5 papers
State space models, emergence, and ergodicity: How many parameters are needed for stable predictions?
Ingvar Ziemann, Nikolai Matni, George J. Pappas
How many parameters are required for a model to execute a given task? It has been argued that large language models, pre-trained via self-supervised learning, exhibit emergent capa…
A Short Information-Theoretic Analysis of Linear Auto-Regressive Learning
Ingvar Ziemann
In this note, we give a short information-theoretic proof of the consistency of the Gaussian maximum likelihood estimator in linear auto-regressive models. Our proof yields nearly…
Finite Sample Analysis for a Class of Subspace Identification Methods
Jiabao He, Ingvar Ziemann, Cristian R. Rojas +1
While subspace identification methods (SIMs) are appealing due to their simple parameterization for MIMO systems and robust numerical realizations, a comprehensive statistical anal…
Rate-Optimal Non-Asymptotics for the Quadratic Prediction Error Method
Charis Stamouli, Ingvar Ziemann, George J. Pappas
We study the quadratic prediction error method -- i.e., nonlinear least squares -- for a class of time-varying parametric predictor models satisfying a certain identifiability cond…
The Fundamental Limitations of Learning Linear-Quadratic Regulators
Bruce D. Lee, Ingvar Ziemann, Anastasios Tsiamis +2
We present a local minimax lower bound on the excess cost of designing a linear-quadratic controller from offline data. The bound is valid for any offline exploration policy that c…