Syllabus

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Course Overview

This course covers selected advanced statistical modeling tools beyond those in STAT 432 and STAT 542. The course is organized around four modules:

• Module 1: Reproducing Kernel Hilbert Space (August 25 to September 17; four weeks)
• Module 2: Causal Inference and Personalized Decision Making (September 22 to October 8; three weeks)
• Module 3: Tree ensembles and uncertainty (October 13 to October 29; three weeks)
• Module 4: Reinforcement Learning (November 3 to December 3; four instructional weeks)

Module 4 spans five calendar weeks because Fall Break, November 21 to 29, is excluded from its four instructional weeks.

The modules are designed to build on one another, with some topics connecting multiple modules. The course combines instructor-led lectures, research-paper mini-project presentations, peer evaluation, and computational homework. There is no required textbook for this course. We will provide lecture notes, selected readings, and homework assignments in R Markdown and/or Jupyter Notebook. You can use either R or Python to complete your computational work. Tentative topics and objectives are summarized below.

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Course Format and Participation

The semester is organized into four modules. In each module, all weeks except the final week will be used for instructor-led lectures. Homework will be due during the second-to-last instructional week of the module. The final instructional week will be a mini-project Present and Challenge week, conducted through Popping, a platform specifically designed for interactive class activities.

• Lectures: All non-final weeks of each module are lecture weeks. Both Tuesday and Thursday class meetings will be used for instructor-led lectures.
• Team presentations: The class will be organized into teams of approximately three students. Depending on enrollment and team assignments, six to eight teams will present in each module across two class sessions. With the current enrollment, we expect eight teams per module so that each student is required to present twice during the semester. The number of teams in each session may vary.
• Presentation content: A presentation should explain the motivation for the topic, identify the main statistical target or formulation, work through the central mathematical or algorithmic idea, include a computational implementation and comparison with appropriate baselines, and discuss at least one limitation or failure mode.
• Peer evaluation: During every presentation session, all students will register the required evaluations through Popping. Peer evaluations should be specific, constructive, and based on the assigned reading and the material presented in class.
• Challengers: During the question period, any student may also serve as a challenger by asking a substantive question that tests the presenting team’s understanding. A good challenge may examine an assumption, derivation, computational design, interpretation, or limitation. The purpose is to deepen the discussion, not simply to make the presentation more difficult.

Every student will submit the required evaluations in every session, including a session in which the student is also presenting. Presenters will evaluate the other teams and challenger contributions, but not their own team. Registering the required evaluation scores earns the regular session participation credit. A student who presents in that session can also earn the separate presentation credit. Peer feedback will be considered together with the instructor’s assessment. The tentative presentation schedule is:

Module	Present and Challenge dates	Topic of focus
1	September 15 and 17	Modern kernel methods
2	October 6 and 8	Causal Inference and Personalized Decision Making
3	October 27 and 29	Ensemble methods and uncertainty for Modeling
4	December 1 and 3	Reinforcement learning and AI

December 8 will be reserved for course synthesis. General presentation and participation procedures are provided on the Present and Challenge page. Module-specific reading lists and detailed evaluation rubrics will be announced separately.

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Module 1: Reproducing Kernel Hilbert Space

Topics covered in this section include:

• Functional approximation using basis expansions and the approximation-estimation tradeoff
• Regression splines, natural cubic splines, and smoothing splines
• Roughness regularization, effective degrees of freedom, and smoothing parameter selection
• Additive and tensor-product spline models and their high-dimensional limitations
• Positive-definite kernels, RKHS construction, the reproducing property, the RKHS norm, and the Moore-Aronszajn and Mercer results
• Kernel ridge regression and kernel principal component analysis
• Kernel mean embeddings and maximum mean discrepancy
• The representer theorem and support vector regression, including loss, primal, dual, and kernel formulations

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Module 2: Causal Inference and Personalized Decision Making

Topics covered in this section include:

• Potential outcomes, average treatment effects, and randomized trials
• Propensity scores, inverse probability weighting, and causal identification assumptions
• Outcome regression, doubly robust estimation, and cross-fitting
• Unobserved confounding, instrumental variables, and weak instruments
• Conditional average treatment effects and meta-learners
• Optimal treatment regimes and outcome weighted learning for binary and continuous treatments
• Dynamic treatment regimes, the G-formula, and backward induction
• Q-learning, A-learning, and policy-value generalization error

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Module 3: Tree ensembles and uncertainty

Topics covered in this section include:

