Welcome! This is the official website of the Statistics Directed Reading Program at UofT. Are you interested in research statistics or eager to explore a statistical topic in more depth? Looking for mentorship and the chance to study material you might not encounter in a course? Then consider applying to our Directed Reading Program (DRP)!
The DRP pairs undergraduate students with graduate mentors in the Department of Statistical Sciences for independent study projects that run through the winter semester. After applying, selected students will be matched with mentors based on common interests and goals.
Who is eligible to participate?
All UofT undergraduate students who are broadly interested in Statistics are eligible. Although students working towards a Statistics major/specialist degree will be prioritized in the application process, we do welcome applicants from mathematics, engineering, computer science etc. with an interest in statistics.
What’s expected from a DRP student?
Students will be paired with a mentor who will guide them through the reading project. The expectation is that students will conduct independent reading and research, having weekly or biweekly meetings with their mentor during the winter semester, until April (exact date TBD). At the end of the program, students will submit a short write-up summarizing and explaining what they have learned, with the possibility of giving a short presentation.
Are there any prerequisites required for the SDRP?
Although there are no formal prerequisites for the SDRP, different mentors may require proficiency in specific topics and will informally suggest prerequisite classes. It is generally assumed that students are comfortable with linear algebra, basic analysis, probability and estimation theory.
Can I choose the topic I want to learn about?
Even though the listed topics were chosen specifically as the mentors’ specialties, we may consider your own personal proposals if you are motivated and clearly state them in your application.
We are now accepting applications! (Deadline December 19th, don’t wait up!)
This DRP is an offshoot of the original program at UChicago’s math department and extends a growing DRP Network.
Projects for the 2026 Session
Topics in Optimal Transport
The transportation problem can be straightforwardly posed as how to optimally move a mass from one area to another. But, this simple question has important applications in economics and, of particular interest to me, generative models in machine learning. My objective to read through the foundations of optimal transport (OT) using the standard textbook “Topics in Optimal Transportation” by Villani, before proceeding (if time permits) to papers that apply this in the context of machine learning.
Mentor: KC Tsiolis. Suggested prerequisites: strong probability skills and ideally some knowledge of measure theory.
Concentration Inequalities: A Nonasymptotic Theory of Independence
The study of random fluctuations can be made explicit by constructing bounds on the probability that some function differs from its mean by more than a certain amount. If a function of many independent random variables does not depend too much on any of the specific variables then it is concentrated in the sense that, with high probability, it is close to its expected value. This way of thinking has been extremely influential in areas such as statistics, machine learning, learning theory, statistical mechanics or information theory.
Mentor: Luis Sierra. Suggested prerequisites: strong knowledge of probability.
How is the admissibility of an estimator related to recurrent diffusions?
Admissibility is a desirable property when constructing an estimator for a random quantity. This paper by Brown shows how questions about admissibility can be translated into questions about diffusions and solving certain boundary value problems from differential equations. Interestingly, some of these mathematical problems turn out to have no solution, and this impossibility reflects situations in statistics where no uniformly best estimator exists. Our goal is to understand how this works and explore deep links between decision theory, probability, and analysis, showing how the structure of random motion can help explain when good estimators do (or don’t) exist.
Mentor: Luis Sierra. Suggested prerequisites: strong analysis skills and some exposure to combinatorics. In particular, knowledge of Markov chains is a big plus.
Causal Effect Identification & Estimation
Mentor: Yaqi Shi. Suggested prerequisites: basic linear regression, probability, and STA314 would be preferred.
Quantifying uncertainty with Conformal Prediction
How good are your predictive models? Conformal prediction (CP) is a modern predictive inference tool for high-stakes prediction problems like tumor segmentation and election polling. It has garnered significant interest in the statistics and machine learning communities for its finite sample distribution-free guarantees. In this DRP, we will read the core papers in the area and then branch into advanced subtopics tailored to the student’s interests.
Mentor: Leo Watson. Suggested prerequisites: Working knowledge of probability (STA347 equivalent), Bayesian statistics (STA365 equivalent).
Analysis of algorithms in Statistics
Modern statistics runs on matrix decompositions the same way modern cities run on electricity: quietly, constantly, and absolutely everywhere. Whether you’re fitting regressions, running PCA, exploring latent structure, or stabilizing ill-conditioned problems, you’re depending on a handful of numerical algorithms that do the real heavy lifting: QR, SVD, eigendecompositions, Cholesky, and their friends. Let’s look at how these algorithms actually work and why they’re the trustworthy backbone of statistical computation, addressing current limitations and opportunities for our own contributions.
Mentor: Luis Sierra. Suggested prerequisites: interest in coding and comfort with linear algebra.
