English
Related papers

Related papers: Minimax Lower Bounds for $\mathcal{H}_\infty$-Norm…

200 papers

We study some of the most commonly used mutual information estimators, based on histograms of fixed or adaptive bin size, $k$-nearest neighbors and kernels, and focus on optimal selection of their free parameters. We examine the consistency…

Data Analysis, Statistics and Probability · Physics 2015-05-13 Angeliki Papana , Dimitris Kugiumtzis

We develop a general class of noise-robust estimators based on the existing estimators in the non-noisy high-frequency data literature. The microstructure noise is a parametric function of the limit order book. The noise-robust estimators…

Statistics Theory · Mathematics 2020-09-18 Simon Clinet , Yoann Potiron

In this paper, we consider a best action identification problem in the stochastic linear bandit setup with a fixed confident constraint. In the considered best action identification problem, instead of minimizing the accumulative regret as…

Machine Learning · Computer Science 2018-12-04 Jun Geng , Lifeng Lai

We prove two lower bounds for the complexity of non-log-concave sampling within the framework of Balasubramanian et al. (2022), who introduced the use of Fisher information (FI) bounds as a notion of approximate first-order stationarity in…

Machine Learning · Statistics 2022-10-07 Sinho Chewi , Patrik Gerber , Holden Lee , Chen Lu

This paper introduces a novel approach to system identification for nonlinear input-output models that minimizes the simulation error and frames the problem as a constrained optimization task. The proposed method addresses vanishing…

Optimization and Control · Mathematics 2025-12-17 Vito Cerone , Sophie M. Fosson , Simone Pirrera , Diego Regruto

A fundamental problem in statistics and machine learning is to estimate a function $f$ from possibly noisy observations of its point samples. The goal is to design a numerical algorithm to construct an approximation $\hat f$ to $f$ in a…

Statistics Theory · Mathematics 2025-05-30 Ronald DeVore , Robert D. Nowak , Rahul Parhi , Guergana Petrova , Jonathan W. Siegel

This paper characterizes the minimax linear estimator of the value of an unknown function at a boundary point of its domain in a Gaussian white noise model under the restriction that the first-order derivative of the unknown function is…

Econometrics · Economics 2017-10-19 Wayne Yuan Gao

This paper presents uniform-in-time finite-sample bounds for regularized linear regression with vector-valued outputs and conditionally zero-mean subgaussian noise. By revisiting classical self-normalized martingale arguments, we obtain…

Statistics Theory · Mathematics 2026-03-20 Léo Simpson , Katrin Baumgärtner , Johannes Köhler , Moritz Diehl

We present a simulation experiment of a pipeline based on machine learning algorithms for neutral hydrogen (HI) intensity mapping (IM) surveys with different telescopes. The simulation is conducted on HI signals, foreground emission,…

Instrumentation and Methods for Astrophysics · Physics 2022-09-14 Lin-Cheng Li , Yuan-Gen Wang

This paper is concerned with the analysis of the $L_p\ (p\in[1,\infty), p=\infty)$ induced norms of continuous-time linear systems where input signals are restricted to be nonnegative. This norm is referred to as the $L_{p+}$ induced norm…

Optimization and Control · Mathematics 2026-03-24 Yoshio Ebihara , Noboru Sebe , Hayato Waki , Dimitri Peaucelle , Sophie Tarbouriech , Victor Magron , Tomomichi Hagiwara

We address the problem of estimating the inputs of a dynamical system from measurements of the system's outputs. To this end, we introduce a novel estimation algorithm that explicitly trades off bias and variance to optimally reduce the…

Machine Learning · Computer Science 2019-09-20 Sebastian Curi , Kfir Y. Levy , Andreas Krause

Approximating a function $f(x)$ on $[-1,1]$ based on $N+1$ samples is a classical problem in numerical analysis. If the samples come with heteroskedastic noise depending on $x$ of variance $\sigma(x)^2$, an $O(N\log N)$ algorithm for this…

Numerical Analysis · Mathematics 2025-08-13 Yuji Nakatsukasa , Yifu Zhang

This paper deals with the problem of finding suboptimal values of an unknown function on the basis of measured data corrupted by bounded noise. As a prior, we assume that the unknown function is parameterized in terms of a number of basis…

Optimization and Control · Mathematics 2025-06-10 Jaap Eising , Jorge Cortes

Practical model building processes are often time-consuming because many different models must be trained and validated. In this paper, we introduce a novel algorithm that can be used for computing the lower and the upper bounds of model…

Machine Learning · Statistics 2014-02-11 Yoshiki Suzuki , Kohei Ogawa , Yuki Shinmura , Ichiro Takeuchi

The kernel-based method has been successfully applied in linear system identification using stable kernel designs. From a Gaussian process perspective, it automatically provides probabilistic error bounds for the identified models from the…

Systems and Control · Electrical Eng. & Systems 2023-03-20 Mingzhou Yin , Roy S. Smith

Estimation of multiple parameters in an unknown Hamiltonian is investigated. We present upper and lower bounds on the time required to complete the estimation within a prescribed tolerance $\delta$. The lower bound is given on the basis of…

Quantum Physics · Physics 2018-01-10 Naoto Kura , Masahito Ueda

This paper studies the mixed $H_-/H_{\infty}$ fault detection filtering of It\^o-type nonlinear stochastic systems. Mixed $H_-/H_{\infty}$ filtering combines the system robustness to the external disturbance and the sensitivity to the fault…

Optimization and Control · Mathematics 2018-12-21 Tianliang Zhang , Feiqi Deng , Weihai Zhang , Bor-Sen Chen

This paper studies the problems of identifiability and estimation in high-dimensional nonparametric latent structure models. We introduce an identifiability theorem that generalizes existing conditions, establishing a unified framework…

Statistics Theory · Mathematics 2025-08-06 Yichen Lyu , Pengkun Yang

This paper mainly discusses the $H_{\infty}$ filtering of general nonlinear discrete time-varying stochastic systems. A nonlinear discrete-time stochastic bounded real lemma (SBRL) is firstly obtained by means of the smoothness of the…

Optimization and Control · Mathematics 2018-12-21 Tianliang Zhang , Feiqi Deng , Weihai Zhang

The minimum achievable statistical uncertainty in the estimation of physical parameters is determined by the quantum Fisher information. Its computation for noisy systems is still a challenging problem. Using a variational approach, we…

Quantum Physics · Physics 2012-11-21 B. M. Escher , L. Davidovich , N. Zagury , R. L. de Matos Filho