Scikit-Learn MultiTaskLassoCV Model

MultiTaskLassoCV is an algorithm for performing multi-task regression, where multiple regression tasks are solved jointly, and the model parameters are regularized.

The key hyperparameters include alphas (array of alpha values to try), cv (cross-validation splitting strategy), and n_jobs (number of jobs to run in parallel).

This algorithm is appropriate for multi-target regression problems, where multiple outputs are predicted simultaneously.

from sklearn.datasets import make_regression
from sklearn.model_selection import train_test_split
from sklearn.linear_model import MultiTaskLassoCV
from sklearn.metrics import mean_squared_error

# generate multi-output regression dataset
X, y = make_regression(n_samples=100, n_features=20, n_targets=3, 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 = MultiTaskLassoCV(cv=5)

# 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 = [[-0.255214, -0.306027, -1.550660, -0.974401, -0.414431, 1.103627, -0.684111, -0.788554, -0.888296, -0.977236,
        -0.435426, 0.252740, 0.202236, -0.939693, 0.042733, -0.191863, -1.577503, -0.637749, 0.421209, -0.503362]]
yhat = model.predict(row)
print('Predicted: %s' % yhat[0])

Running the example gives an output like:

Mean Squared Error: 0.212
Predicted: [-366.49365558 -309.28908121 -327.604364  ]

The steps are as follows:

1. First, a synthetic multi-output regression dataset is generated using the make_regression() function. This creates a dataset with a specified number of samples (n_samples), features (n_features), targets (n_targets), and noise level (noise), with a fixed random seed (random_state) for reproducibility. The dataset is split into training and test sets using train_test_split().

2. Next, a MultiTaskLassoCV model is instantiated with the cross-validation parameter set to 5. 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 metric.

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 MultiTaskLassoCV model for multi-target regression tasks, showcasing the simplicity and effectiveness of this algorithm in scikit-learn.

The model can handle multiple outputs simultaneously and is particularly useful when the outputs are related or when there is a need to enforce sparsity in the model coefficients. Once fit, the model can be used to make predictions on new data, enabling its use in real-world multi-target regression problems.