Multitask coupled logistic regression and its fast implementation for large multitask datasets

When facing multitask-learning problems, it is desirable that the learning method could find the correct input-output features and share the commonality among multiple domains and also scale-up for large multitask datasets. We introduce the multitask coupled logistic regression (LR) framework called LR-based multitask classification learning algorithm (MTC-LR), which is a new method for generating each classifier for each task, capable of sharing the commonality among multitask domains. The basic idea of MTC-LR is to use all individual LR based classifiers, each one appropriate for each task domain, but in contrast to other support vector machine (SVM)-based proposals, learning all the parameter vectors of all individual classifiers by using the conjugate gradient method, in a global way and without the use of kernel trick, and being easily extended into its scaled version. We theoretically show that the addition of a new term in the cost function of the set of LRs (that penalizes the diversity among multiple tasks) produces a coupling of multiple tasks that allows MTC-LR to improve the learning performance in a LR way. This finding can make us easily integrate it with a state-of-the-art fast LR algorithm called dual coordinate descent method (CDdual) to develop its fast version MTC-LR-CDdual for large multitask datasets. The proposed algorithm MTC-LR-CDdual is also theoretically analyzed. Our experimental results on artificial and real-datasets indicate the effectiveness of the proposed algorithm MTC-LR-CDdual in classification accuracy, speed, and robustness.