Scikit-Learn PLSRegression Model

PLSRegression (Partial Least Squares Regression) is useful for regression problems where the predictor variables are many and highly collinear. It extracts a set of orthogonal factors (components) that maximize the covariance between the predictors and the response.

The key hyperparameters of PLSRegression include the n_components (number of PLS components to extract) and scale (whether to scale the predictors before applying the model).

The algorithm is appropriate for regression problems.

from sklearn.datasets import make_regression
from sklearn.model_selection import train_test_split
from sklearn.cross_decomposition import PLSRegression
from sklearn.metrics import mean_squared_error

# generate regression dataset
X, y = make_regression(n_samples=100, n_features=10, noise=0.1, random_state=1)

# split into train and test sets
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=1)

# create model
model = PLSRegression(n_components=2)

# fit model
model.fit(X_train, y_train)

# evaluate model
yhat = model.predict(X_test)
mse = mean_squared_error(y_test, yhat)
print('Mean Squared Error: %.3f' % mse)

# make a prediction
row = [[-0.332, 0.029, 0.436, 0.147, 1.206, -0.374, 0.555, 0.098, -0.238, -1.677]]
yhat = model.predict(row)
print('Predicted: %.3f' % yhat[0])

Running the example gives an output like:

Mean Squared Error: 157.686
Predicted: -61.811

The steps are as follows:

1. A synthetic regression dataset is generated using the make_regression() function. This creates a dataset with a specified number of samples (n_samples), features (n_features), and a fixed random seed (random_state) for reproducibility. The dataset is split into training and testing sets using train_test_split().

2. Next, a PLSRegression model is instantiated with n_components=2. The model is then fit on the training data using the fit() method.

3. The performance of the model is evaluated by comparing the predictions (yhat) to the actual values (y_test) using the Mean Squared Error (MSE).

4. A single prediction can be made by passing a new data sample to the predict() method.

This example demonstrates how to set up and use a PLSRegression model for regression tasks, highlighting its ability to handle datasets with many and collinear predictor variables effectively.