AI Model Optimization: Balancing Accuracy & Complexity with Semilattices
Better than Trees: Applying Semilattices to Balance the Accuracy and Complexity of Machine Learning Models
This paper introduces semilattices as a superior alternative to traditional tree-based models for enhancing machine learning interpretability and efficiency. By providing a more expressive and less complex representation, algebraic machine learning (AML) leveraging semilattices offers a novel approach to building accurate and transparent AI models, particularly for complex real-world problems like urban food access landscapes.
Semilattices and Algebraic Machine Learning (AML) offer a paradigm shift for enterprise AI, moving beyond the limitations of tree-based models to deliver more interpretable, efficient, and accurate solutions for complex business challenges.
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Improved Accuracy (Deserts vs Swamps)
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Reduced Atom Count
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Integrated Semantic Framework
Deep Analysis & Enterprise Applications
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Advanced Model Architectures
Advanced Model Architectures
This paper delves into advanced model architectures, specifically focusing on semilattices as a method to improve the balance between model accuracy and complexity in machine learning, offering a more nuanced approach than traditional tree structures.
Atomisation: Drastically Reducing Model Complexity
Atomisation dramatically reduces the complexity of semilattice models. Before atomisation, a global model can have an exponentially growing number of elements (2^N), making it computationally intractable. This highlights the crucial role of atomisation in enabling efficient computation and manipulation of complex models.
2^N Elements in global model (before atomisation)AML Model Formulation Flow
The process of formulating an algebraic machine learning model based on semilattices involves several key steps. It begins with defining constants and their relations, then progressively refines the model through atomisation to create an efficient and interpretable structure. This structured approach ensures that complex real-world problems can be effectively translated into a semilattice framework for analysis and prediction.
Embed problem as semilattice model
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Identify constants and relations (C, R)
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Formulate algebraic relations (e.g., Fd < I_l ⊙ C < Tr)
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Update atomisation using sparse crossing algorithm
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Predict class for new data (e.g., food desert, swamp, oasis)
| Feature | Trees (Decision Trees) | Semilattices (AML) |
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| Complexity & Redundancy |
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| Interpretability |
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| Computational Efficiency |
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Urban Food Access Landscapes: A Real-World Application
The application of Algebraic Machine Learning (AML) with semilattices to model urban food access landscapes in the US demonstrates its practical utility. This case study highlights AML's ability to handle complex, interconnected data, achieve high predictive accuracy, and generate interpretable insights, offering a powerful tool for policymakers to address critical social challenges.
Problem: Modelling urban food access (deserts, swamps, oases) is a complex challenge requiring nuanced relationships between socioeconomic factors and geographical data.
AML Solution: AML used semilattices and atomisation to build a model for US food desert landscapes in 2010. By defining constants for census tracts, food classifications (Fd, Fs, Fo), and socioeconomic predictors (income, car availability), AML efficiently represents complex interdependencies.
Key Findings:
- Achieved comparable or better accuracy than XGBoost in distinguishing food classifications (e.g., 71.51% for Deserts vs. Swamps).
- Reduced model to 13,000 atoms from potentially 2^N elements, making it computationally tractable.
- Provided interpretable rules for policymakers, such as identifying food deserts based on tract income and population density.
- Demonstrated ability to balance accuracy and complexity in a challenging real-world problem.
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Our Structured Path to Interpretable AI
Our phased approach ensures a smooth integration of Algebraic Machine Learning into your enterprise, maximizing value and minimizing disruption.
Discovery & Data Semilatticisation
Collaborate with your team to identify key data points and business logic. We'll map these elements into an initial semilattice structure, defining constants and their hierarchical and non-hierarchical relationships. This phase translates your domain expertise into a foundational algebraic model.
Algebraic Model Formulation & Atomisation
Our experts will formalize the semilattice model using algebraic machine learning principles. This involves applying atomisation to compress the model while preserving all critical information, ensuring computational efficiency and interpretability. We build the core structure that balances complexity with accuracy.
Model Training & Refinement
With the atomised model, we train it on your historical data. This iterative process refines the model's predictive capabilities, focusing on achieving optimal balance between accuracy and desired interpretability. We'll fine-tune parameters to align with your specific business objectives.
Deployment & Interpretability Integration
The refined semilattice model is deployed into your operational environment. We integrate tools and dashboards that leverage the inherent interpretability of semilattices, allowing your business users to understand and trust the AI's predictions and underlying logic. This ensures shared interpretability across stakeholders.
Continuous Monitoring & Evolution
Post-deployment, we establish continuous monitoring to track model performance and identify any drift. As business needs evolve or new data becomes available, we iterate on the semilattice model, ensuring its ongoing relevance, accuracy, and interpretability, providing sustained value.
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