相关论文: Prony's method under an almost sharp multivariate …
This paper considers inference for a function of a parameter vector in a partially identified model with many moment inequalities. This framework allows the number of moment conditions to grow with the sample size, possibly at exponential…
We study the multifractal analysis of self-similar measures arising from random homogeneous iterated function systems. Under the assumption of the uniform strong separation condition, we see that this analysis parallels that of the…
A novel framework is introduced to formalize identifiability in well-specified but ill-posed linear regression models. The framework is distribution-free and accommodates highly correlated features that may or may not relate to the…
Multivariate functions encountered in high-dimensional uncertainty quantification problems often vary most strongly along a few dominant directions in the input parameter space. We propose a gradient-based method for detecting these…
Prony's method, in its various concrete algorithmic realizations, is concerned with the reconstruction of a sparse exponential sum from integer samples. In several variables, the reconstruction is based on finding the variety for a zero…
In the paper, we propose an analytical and numerical approach to identify scalar parameters (coefficients, orders of fractional derivatives) in the multi-term fractional differential operator in time, $\mathbf{D}_t$. To this end, we analyze…
Person re-identification is a challenging task because of the high intra-class variance induced by the unrestricted nuisance factors of variations such as pose, illumination, viewpoint, background, and sensor noise. Recent approaches…
We study the application of the Augmented Lagrangian Method to the solution of linear ill-posed problems. Previously, linear convergence rates with respect to the Bregman distance have been derived under the classical assumption of a…
The uniqueness question of the multivariate moment problem is studied by different methods: Hilbert space operators, complex function theory, polynomial approximation, disintegration, integral geometry. Most of the known results in the…
Prony's method is a standard tool exploited for solving many imaging and data analysis problems that result in parameter identification in sparse exponential sums $$f(k)=\sum_{j=1}^{T}c_{j}e^{-2\pi i\langle t_{j},k\rangle},\quad k\in…
We consider the reconstruction of a diffusion coefficient in a quasilinear elliptic problem from a single measurement of overspecified Neumann and Dirichlet data. The uniqueness for this parameter identification problem has been established…
The main contributions of this paper are the proposition and the convergence analysis of a class of inertial projection-type algorithm for solving variational inequality problems in real Hilbert spaces where the underline operator is…
Existing high-dimensional statistical methods are largely established for analyzing individual-level data. In this work, we study estimation and inference for high-dimensional linear models where we only observe "proxy data", which include…
Most papers on high-dimensional statistics are based on the assumption that none of the regressors are correlated with the regression error, namely, they are exogenous. Yet, endogeneity can arise incidentally from a large pool of regressors…
The multivariate probit is popular for modeling correlated binary data, with an attractive balance of flexibility and simplicity. However, considerable challenges remain in computation and in devising a clear statistical framework. Interest…
Measuring inequalities in a multidimensional framework is a challenging problem which is common to most field of science and engineering. Nevertheless, despite the enormous amount of researches illustrating the fields of application of…
The scope of this research is the identification of unknown piecewise constant parameters of linear regression equation under the finite excitation condition. Compared to the known methods, to make the computational burden lower, only one…
In this paper, we develop a unified framework able to certify both exponential and subexponential convergence rates for a wide range of iterative first-order optimization algorithms. To this end, we construct a family of parameter-dependent…
We consider determining $\R$-minimizing solutions of linear ill-posed problems $A x = y$, where $A: {\mathscr X} \to {\mathscr Y}$ is a bounded linear operator from a Banach space ${\mathscr X}$ to a Hilbert space ${\mathscr Y}$ and…
For absolutely convergent series we state explicitly a one-sided summation estimate that can be viewed as the discrete analogue of the change of variable formula on the half line. This estimate is implicit in Pascal Lef\`evre's recent…