Mean-field analysis of neural network training dynamics
In spite of their tremendous success in practice, neural networks remain in many ways a black box whose evolution over the course of training is poorly understood. One attempt to (partially) remedy this is to study networks in the limit of infinite parameters and infinite training time. These “mean-field dynamics” have given a new perspective on neural network training — one that leverages ideas from the study of interacting particle systems in physics. For some representative papers, see https://arxiv.org/abs/1805.01053, https://arxiv.org/abs/1808.09372, https://arxiv.org/pdf/1804.06561, and https://arxiv.org/pdf/1805.09545.
Mentor: KC Tsiolis. Suggested prerequisites: analysis, probability, and an introductory Machine Learning course (e.g. STA314).
Theory of feature learning in neural networks
Neural networks set themselves apart from other machine learning methods through their ability to learn useful representations (features) of high-dimensional data. How can we mathematically prove the emergence of these features in neural network training? How can we show a strict separation between those models that learn representations (the “feature learning regime”) and to those that don’t (the “lazy regime”)? Representative papers include https://arxiv.org/pdf/2011.14522, https://arxiv.org/pdf/1812.07956, https://arxiv.org/abs/1906.08899, and https://arxiv.org/pdf/2205.01445.
Mentor: KC Tsiolis. Suggested prerequisites: analysis, probability, and an introductory Machine Learning course (e.g. STA314).
Free Probability to understand random matrices
Analyzing random matrices has become a fundamental problem in modern statistics. Many complicated properties of large random matrices become simpler when viewed through the lens of “freeness”, a concept that plays a role similar to independence in classical probability, but that requires a redefinition of probability spaces. By studying free convolution, limit theorems, and connections to eigenvalue distributions, the project shows how free probability provides clear explanations for phenomena like the semicircle law and universality. We will be exploring free probability as a powerful modern tool for understanding the behavior of large random matrices, offering an accessible pathway from standard probability ideas to advanced techniques used in random matrix theory, operator algebras, and modern mathematical physics.
Mentor: Luis Sierra. Suggested prerequisites: strong analysis and probability skills and a confident command of linear algebra.
Inverse Problems and Data Assimilation: A Machine Learning Approach
Mentor: Yichen Ji. Suggested prerequisites: probability (STA257), linear algebra (MAT223/224), multivariable calculus (MAT237), matrix calculus; basic familiarity with optimization and machine learning concepts is a plus.
Topics in Experimental Design
Mentor: Huanlin Mao. Suggested prerequisites: analysis, probability, and introductory statistical decision theory.
Statistical Rethinking: A Bayesian Course with Examples in R and Stan
Mentor: Yichen Ji. Suggested prerequisites: intro probability (STA237/257), linear regression (STA302); basic Bayesian stats (STA365) or computational stats (STA410) is not required but a plus.
Empirical Bayes: From Herbert Robbins to Modern Theory and Applications
Mentor: Yichen Ji. Suggested prerequisites: rigorous probability and statistics (STA347&STA355); mathematical statistics (STA452) is a plus.
Current topics in Actuarial Science
Students will read about current research areas in actuarial science, which can include theoretical topics such as optimal (re)insurance or applied topics like fraud detection. Depending on the students’ background, they will gain some practical experiences in implementation or study potential extensions.
Mentor: PH Chan. Suggested prerequisites: (ACT348 or ACT351) with (STA314 or equivalent) or (MAT257 or equivalent) or (STA257 and STA261).
Flow Matching Guide to Code
Mentor: Yichen Ji. Suggested prerequisites: ODEs (MAT244), probability (STA257), PyTorch, familiarity with deep learning (STA414/CSC413).
Diffusion Models: A Comprehensive Survey of Methods and Applications
Mentor: Yichen Ji. Suggested prerequisites: probability (STA257), multivariate calculus (MAT237), optimization, familiarity with stochastic process and/or deep learning (STA414/CSC413); generative modeling (flows and VAEs) is a plus.
Dimensionality reduction
This project will be focused on classic dimensionality reduction techniques such as PCA, CCA, ICA and their variants.
Mentor: Arian Hashemzadeh. Suggested prerequisites: STA220 and STA257 (or similar) and knowledge of linear algebra.
Topics in Causal Discovery
This project will involve an overview of the constraint-based and score-based causal discovery methods and their challenges.
Mentor: Arian Hashemzadeh. Suggested prerequisites: STA257 or similar, knowledge of linear algebra and introductory knowledge of graph theory.
Statistical Mechanics models for Machine Learning
Mentor: Alex Valencia. Suggested prerequisites: analysis and probability, with some knowledge of statistical/machine learning.
luis.sierra[at]mail[dot]utoronto[dot]ca
kc.tsiolis[at]mail[dot]utoronto[dot]ca