• Tree ensembles, bagging, and bias-variance tradeoffs
• Random forests as adaptive weights and data-dependent kernels
• Purely random forests, Mondrian partitions, and kernel approximations
• AdaBoost, gradient boosting, and the boosting training-error bound
• Influence functions, local moment equations, generalized random forests, and causal forests
• Honesty, asymptotic normality, and pointwise confidence intervals
• Bootstrap, jackknife, infinitesimal jackknife, U-statistics, and variable importance
• Conditional distributions and prediction intervals with random forests

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Module 4: Reinforcement Learning

Topics covered in this section include:

• Markov decision processes, the Markov property, and discounted rewards
• Value functions, Q-functions, and Bellman equations
• Bellman operators, contraction mappings, and value iteration
• Policy evaluation, policy improvement, and model-based versus model-free learning
• Fitted Q-iteration with linear, nonlinear, and forest-based function approximation
• Policy gradients, occupancy measures, and on-policy versus off-policy learning
• Maximum-entropy objectives, soft actor-critic, and behavior regularization in offline reinforcement learning

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Prerequisites

You should be familiar with basic statistical theory, linear algebra, linear regression, and common machine learning models. You are expected to have completed at least one graduate-level course in theoretical statistics. We assume that you can use the models covered in STAT 432, at least computationally, as building blocks for the methods introduced in this course.

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Software

You need to be familiar with basic programming in R and Python. Lecture notes, selected readings, and homework assignments will be provided in R Markdown and/or Jupyter Notebook. You can use either R or Python to complete homework assignments and computational demonstrations for presentations. You are also expected to utilize AI tools, including agentic tools, as part of your computational work, subject to the disclosure and responsibility requirements below. However, you are responsible for installing the required packages and libraries.

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Using AI Tools

As we explore programming and machine learning, you are expected to use and experiment with AI tools, including agentic tools, to improve your work and enrich your learning. However, two points are important. First, homework is designed to help you gain insights, improve your understanding, and practice course ideas and methods. Using AI to bypass this process works against the purpose of the assignment. Second, you must report any use of AI tools, and you are ultimately responsible for the work you submit, including its reasoning, code, interpretation, and correctness. AI tools may produce errors or misleading results. Treat them as tools for exploration and learning, and ensure that your final work reflects your own understanding and judgment.

The university provides guidance for teaching and learning with AI and Guidance for Students. When preparing assessed coursework, I would also consider this statement by Elsevier. If you have questions or concerns, please let me know or talk to an expert.

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Grading

The course grade has two broad components: homework and Present and Challenge activities.

Component	Weight
Homework	50%
Present and Challenge session participation	40%
Team presentations	10%

There will be one homework assignment for each module, for a total of four assignments. Each homework assignment will be due during the second-to-last instructional week of its module. Together, the four assignments account for 50% of the course grade.

There are eight Present and Challenge sessions, with two sessions for each module. Registering the required evaluation scores through Popping in each session earns 5% of the course grade, for a total of 40%. Every student will submit the required evaluations in each session and may also serve as a challenger.

Each student will be required to present twice during the semester. Each team presentation is worth 5% of the course grade, for a total of 10%. Students who present can earn both the regular session participation credit and the separate presentation credit.

Highly rated presentation teams and challengers may receive bonus points. These ratings will consider peer evaluations together with the instructor’s assessment. The detailed evaluation rubric and bonus mechanism will be announced before the first presentation week.

Letter grades are based on the weighted total course score, together with any announced bonus points.

A+	A	A-	B+	B	B-	C+	C	C-	D+	D	D-
TBD	93%	90%	87%	83%	80%	77%	73%	70%	67%	63%	60%

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Academic Integrity

The official University of Illinois policy related to academic integrity can be found in Article 1, Part 4 of the Student Code. Section 1-402 in particular outlines behavior which is considered an infraction of academic integrity. These sections of the Student Code will be upheld in this course. Any violations will be dealt with in a swift, fair and strict manner. Homework assignments are meant to be learning experiences. You may discuss the exercises with other students, but you must complete the solutions on your own (with or without help from AI). Team presentations are collaborative within the assigned team, but all sources, code, and uses of AI tools must be properly cited or disclosed. Peer evaluations and challenger questions must reflect your own reading and judgment. In short, do not cheat, it is not worth the risk. You are more likely to get caught than you believe. If you think you may be operating in a gray area, you most likely are.

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Changes

The instructor reserves the right to make any changes he considers academically advisable. Such changes, if any, will be announced on this website and through email. Please note that it is your responsibility to keep track of the proceedings.

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