7 citations · 27 across the 27 of their papers we have counts for
27 papers
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…
An Elementary Proof of the Hanson-Wright Inequality
Ingvar Ziemann
The Hanson-Wright inequality establishes exponential concentration for quadratic forms , where is a vector with independent sub-Gaussian entries and with parameters de…
Nonconvex Linear System Identification with Minimal State Representation
Uday Kiran Reddy Tadipatri, Benjamin D. Haeffele, Joshua Agterberg +2
Low-order linear System IDentification (SysID) addresses the challenge of estimating the parameters of a linear dynamical system from finite samples of observations and control inp…
A Vector Bernstein Inequality for Self-Normalized Martingales
Ingvar Ziemann
We prove a Bernstein inequality for vector-valued self-normalized martingales. We first give an alternative perspective of the corresponding sub-Gaussian bound due to Abbasi-Yadkor…
Finite Sample Analysis of Open-loop Subspace Identification Methods
Jiabao He, Ingvar Ziemann, Cristian R. Rojas +2
Subspace identification methods (SIMs) are known for their simple parameterization for MIMO systems and robust numerical properties. However, a comprehensive statistical analysis o…
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…
Guarantees for Nonlinear Representation Learning: Non-identical Covariates, Dependent Data, Fewer Samples
Thomas T. Zhang, Bruce D. Lee, Ingvar Ziemann +2
A driving force behind the diverse applicability of modern machine learning is the ability to extract meaningful features across many sources. However, many practical domains invol…
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…
Active Learning for Control-Oriented Identification of Nonlinear Systems
Bruce D. Lee, Ingvar Ziemann, George J. Pappas +1
Model-based reinforcement learning is an effective approach for controlling an unknown system. It is based on a longstanding pipeline familiar to the control community in which one…
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}…
A Tutorial on the Non-Asymptotic Theory of System Identification
Ingvar Ziemann, Anastasios Tsiamis, Bruce Lee +3
This tutorial serves as an introduction to recently developed non-asymptotic methods in the theory of -- mainly linear -- system identification. We emphasize tools we deem particul…
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…
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…
A note on the smallest eigenvalue of the empirical covariance of causal Gaussian processes
Ingvar Ziemann
We present a simple proof for bounding the smallest eigenvalue of the empirical covariance in a causal Gaussian process. Along the way, we establish a one-sided tail inequality for…
Statistical Learning Theory for Control: A Finite Sample Perspective
Anastasios Tsiamis, Ingvar Ziemann, Nikolai Matni +1
This tutorial survey provides an overview of recent non-asymptotic advances in statistical learning theory as relevant to control and system identification. While there has been su…
How are policy gradient methods affected by the limits of control?
Ingvar Ziemann, Anastasios Tsiamis, Henrik Sandberg +1
We study stochastic policy gradient methods from the perspective of control-theoretic limitations. Our main result is that ill-conditioned linear systems in the sense of Doyle inev…
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…