Sparse Classification with Positive-Confidence Data in High Dimensions

This paper addresses the challenge of high-dimensional classification when only positive samples with confidence scores are available (Positive-Confidence or Pconf learning). It proposes a novel sparse-penalization framework using Lasso, SCAD, and MCP penalties to improve prediction and variable selection in this weak-supervision setting. The paper provides theoretical guarantees and an efficient algorithm, demonstrating performance comparable to fully supervised methods.

• •Addresses high-dimensional classification with Positive-Confidence data.
• •Proposes sparse-penalization methods using Lasso, SCAD, and MCP.
• •Provides theoretical guarantees (estimation and prediction error bounds).
• •Develops an efficient proximal gradient algorithm.
• •Achieves performance comparable to fully supervised approaches.