📅 Module 1 – Data Foundations & Statistical Learning

• Focus: Hypothesis Testing & Distributions
• AM Session: Dive deep into Kolmogorov-Smirnov tests on spam datasets and explore Bayesian inference for prioritizing real-time data streams.
• Hands-On: Compare Poisson and Gaussian distributions in email patterns and calculate p-values to understand feature significance in spam filtering.

📅 Module 2 – Model Optimization & Validation

• Focus: ROC Analysis & Gradient Descent
• AM Session: Learn how to derive Fβ-score thresholds for filters and understand Wolfe conditions for setting optimal learning rates in PySpark ML.
• Hands-On: Plot ROC curves and confidence intervals, and explore optimization techniques like line search for decision tree pruning.

📅 Module 3 – RAG Architecture & Vector Math

• Focus: Topological Data Analysis
• AM Session: Visualize document embeddings with manifold learning and understand the convergence of iterative re-ranking algorithms.
• Hands-On: Use Lagrange multipliers to balance MMR (Maximal Marginal Relevance) and perform persistent homology analysis on knowledge graph connections.

📅 Module 4 – Multi-Modal Systems & Metrics

• Focus: Measure Theory for AI
• AM Session: Learn Hausdorff distance for cross-modal alignment (e.g., text and sensor data) and explore σ-algebra construction for academic knowledge bases.
• Hands-On: Compute BLEU-4 scores with statistical significance testing and apply optimal transport theory for database alignment.

📅 Module 5 – Embedded AI & Optimization

• Focus: Convex Relaxation
• AM Session: Understand Karush-Kuhn-Tucker conditions for optimizing edge device power constraints and explore semidefinite programming for model quantization.
• Hands-On: Solve sensor deployment as a traveling salesman problem and optimize FPGA resource allocation with integer linear programming.

📅 Module 6 – Integrated Capstone & Validation

• Focus: Causal Inference
• AM Session: Learn how to evaluate AI system impact using Do-calculus and conduct Shapley value analysis for multi-component systems.
• Hands-On: Build counterfactual scenarios for edge AI failure modes and perform sensitivity analysis across Big Data → RAG → Edge pipelines.

Course Outcomes

• Master the Math: Gain a solid understanding of the core mathematical principles behind AI models and how they generalize to new data.
• Visualize High-Dimensional Data: Use geometric tools to analyze and visualize complex, high-dimensional data.
• Develop Robust Models: Learn to build probabilistic models that quantify uncertainty and make robust predictions.
• Apply Causal Inference: Master the use of causal inference to make AI systems more transparent and decision-ready.
• Certificate of Mastery: Receive a certificate that showcases your advanced AI methodology training, demonstrating your expertise to peers and employers.