservative = 100, moderate = 010, liberal = 001).
The numeric predictors should be normalized to all the same range -- typically 0.0 to 1.0 or -1.0 to +1.0 -- as normalizing prevents predictors with large magnitudes from overwhelming those with small magnitudes.
For categorical predictor variables, I recommend one-hot encoding. For example, if there were five states instead of just three, the states would be encoded as 10000, 01000, 00100, 00010, 00001.
For binary predictor variables, such as sex, you can encode using either zero-one encoding or minus-one-plus-one encoding. The demo uses minus-one-plus-one encoding. In spite of decades of research, there are some topics, such as binary predictor encoding, that are not well understood (see "Encoding Binary Predictor Variables for Neural Networks").
The Demo Program
The complete demo program is presented in Listing 1. Notepad is my preferred code editor but most of my colleagues prefer one of the many excellent IDEs that are available for Python. I indent my Python program using two spaces rather than the more common four spaces.
The program imports the NumPy library, which contains numeric array functionality, and the MLPRegressor module, which contains neural network functionality. Notice the name of the root scikit module is sklearn rather than scikit.
import numpy as np
from sklearn.neural_network import MLPRegressor
import warnings
warnings.filterwarnings('ignore') # early-stop warnings
The demo specifies that no Python warnings should be displayed. I do this to keep the output tidy, but in a non-demo scenario you definitely want to see warning messages.
Listing 1:
Complete Demo Program
# people_income_nn_sckit.py
# predict income
# from sex, age, state, politics
# sex age state income politics
# 1 0.24 1 0 0 0.2950 0 0 1
# -1 0.39 0 0 1 0.5120 0 1 0
# state: michigan = 100, nebraska = 010, oklahoma = 001
# conservative = 100, moderate = 010, liberal = 001
# Anaconda3-2020.02 Python 3.7.6 scikit 0.22.1
# Windows 10/11
import numpy as np
from sklearn.neural_network import MLPRegressor
import warnings
warnings.filterwarnings('ignore') # early-stop warnings
# ---------------------------------------------------------
def accuracy(model, data_x, data_y, pct_close=0.10):
# accuracy predicted within pct_close of actual income
# item-by-item allows inspection but is slow
n_correct = 0; n_wrong = 0
predicteds = model.predict(data_x) # all predicteds
for i in range(len(predicteds)):
actual = data_y[i]
pred = predicteds[i]
if np.abs(pred - actual) < np.abs(pct_close * actual):
n_correct += 1
else:
n_wrong += 1
acc = (n_correct * 1.0) / (n_correct + n_wrong)
return acc
# ---------------------------------------------------------
def accuracy_q(model, data_x, data_y, pct_close=0.10):
# accuracy within pct_close of actual income
# all-at-once is quick
n_items = len(data_y)
preds = model.predict(data_x) # all predicteds
n_correct = np.sum((np.abs(preds - data_y) < \
np.abs(pct_close * data_y)))
result = (n_correct / n_items)
return result
# ---------------------------------------------------------
def main():
# 0. get ready
print("\nBegin scikit neural network regression example ")
print("Predict income from sex, age, State, politics ")
np.random.seed(1)
np.set_printoptions(precision=4, suppress=True)
# 1. load data
print("\nLoading data into memory ")
train_file = ".\\Data\\people_train.txt"
train_xy = np.loadtxt(train_file, usecols=range(0,9),
delimiter="\t", comments="#", dtype=np.float32)
train_x = train_xy[:,[0,1,2,3,4,6,7,8]]
train_y = train_xy[:,5]
test_file = ".\\Data\\people_test.txt"
test_xy = np.loadtxt(test_file, usecols=range(0,9),
delimiter="\t", comments="#", dtype=np.float32)
test_x = test_xy[:,[0,1,2,3,4,6,7,8]]
test_y = test_xy[:,5]
print("\nTraining data:")
print(train_x[0:4])
print(". . . \n")
print(train_y[0:4])
print(". . . ")
# ---------------------------------------------------------
# 2. create network
# MLPRegressor(hidden_layer_sizes=(100,),
# activation='relu', *, solver='adam', alpha=0.0001,
# batch_size='auto', learning_rate='constant',
# learning_rate_init=0.001, power_t=0.5, max_iter=200,
# shuffle=True, random_state=None, tol=0.0001,
# verbose=False, warm_start=False, momentum=0.9,
# nesterovs_momentum=True, early_stopping=False,
# validation_fraction=0.1, beta_1=0.9, beta_2=0.999,
# epsilon=1e-08, n_iter_no_change=10, max_fun=15000)
params = { 'hidden_layer_sizes' : [10,10],
'activation' : 'relu',
'solver' : 'adam',
'alpha' : 0.0,
'batch_size' : 10,
'random_state' : 0,
'tol' : 0.0001,
'nesterovs_momentum' : False,
'learning_rate' : 'constant',
'learning_rate_init' : 0.01,
'max_iter' : 1000,
'shuffle' : True,
'n_iter_no_change' : 50,
