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In this paper, we consider an anticipative nonlinear filtering problem, in which the observation noise is correlated with the past of the signal. This new signal-observation model has its applications in both finance models with insider…

Probability · Mathematics 2019-02-22 Guang Lin , Yanghui Liu , Samy Tindel

We consider estimation of covariance matrices and their inverses (a.k.a. precision matrices) for high-dimensional stationary and locally stationary time series. In the latter case the covariance matrices evolve smoothly in time, thus…

Statistics Theory · Mathematics 2014-01-07 Xiaohui Chen , Mengyu Xu , Wei Biao Wu

We study iterative regularization for linear models, when the bias is convex but not necessarily strongly convex. We characterize the stability properties of a primal-dual gradient based approach, analyzing its convergence in the presence…

Machine Learning · Statistics 2020-10-30 Cesare Molinari , Mathurin Massias , Lorenzo Rosasco , Silvia Villa

The problem of estimating certain distributions over $\{0,1\}^d$ is considered here. The distribution represents a quantum system of $d$ qubits, where there are non-trivial dependencies between the qubits. A maximum entropy approach is…

Computation · Statistics 2019-03-08 Ryan Bennink , Ajay Jasra , Kody J. H. Law , Pavel Lougovski

We consider the problem of learning error covariance matrices for robotic state estimation. The convergence of a state estimator to the correct belief over the robot state is dependent on the proper tuning of noise models. During inference,…

Robotics · Computer Science 2023-09-19 Mohamad Qadri , Zachary Manchester , Michael Kaess

We present a computational framework for estimating the uncertainty in the numerical solution of linearized infinite-dimensional statistical inverse problems. We adopt the Bayesian inference formulation: given observational data and their…

Numerical Analysis · Mathematics 2013-08-07 Tan Bui-Thanh , Omar Ghattas , James Martin , Georg Stadler

This paper is concerned with the selection and estimation of fixed and random effects in linear mixed effects models. We propose a class of nonconcave penalized profile likelihood methods for selecting and estimating important fixed…

Statistics Theory · Mathematics 2012-11-05 Yingying Fan , Runze Li

We consider the problem of discrete-time signal denoising, focusing on a specific family of non-linear convolution-type estimators. Each such estimator is associated with a time-invariant filter which is obtained adaptively, by solving a…

Statistics Theory · Mathematics 2018-06-13 Dmitrii Ostrovskii , Zaid Harchaoui

Recent diffusion models provide a promising zero-shot solution to noisy linear inverse problems without retraining for specific inverse problems. In this paper, we reveal that recent methods can be uniformly interpreted as employing a…

Computer Vision and Pattern Recognition · Computer Science 2024-06-04 Xinyu Peng , Ziyang Zheng , Wenrui Dai , Nuoqian Xiao , Chenglin Li , Junni Zou , Hongkai Xiong

We consider a class of linear ill-posed inverse problems arising from inversion of a compact operator with singular values which decay exponentially to zero. We adopt a Bayesian approach, assuming a Gaussian prior on the unknown function.…

Statistics Theory · Mathematics 2013-12-09 Sergios Agapiou , Andrew M. Stuart , Yuan-Xiang Zhang

The unfolding problem in particle physics is to make inferences about the true particle spectrum based on smeared observations from a detector. This is an ill-posed inverse problem, where small changes in the smeared distribution can lead…

High Energy Physics - Experiment · Physics 2026-03-23 Huanbiao Zhu , Andrea Carlo Marini , Mikael Kuusela , Larry Wasserman

Among other uses, neural networks are a powerful tool for solving deterministic and Bayesian inverse problems in real-time, where variational autoencoders, a specialized type of neural network, enable the Bayesian estimation of model…

Machine Learning · Computer Science 2025-09-25 Andrea Tonini , Luca Dede'

This paper tackles the problem of robust covariance matrix estimation when the data is incomplete. Classical statistical estimation methodologies are usually built upon the Gaussian assumption, whereas existing robust estimation ones assume…

We show how pre-averaging can be applied to the problem of measuring the ex-post covariance of financial asset returns under microstructure noise and non-synchronous trading. A pre-averaged realised covariance is proposed, and we present an…

Econometrics · Economics 2026-02-24 Kim Christensen , Silja Kinnebrock , Mark Podolskij

We consider the problem of stabilization of a linear system, under state and control constraints, and subject to bounded disturbances and unknown parameters in the state matrix. First, using a simple least square solution and available…

Systems and Control · Electrical Eng. & Systems 2020-07-22 Edouard Leurent , Denis Efimov , Odalric-Ambrym Maillard

A posteriori error estimates are an important tool to bound discretization errors in terms of computable quantities avoiding regularity conditions that are often difficult to establish. For non-linear and non-differentiable problems,…

Numerical Analysis · Mathematics 2024-06-12 Sören Bartels , Alex Kaltenbach

Quantifying and reducing uncertainty in Earth system model parameterizations is essential to improving their reliability in decision-making. Forward uncertainty propagation is used to derive parameter sensitivity but requires physically…

Atmospheric and Oceanic Physics · Physics 2026-04-22 Ethan YoungIn Shin , Baris Kale , Michael F. Howland

We consider nonlinear mixed effects models including high-dimensional covariates to model individual parameters variability. The objective is to identify relevant covariates among a large set under sparsity assumption and to estimate model…

Statistics Theory · Mathematics 2025-08-06 Antoine Caillebotte , Estelle Kuhn , Sarah Lemler

Variance estimation in the linear model when $p > n$ is a difficult problem. Standard least squares estimation techniques do not apply. Several variance estimators have been proposed in the literature, all with accompanying asymptotic…

Methodology · Statistics 2014-01-30 Stephen Reid , Robert Tibshirani , Jerome Friedman

Robust and sparse estimation of linear regression coefficients is investigated. The situation addressed by the present paper is that covariates and noises are sampled from heavy-tailed distributions, and the covariates and noises are…

Machine Learning · Statistics 2022-10-11 Takeyuki Sasai