相关论文: Element-wise estimation error of a total variation…

For the identification of switched systems with a measured switching signal, this work aims to analyze the effect of switching strategies on the estimation error. The data for identification is assumed to be collected from globally…

We consider the consistency properties of a regularised estimator for the simultaneous identification of both changepoints and graphical dependency structure in multivariate time-series. Traditionally, estimation of Gaussian Graphical…

In applied time-to-event analysis, a flexible parametric approach is to model the hazard rate as a piecewise constant function of time. However, the change points and values of the piecewise constant hazard are usually unknown and need to…

In this work, we investigate the regularized solutions and their finite element solutions to the inverse source problems governed by partial differential equations, and establish the stochastic convergence and optimal finite element…

This dissertation presents a general framework for changepoint detection based on L0 model selection. The core method, Iteratively Reweighted Fused Lasso (IRFL), improves upon the generalized lasso by adaptively reweighting penalties to…

We study the theoretical properties of the fused lasso procedure originally proposed by \cite{tibshirani2005sparsity} in the context of a linear regression model in which the regression coefficient are totally ordered and assumed to be…

Assuming stationarity is unrealistic in many time series applications. A more realistic alternative is to allow for piecewise stationarity, where the model is allowed to change at given time points. In this article, the problem of detecting…

This article is a review on basic concepts and tools devoted to a posteriori error estimation for problems solved with the Finite Element Method. For the sake of simplicity and clarity, we mostly focus on linear elliptic diffusion problems,…

Detecting changepoints in a one-dimensional signal is a classical yet fundamental problem. The fused lasso provides an elegant convex formulation that produces a stepwise estimate of the mean, but quantifying the uncertainty of the detected…

This paper addresses the problem of segmenting a time-series with respect to changes in the mean value or in the variance. The first case is when the time data is modeled as a sequence of independent and normal distributed random variables…

In this paper the problem of retrospective change-point detection and estimation in multivariate linear models is considered. The lower bounds for the error of change-point estimation are proved in different cases (one change-point:…

We propose an adaptive refinement algorithm to solve total variation regularized measure optimization problems. The method iteratively constructs dyadic partitions of the unit cube based on i) the resolution of discretized dual problems and…

We study a class of fused lasso problems where the estimated parameters in a sequence are regressed toward their respective observed values (fidelity loss), with $\ell_1$ norm penalty (regularization loss) on the differences between…

We consider a linear-quadratic elliptic optimal control problem with point evaluations of the state variable in the cost functional. The state variable is discretized by conforming linear finite elements. For control discretization, three…

Assuming stationarity is unrealistic in many time series applications. A more realistic alternative is to allow for piecewise stationarity, where the model is allowed to change at given time points. We propose a three-stage procedure for…

We consider a singularly perturbed semilinear boundary value problem of a general form that allows various types of turning points. A solution decomposition is derived that separates the potential exponential boundary layer terms. The…

The fused lasso, also known as (anisotropic) total variation denoising, is widely used for piecewise constant signal estimation with respect to a given undirected graph. The fused lasso estimate is highly nontrivial to compute when the…

We consider the problem of predicting an outcome variable using $p$ covariates that are measured on $n$ independent observations, in the setting in which flexible and interpretable fits are desirable. We propose the fused lasso additive…

In an error estimation of finite element solutions to the Poisson equation, we usually impose the shape regularity assumption on the meshes to be used. In this paper, we show that even if the shape regularity condition is violated, the…

We present an a posteriori error analysis for the mixed virtual element method (mixed VEM) applied to second order elliptic equations in divergence form with mixed boundary conditions. The resulting error estimator is of residual-type. It…