Continuous Probability Distributions generated by the PIPE Algorithm.

Area of Science:

• Computational Statistics
• Machine Learning
• Data Modeling

Background:

• Traditional methods for modeling data distributions often involve parameterizing existing probability distributions.
• Model selection and parameter estimation are typically separate, sequential processes.
• Controlling the complexity of derived models can be challenging with existing techniques.

Purpose of the Study:

• To investigate the Probabilistic Incremental Programming Evolution (PIPE) algorithm for constructing continuous cumulative distribution functions.
• To evaluate PIPE's capability in fitting empirical data distributions.
• To compare PIPE's performance against existing distribution modeling approaches.

Main Methods:

• Utilizing the PIPE algorithm to generate candidate functions based on evolving probability rules.
• Applying optimality criteria to iteratively refine candidate functions.
• Controlling model complexity by defining allowed mathematical functions and expression length.
• Simultaneously performing model selection and parameter estimation.

Main Results:

• The PIPE algorithm successfully generated candidate functions to fit empirical data distributions.
• PIPE demonstrated superior performance on both simulated and real-world datasets.
• For real data, PIPE achieved higher data likelihoods than existing models.
• PIPE-generated models were found to be mathematically simpler than those from conventional methods.

Conclusions:

• The PIPE algorithm provides a robust and flexible framework for continuous cumulative distribution function construction.
• PIPE offers advantages in controlling model complexity and integrating model selection with estimation.
• This approach yields competitive or superior results compared to traditional methods, with enhanced model parsimony.