PolyMath AI Workshop Series: From Data Manifolds to Causal Inference

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Analytical Focus: Hypothesis Testing & Distributions

• AM Session

• Kolmogorov-Smirnov tests for data quality in spam datasets

• Bayesian inference for real-time data stream prioritization

• Hands-On

• Compare Poisson vs Gaussian distributions in email arrival patterns

• Calculate p-values for spam feature significance
  

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Analytical Focus: ROC Analysis & Gradient Descent

• AM Session:

• Deriving Fβ-score thresholds for medical vs commercial spam filters

• Wolfe conditions analysis for optimal learning rates in PySpark ML

• Hands-On:

• Plot ROC curves with confidence intervals using bootstrapping

• Implement line search optimization for decision tree pruning
  

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Analytical Focus: Topological Data Analysis

• AM Session:

• Manifold learning for document embedding visualization

• Proof of convergence for iterative re-ranking algorithms

• Hands-On:

• Calculate MMR (Maximal Marginal Relevance) balance using Lagrange multipliers

• Persistent homology analysis of knowledge graph connections
  

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Analytical Focus: Measure Theory for AI

• AM Session:

• Hausdorff distance for cross-modal (text/sensor) alignment

• σ-algebra construction for academic knowledge bases

• Hands-On:

• Compute BLEU-4 scores with statistical significance testing

• Optimal transport theory for PDF-to-database alignment
  

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Analytical Focus: Convex Relaxation

• AM Session:

• Karush-Kuhn-Tucker conditions for edge device power constraints

• Semidefinite programming for model quantization

• Hands-On:

• Solve sensor deployment as traveling salesman problem (TSP)

• FPGA resource allocation using integer linear programming
  

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Analytical Focus: Causal Inference

• AM Session:

• Do-calculus for evaluating AI system impact on research outcomes

• Shapley value analysis of multi-component systems

• Hands-On:

• Build counterfactual scenarios for edge AI failure modes

• Perform sensitivity analysis on full pipeline (Big Data → RAG → Edge)