'verbose' : False }
print("\nCreating 8-(10-10)-1 relu neural network ")
net = MLPRegressor(**params)
# ---------------------------------------------------------
# 3. train
print("\nTraining with bat sz = " + \
str(params['batch_size']) + " lrn rate = " + \
str(params['learning_rate_init']) + " ")
print("Stop if no change " + \
str(params['n_iter_no_change']) + " iterations ")
net.fit(train_x, train_y)
print("Done ")
# ---------------------------------------------------------
# 4. evaluate model
# score() is coefficient of determination for MLPRegressor
print("\nCompute model accuracy (within 0.10 of actual) ")
acc_train = accuracy(net, train_x, train_y, 0.10)
print("\nAccuracy on train = %0.4f " % acc_train)
acc_test = accuracy(net, test_x, test_y, 0.10)
print("Accuracy on test = %0.4f " % acc_test)
# print("\nModel accuracy quick (within 0.10 of actual) ")
# acc_train = accuracy_q(net, train_x, train_y, 0.10)
# print("\nAccuracy on train = %0.4f " % acc_train)
# acc_test = accuracy_q(net, test_x, test_y, 0.10)
# print("Accuracy on test = %0.4f " % acc_test)
# ---------------------------------------------------------
# 5. use model
# no proba() for MLPRegressor
print("\nSetting X = M 34 Oklahoma moderate: ")
X = np.array([[-1, 0.34, 0,0,1, 0,1,0]])
income = net.predict(X) # divided by 100,000
income *= 100000 # denormalize
print("Predicted income: %0.2f " % income)
# ---------------------------------------------------------
# 6. TODO: save model using pickle
print("\nEnd scikit binary neural network demo ")
if __name__ == "__main__":
main()
All the program logic is contained in a main() function. The demo defines an accuracy() function that optimizes clarity at the expense of speed and a second accuracy_q() function (the "q" means "quick") that optimizes performance. The demo begins by setting the NumPy random seed:
def main():
# 0. get ready
print("Begin scikit neural network regression example ")
print("Predict income from sex, age, State, politics ")
np.random.seed(1)
np.set_printoptions(precision=4, suppress=True)
. . .
Technically, setting the random seed value isn't necessary, but doing so helps you to get reproducible results in most situations. The set_printoptions() function formats NumPy arrays to four decimals without using scientific notation.
Loading the Training and Test Data
The demo program loads the training data into memory using these statements:
# 1. load data
print("Loading data into memory ")
train_file = ".\\Data\\people_train.txt"
train_xy = np.loadtxt(train_file, usecols=range(0,9),
delimiter="\t", comments="#", dtype=np.float32)
train_x = train_xy[:,[0,1,2,3,4,6,7,8]]
train_y = train_xy[:,5]
This code assumes the data files are stored in a directory named Data. There are many ways to load data into memory. I prefer using the NumPy library loadtxt() function but a common alternative is the Pandas library read_csv() function.
The code reads all 200 lines of training data (columns 0 to 8 inclusive) into a matrix named train_xy and then splits the data into a matrix of predictor values and a vector of target income values. The colon syntax means "all rows."
The 40-item test data is read into memory in the same way as the training data:
test_file = ".\\Data\\people_test.txt"
test_xy = np.loadtxt(test_file, usecols=range(0,9),
delimiter="\t", comments="#", dtype=np.float32)
test_x = test_xy[:,[0,1,2,3,4,6,7,8]]
test_y = test_xy[:,5]
The demo program prints the first four predictor items and the first four target politics values:
print("Training data:")
print(train_x[0:4])
print(". . . ")
print(train_y[0:4])
print(". . . ")
In a non-demo scenario you might want to display all the training data and all the test data to verify the data has been read properly.
Creating the Neural Network Model
Creating the multi-class classification neural network model is simultaneously simple and complicated. First, the demo program sets up the network parameters in a Python Dictionary object like so:
# 2. create network
params = { 'hidden_layer_sizes' : [10,10],
'activation' : 'relu', 'solver' : 'adam',
'alpha' : 0.0, 'batch_size' : 10,
'random_state' : 0, 'tol' : 0.0001,
'nesterovs_momentum' : False,
'learning_rate' : 'constant',
'learning_rate_init' : 0.01,
'max_iter' : 1000, 'shuffle' : True,
'n_iter_no_change' : 50, 'verbose' : False }
After the parameters are set, they are fed to a neural network constructor:
print("Creating 8-(10-10)-1 relu neural network ")
net = MLPRegressor(**params)
The ** syntax means to unpack the Dictionary values and pass them to the constructor. Like many scikit models, the MLPClassifier class has a lot of parameters and default values. The constructor signature is: