# NMAK24008U Targeted Learning

Volume 2024/2025
Education

MSc Programme in Statistics

MSc Programme in Mathematics-Economics

Content

This course provides an introduction to targeted learning as a general framework for nonparametric inference in settings where the target parameter is low-dimensional but estimation has to deal with high-dimensional nuisance parameters. In these settings, efficient influence function based estimation provides a popular basis for combining machine learning techniques with valid statistical inference. In the course, students will be introduced to key concepts from efficiency theory to understand the fundamental principles of statistical inference when incorporating machine learning methods. The bias correction abilities of influence function based estimation will be emphasized, and the asymptotic properties will be analyzed and compared to related estimation methods. Students will translate real-world applications into a mathematical and statistical formulation of the estimation problem that needs to be solved, and implement targeted learning procedures using R software to estimate well-defined estimands based on simulated data.

Learning Outcome

Knowledge:

• Explain the fundamental principles of statistical inference using targeted learning and its application as a general framework for estimation.
• Describe the concept of estimands and the differences between estimands and their associated estimators.
• Summarize the advantages and limitations of leveraging machine learning flexibility, and the implications it holds for providing inference for interpretable parameters.

Skills:

• Utilize the estimand framework to translate relevant scientific questions to well-defined statistical parameters in (bio)statistical applications.
• Derive the efficient influence curve for a given estimand, and construct an estimation procedure to solve the efficient influence curve equation.
• Analyze the asymptotic properties of the targeted estimator for a given estimand.
• Implement targeted learning estimation procedures using R software to estimate well-defined estimands based on simulated data, and assess the accuracy and efficiency of the estimators.
• Compare the assumptions and performance of targeted estimation to related estimation methods, and discuss the strengths and limitations of each approach.

Competences:

• Integrate theoretical knowledge with practical skills to formulate and solve complex estimation problems.
• Make informed decisions about the selection and application of appropriate estimators based on the characteristics of the data and research questions.
• Evaluate the trade-offs, strengths, and limitations of different estimation techniques, particularly in scenarios involving high-dimensional nuisance parameters.

A combination of research papers, textbooks, and lecture notes.

Matematisk statistik (MStat), Statistiske metoder (StatMet), Sandsynlighedsteori 2 (Sand 2).
Academic qualifications equivalent to a BSc degree is recommended.
This course requires a certain statistical maturity at the level of MSc students in Statistics.
4 hours of a mixture between lectures and student presentations per week for 7 weeks.
2 hours of exercises per week for 7 weeks.
• Category
• Hours
• Lectures
• 28
• Preparation
• 133
• Exercises
• 14
• Exam Preparation
• 30
• Exam
• 1
• Total
• 206
Continuous feedback during the course of the semester
Credit
7,5 ECTS
Type of assessment
Oral examination, 25 minutes (no preparation time)
Type of assessment details
Five assignments will be distributed throughout the course. Students must prepare solutions for each assignment in advance of the exam. During the oral exam, one assignment is randomly chosen from the five prepared by the student. The student presents it without prior preparation, followed by a discussion with the examiners on topics within the course. The grade is based on both the presentation and the following discussion.
Exam registration requirements

To participate in the final exam, one oral presentation must have been given during the course. Students will in small groups sign up to present a piece of course material during lecture. Presenters should read the content to be presented and prepare slides in advance.

Aid
All aids allowed
Marking scale