Distribution Search

About

This skill provides a structured methodology for constructing discrete or continuous probability distributions that meet precise statistical requirements. It guides users through feasibility analysis, efficient parameterization—including group-based methods for large vocabularies—and the selection of appropriate optimization strategies like root-finding or gradient-free methods. By emphasizing mathematical rigor and modular code design, it ensures that derived distributions are both computationally efficient and statistically verified against target measures like information projection and moment projection.

Key Features

• Efficient parameterization strategies for large-scale vocabularies
• Rigorous verification checklists for distributional properties and precision
• Numerical optimization techniques including root-finding and least-squares
• Mathematical feasibility analysis and degrees of freedom assessment
• Standardized implementation patterns for forward and backward KL divergence
• 16 GitHub stars

Use Cases

• Designing probability mass functions with target entropy levels for information theory tasks
• Constructing distributions with specific KL divergence values for model alignment and benchmarking
• Solving optimization problems involving probability density functions and moment constraints