Course: MATH 7243 Machine Learning & Statistical Learning I Term: Spring 2026

MATH 7243 — Machine Learning & Statistical Learning I

A graduate-level introduction to statistical learning: supervised learning, optimization basics, generalization, regularization, model selection, and modern ML workflows.

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📌Course Overview

This course develops core concepts and tools of modern machine learning with a statistical learning lens. You will learn how models are trained, validated, and deployed in a principled way, with emphasis on: objective functions, optimization, regularization, generalization, and interpreting model behavior.

Topics (high-level)

  • Supervised learning: regression & classification
  • Loss functions, risk, empirical risk minimization
  • Optimization: GD/SGD, conditioning, early stopping
  • Regularization: L1/L2, sparsity, bias–variance
  • Model selection: CV, metrics, calibration
  • Linear models, kernels, trees/ensembles, intro to NNs

Course philosophy

We aim for fluency across math (derivations), code (implementations), and judgment (choosing methods, diagnosing failure modes).

Expect a mix of proofs/derivations, coding labs, and short writing to explain results.

🎯Learning Outcomes

By the end of the course, you should be able to:

  • Formulate ML problems via loss functions and (regularized) ERM objectives.
  • Derive gradients for common models and implement optimization loops.
  • Explain generalization and overfitting using bias–variance and validation strategies.
  • Design experiments with proper splits, cross-validation, and leakage prevention.
  • Evaluate models using appropriate metrics (including imbalanced settings).
  • Communicate results with clear assumptions, limitations, and reproducible code.

🗓️Logistics

InstructorDr. He Wang (edit as needed)
Email(add email)
Class meetings(days/time) • (location / Zoom)
Office hours(days/time) • (location / Zoom link)
Course siteCanvas / (link)
PrerequisitesLinear algebra, probability/statistics, calculus; basic Python recommended
SoftwarePython (NumPy, pandas, scikit-learn), optional PyTorch; Jupyter notebooks
Recommended background refreshers
  • Linear algebra: norms, projections, eigenvalues, SVD
  • Probability: expectation, variance, conditioning, MLE/MAP basics
  • Optimization: gradients, convexity, Taylor approximation
  • Python: vectorization, plotting, reproducible notebooks

🧭Proposed Schedule (editable)

Below is a sample 12-week outline. You can edit the titles/topics directly in the HTML.

Week 1 — Foundations of Statistical Learning
riskERMtrain/test
Problem setup, loss functions, empirical risk, baseline models, evaluation workflow.
Week 2 — Linear Regression & Geometry
least squaresprojectionsSVD
Normal equations, conditioning, regularization preview, diagnostics.
Week 3 — Optimization Basics
GDSGDstep size
Gradient descent, stochastic gradients, convergence intuition, practical tuning.
Week 4 — Regularization & Bias–Variance
L2L1overfitting
Ridge/Lasso, sparsity, model complexity, early stopping.
Week 5 — Classification: Logistic Regression
cross-entropycalibrationROC
Logistic model, likelihood, gradient, thresholding, metrics.
Week 6 — Model Selection & Cross-Validation
CVleakagepipelines
k-fold CV, nested CV, hyperparameter tuning, data leakage checklist.
Week 7 — Kernel Methods & SVM (Intro)
kernelsmarginduality
Kernel trick, soft margin, intuition and practical usage.
Week 8 — Trees & Ensembles
CARTRFboosting
Decision trees, bagging, random forests, boosting; interpretability.
Week 9 — Feature Engineering & Pipelines
scalingencodingsklearn
Preprocessing, leakage-safe pipelines, embeddings overview.
Week 10 — Intro to Neural Networks
backpropMLPregularization
Perceptron → MLP, backprop intuition, training stability, overfitting controls.
Week 11 — Generalization, Robustness, and Failure Modes
distribution shiftfairnessrobustness
Out-of-distribution behavior, error analysis, reliability and limitations.
Week 12 — Project Presentations & Review
communicationreproducibilityethics
Project demos, peer feedback, wrap-up and exam review.
Want a more detailed schedule?

Replace the “Proposed Schedule” with a table by lecture (date/topic/reading/lab/homework) once your term calendar is set. If you paste your real meeting days/dates, I can generate the full dated schedule.

🧪Assessment (editable)

Example structure (edit to match your course):

  • Homework weekly/biweekly problem sets (theory + coding)
  • Labs Jupyter-based labs (scikit-learn / PyTorch)
  • Quizzes short concept checks (optional)
  • Project team/individual final project with report + presentation
  • Participation discussions, peer review, in-class exercises
Suggested late policy: A small grace window + limited late days encourages pacing without harsh penalties. (Edit as needed.)

📚Resources

Primary references

  • Lecture notes / slides (Canvas)
  • ISLR (Introduction to Statistical Learning)
  • Elements of Statistical Learning (ESL) (optional)

Tools

  • Python + Jupyter
  • scikit-learn pipelines
  • PyTorch (selected labs)
Reproducibility expectations
  • Use a fixed random seed when appropriate.
  • Report data splits and hyperparameters.
  • Include a short README: how to run your notebook/script.

🤖AI (ChatGPT) Policy

You may use AI tools in MATH 7243 as a tutor, not as an author. Use AI to learn, debug, and practice; do not use AI to bypass required reasoning.

Allowed

  • Concept explanations, alternative intuitions
  • Small synthetic examples
  • Debugging your code (after you try)
  • Practice questions and self-quizzes
  • Outlines for reports (you rewrite/verify)

Not allowed

  • Submitting AI-generated solutions as your own
  • Generating full homework derivations
  • Fabricating experiments/citations/results
  • Copy-paste answers without verification

AI Use Disclosure (required when used)

AI Use Statement:
I used ChatGPT to (describe what you asked) and to (describe what you used).
I verified all derivations/results independently and rewrote all explanations in my own words.

Prompt starters

  • “Explain cross-entropy vs MSE for classification, and when each is appropriate.”
  • “Derive the gradient for logistic regression with L2 regularization; include dimensions.”
  • “My model overfits—list 3 fixes and how to test each (with code suggestions).”
  • “Check my experimental design for leakage risks: (describe split + features).”

🧩Projects

A course project emphasizes end-to-end ML: problem framing, data handling, modeling, validation, and communication.

Deliverables (example)
  • Proposal (1–2 pages): question, dataset, baseline, plan
  • Checkpoint: preliminary results + challenges
  • Final report: methods, experiments, results, limitations
  • Presentation: 6–8 minutes + Q&A
  • Repro package: code/notebook + README
Project ideas (starter list)
  • Classification with imbalanced data (PR curves, calibration, thresholding)
  • Regression with uncertainty (prediction intervals, bootstrapping)
  • Model interpretability (SHAP, permutation importance, partial dependence)
  • Domain shift / robustness analysis
  • Fairness metrics + mitigation strategies (careful: define fairness precisely)

❓FAQ

Do I need strong programming experience?

You should be comfortable reading and modifying Python code. We will provide templates and emphasize best practices. Start early and use office hours.

How should I study?
  • Do derivations by hand for core models (LR, logistic, regularization).
  • Re-implement small models from scratch before relying on libraries.
  • Use validation plots: learning curves, confusion matrices, residuals.
  • Write short “explain it to a peer” summaries.
Can I use ChatGPT for homework?

Yes for learning support (explanations, debugging), but not for generating full solutions. If you use AI, include the AI Use Statement.

How do I avoid data leakage?

Build preprocessing inside cross-validation via pipelines; never fit scalers/encoders on the full dataset before splitting. Keep a leakage checklist in your notebook.