Machine Learning Morphisms
Machine Learning Morphisms (MLM) are a mathematical framework to describe Machine Learning Applications. They are designed to encode as many operations as possible, from preprocessing to feature engineering to model training.
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MLM's can mathematically be described as a 5tuple:
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Input probability space

Output probability space

Learning morphism

Prior distribution on parameters

Empirical risk function
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The parameters are learned by optimizing the empirical risk function over a set of data.
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The key idea with MLM's is the idea of composition which allows us to chain together operations and represent a workflow as a single mathematical object. This allows for potential joint optimization and modular design.
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As an application, I built a machine learning model to predict 30Day hospital readmissions. This model incorporates the TDA Mapper algorithm in a novel way to create an ensemble model that improves over the current tools used by Barnes Jewish Hospital.
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A full description of MLM's can be found here.
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A set of properties and operations used to design MLM's:

Asymptotic Equality: Concept of equality of two workflows based on the expected risk.

Structural Composition: Joint Optimization of Parameters.

Output Composition: Sequential Optimization of Parameters.

Workflow: Sequence of compositions.

Separability: Parameters can be learned by solving smaller dimensional Problems.
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Publications:
[1]: E. Cawi, P. S. La Rosa, and A. Nehorai, "Designing machine learning workflows with an application to topological data analysis," PLOS ONE, Vol. 14, No. 12, pp. 126, Dec. 2019.
[2]: A. C. Tukpah, E. Cawi (CoFirst), L. Wolf, A. Nehorai; L. CummingsVaughn (2020), "Development of an Institution Specific Readmission Risk PredictionModel for RealTime Prediction and PatientCentered Interventions",in revision for Journal of General Internal Medicine, 2020.
[3]: E. Cawi, P.S. La Rosa, and A. Nehorai, "Conditions for Separability of Machine Learning Workflows", submitted, Journal of Artficial Intelligence Research
[4]: E. Cawi, P.S. La rosa, and A. Nehorai, "Covariance Bounds for Machine Learning Workflows" (Working title), in preparation.
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