Multi-task lasso

Fit a multi-task lasso model with combined lasso (within task) and group lasso (across tasks) penalties.

References:

• Lee et al. “Adaptive Multi-Task Lasso: with Application to eQTL Detection” NIPS 2010
• Hu et al. “A statistical framework for cross-tissue transcriptome-wide association analysis” Nat Genet 2019.

Installation

pip install git+https://www.github.com/aksarkar/mtlasso.git

Example

import numpy as np
import mtlasso
import pandas as pd
import sklearn.model_selection as skms

np.random.seed(0)
n = 500
p = 1000
m = 5
scale = 1

X = np.random.normal(size=(n, p))
B = np.zeros((p, m))
B[0,:] = np.random.normal(size=m, scale=scale)
Y = X @ B + np.random.normal(size=(n, m))

# c.f. https://github.com/scikit-learn/scikit-learn/blob/1495f69242646d239d89a5713982946b8ffcf9d9/sklearn/linear_model/coordinate_descent.py#L112
grid = np.geomspace(.1, 1, 10) * X.shape[0]
cv_scores = mtlasso.lasso.sparse_multi_task_lasso_cv(
  X,
  Y,
  cv=skms.KFold(n_splits=5),
  lambda1=grid,
  lambda2=grid,
  max_iter=500,
  verbose=True)
cv_scores = pd.DataFrame(cv_scores)
cv_scores.columns = ['fold', 'lambda1', 'lambda2', 'mse']
lambda1, lambda2 = cv_scores.groupby(['lambda1', 'lambda2'])['mse'].agg(np.mean).idxmin()
Bhat, B0hat = mtlasso.lasso.sparse_multi_task_lasso(X, Y, lambda1=lambda1, lambda2=lambda2)