Low-rank regression models for multiple binary responses and their applications to cancer cell-line encyclopedia data

Area of Science:

• Biostatistics
• Statistical Learning
• Bioinformatics

Background:

• High-dimensional data in biomedical studies often involve multiple correlated binary outcomes.
• Existing methods may not effectively handle the complexity of simultaneously predicting these outcomes.

Purpose of the Study:

• To develop a robust framework for high-dimensional multivariate logistic regression with low-rank and row-wise sparse coefficient matrices.
• To improve estimation accuracy and variable selection for predicting multiple binary responses concurrently.

Main Methods:

• Proposed a novel selection and estimation framework utilizing marginal model likelihood.
• Developed an efficient algorithm for inference and introduced a new non-convex penalty (smooth clipped absolute deviation nuclear norm).
• Established high-dimensional theory, including non-asymptotic error bounds and rank/row support consistency.

Main Results:

• The proposed method demonstrates improved estimation accuracy by jointly considering multiple responses.
• Achieved theoretical guarantees for rank and row support consistency.
• Developed a consistent rule for selecting the rank and row dimensions of the coefficient matrix.
• Extended methods to a joint Ising model to account for dependence relationships.

Conclusions:

• The novel approach effectively handles high-dimensional, correlated multiple binary outcomes in logistic regression.
• Outperforms existing methods in prediction accuracy, as shown in simulations and real-world data analysis (Cancer Cell Line Encyclopedia).
• Provides a theoretically sound and computationally efficient solution for complex biomedical data analysis.