Designing machine learning workflows with an application to topological data analysis.

Area of Science:

• Machine Learning
• Topological Data Analysis
• Statistical Learning

Background:

• Machine learning operations like data preprocessing, feature extraction, and model training lack a unified structural representation.
• Existing frameworks can be complex for organizing and optimizing multi-step machine learning processes.

Purpose of the Study:

• To introduce Machine Learning Morphisms (MLMs) as a foundational concept for representing machine learning operations.
• To explore the composition of MLMs and their potential to form vector spaces for workflow construction.
• To demonstrate the application of MLMs, including the Mapper Algorithm, in building and optimizing machine learning workflows for classification tasks.

Main Methods:

• Defined Machine Learning Morphisms (MLMs) inspired by statistical learning, where parameters are minimized via a risk function.
• Investigated operations on MLMs, including composition and the conditions under which sets of MLMs form a vector space.
• Applied the MLM framework to construct machine learning workflows for binary classification using the Mapper Algorithm on Hospital Readmissions and Credit Evaluation datasets.

Main Results:

• Established MLMs as a versatile building block for expressing diverse machine learning operations.
• Demonstrated that compositions of MLMs can form structured mathematical entities like vector spaces.
• Successfully built and evaluated machine learning workflows incorporating the Mapper Algorithm for practical classification problems.

Conclusions:

• The MLM framework provides a powerful and organized approach to constructing and managing machine learning workflows.
• This approach facilitates the easy building, organization, and comparison of multiple workflows.
• MLMs enable joint optimization of parameters across different stages of a machine learning application, enhancing efficiency and performance.