7 citations · 27 across the 27 of their papers we have counts for
11 papers · 1 filter
Nearly Instance-Optimal Parameter Recovery from Many Trajectories via Hellinger Localization
Eliot Shekhtman, Yichen Zhou, Ingvar Ziemann +2
Learning from temporally-correlated data is a core facet of modern machine learning. Yet our understanding of sequential learning remains incomplete, particularly in the multi-traj…
Logarithmic Regret for Nonlinear Control
James Wang, Bruce D. Lee, Ingvar Ziemann +1
We address the problem of learning to control an unknown nonlinear dynamical system through sequential interactions. Motivated by high-stakes applications in which mistakes can be…
Shallow diffusion networks provably learn hidden low-dimensional structure
Nicholas M. Boffi, Arthur Jacot, Stephen Tu +1
Diffusion-based generative models provide a powerful framework for learning to sample from a complex target distribution. The remarkable empirical success of these models applied t…
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…
Sharp Rates in Dependent Learning Theory: Avoiding Sample Size Deflation for the Square Loss
Ingvar Ziemann, Stephen Tu, George J. Pappas +1
In this work, we study statistical learning with dependent (-mixing) data and square loss in a hypothesis class where is the norm $\|f\|_{Ψ_p}…
The noise level in linear regression with dependent data
Ingvar Ziemann, Stephen Tu, George J. Pappas +1
We derive upper bounds for random design linear regression with dependent (-mixing) data absent any realizability assumptions. In contrast to the strictly realizable martingale…
Learning with little mixing
Ingvar Ziemann, Stephen Tu
We study square loss in a realizable time-series framework with martingale difference noise. Our main result is a fast rate excess risk bound which shows that whenever a trajectory…
Learning to Control Linear Systems can be Hard
Anastasios Tsiamis, Ingvar Ziemann, Manfred Morari +2
In this paper, we study the statistical difficulty of learning to control linear systems. We focus on two standard benchmarks, the sample complexity of stabilization, and the regre…
Single Trajectory Nonparametric Learning of Nonlinear Dynamics
Ingvar Ziemann, Henrik Sandberg, Nikolai Matni
Given a single trajectory of a dynamical system, we analyze the performance of the nonparametric least squares estimator (LSE). More precisely, we give nonasymptotic expected …
Regret Lower Bounds for Learning Linear Quadratic Gaussian Systems
Ingvar Ziemann, Henrik Sandberg
TWe establish regret lower bounds for adaptively controlling an unknown linear Gaussian system with quadratic costs. We combine ideas from experiment design, estimation theory and…