PUlasso: High-Dimensional Variable Selection With Presence-Only Data.

Area of Science:

• Machine Learning
• Statistical Learning
• Bioinformatics

Background:

• Real-world classification often involves positive and unlabeled data (presence-only responses).
• High dimensionality (large number of features, p) combined with presence-only data poses significant statistical and computational challenges.

Purpose of the Study:

• To develop a scalable algorithm, PUlasso, for variable selection and classification with positive and unlabeled data.
• To address the challenges posed by high dimensionality in presence-only response scenarios.

Main Methods:

• The PUlasso algorithm utilizes the majorization-minimization framework, a generalization of the expectation-maximization (EM) algorithm.
• Two computational speed-ups are incorporated to enhance the scalability of the standard EM algorithm.
• Theoretical convergence to a stationary point is established, with guarantees of minimax optimal mean-squared error under sparsity assumptions.

Main Results:

• The PUlasso algorithm demonstrates convergence to a stationary point.
• Theoretical analysis shows minimax optimal mean-squared error achievement under strict and group sparsity.
• Simulations indicate superior classification performance compared to state-of-the-art methods in moderate p settings.
• Successful application of PUlasso is shown in a biochemistry example.

Conclusions:

• PUlasso provides an effective and scalable solution for variable selection and classification with positive and unlabeled data.
• The algorithm offers strong theoretical guarantees and practical performance benefits, particularly in high-dimensional contexts.
• The study highlights the utility of PUlasso in real-world applications, including biochemistry.