PhD Courses in Denmark

Welcome to Statistical learning theory for time-series

Description:

This course provides a comprehensive introduction to the theory, algorithms, and statistical guarantees for learning dynamical systems and performing time-series prediction. The course combines classical modeling techniques with modern deep learning architectures, addressing both the estimation of unknown physical quantities and the construction of predictive models for applications such as forecasting the yearly energy consumption of buildings.

The theoretical foundation lies at the intersection of system identification, econometrics, statistics, and machine learning. Students will study both linear models and nonlinear sequence models, including:

• Autoregressive and state-space models
• Parameter estimation and subspace methods
• Recurrent Neural Networks (RNNs)
• Transformers for sequential data
• Deep Structured State-Space Models (SSMs), including Mamba and related architectures architectures

In addition to understanding these models, the course emphasizes statistical performance guarantees, covering:

• Asymptotic consistency for learning linear autoregressive and state-space models
• Finite-sample error bounds for algorithms based on linear regression and subspace methods
• Probably Approximately Correct (PAC) and PAC-Bayesian guarantees for learning sequential models, including deep architecture

The course is conducted as an intensive lecture series with physical attendance. Evaluation will be based on attendance and homework assignments.

Modern time-series prediction increasingly relies on deep learning methods such as RNNs, transformers, and structured state-space models, yet these models are often used as black boxes without rigorous performance understanding. This course bridges classical dynamical systems theory with modern sequence modeling, providing both practical tools and theoretical foundations to evaluate when and why these methods work, and under what statistical guarantees they can be trusted.

For additional information, updates, and registration, please refer to AAU PhD Moodle via the link provided on the right side of this page.