相关论文: Exploring recursion for optimal estimators under c…

Different from a typical independent identically distributed (IID) element assumption, this paper studies the estimation of IID row random matrix for the generalized linear model constructed by a linear mixing space and a row-wise mapping…

Linear regression without correspondences is the problem of performing a linear regression fit to a dataset for which the correspondences between the independent samples and the observations are unknown. Such a problem naturally arises in…

Small area estimation methods are used in surveys, where sample sizes are too small to get reliable direct estimates of parameters in some population domains. We consider design-based linear combinations of direct and synthetic estimators…

We consider the classical problems of estimating the mean of an $n$-dimensional normally (with identity covariance matrix) or Poisson distributed vector under the squared loss. In a Bayesian setting the optimal estimator is given by the…

The purpose of the paper is to introduce two new algorithms. The first one computes a linear recursion for proper hypergeometric multisums, by treating one summation variable at a time, and provides rational certificates along the way. A…

We present a randomized maximum a posteriori (rMAP) method for generating approximate samples of posteriors in high dimensional Bayesian inverse problems governed by large-scale forward problems. We derive the rMAP approach by: 1) casting…

An autoregressive-moving average model in which all roots of the autoregressive polynomial are reciprocals of roots of the moving average polynomial and vice versa is called an all-pass time series model. All-pass models are useful for…

We propose a new formulation of robust regression by integrating all realizations of the uncertainty set and taking an averaged approach to obtain the optimal solution for the ordinary least squares regression problem. We show that this…

Sparse principal component analysis (PCA) involves nonconvex optimization for which the global solution is hard to obtain. To address this issue, one popular approach is convex relaxation. However, such an approach may produce suboptimal…

We formulate and discuss two conjectures concerning recursive formulae for Branson's $Q$-curvatures. The proposed formulae describe all $Q$-curvatures on manifolds of all even dimensions in terms of respective lower order $Q$-curvatures and…

Sequential estimation of a vector of linear regression coefficients is considered under both centralized and decentralized setups. In sequential estimation, the number of observations used for estimation is determined by the observed…

We obtain robust and computationally efficient estimators for learning several linear models that achieve statistically optimal convergence rate under minimal distributional assumptions. Concretely, we assume our data is drawn from a…

State-of-the-art Machine Reading Comprehension (MRC) models for Open-domain Question Answering (QA) are typically trained for span selection using distantly supervised positive examples and heuristically retrieved negative examples. This…

This paper proposes an elegant optimization framework consisting of a mix of linear-matrix-inequality and second-order-cone constraints. The proposed framework generalizes the semidefinite relaxation (SDR) enabled solution to the typical…

We consider optimal design of PDE-based Bayesian linear inverse problems with infinite-dimensional parameters. We focus on the A-optimal design criterion, defined as the average posterior variance and quantified by the trace of the…

Compressive sampling has become a widely used approach to construct polynomial chaos surrogates when the number of available simulation samples is limited. Originally, these expensive simulation samples would be obtained at random locations…

We report on progress in algorithms for iterative phase retrieval. The theory of convex optimization is used to develop and to gain insight into counterparts for the nonconvex problem of phase retrieval. We propose a relaxation of averaged…

Surrogate models are used to alleviate the computational burden in engineering tasks, which require the repeated evaluation of computationally demanding models of physical systems, such as the efficient propagation of uncertainties. For…

We investigate in this paper an alternative method to simulation based recursive importance sampling procedure to estimate the optimal change of measure for Monte Carlo simulations. We propose an algorithm which combines (vector and…

In the problem of matrix compressed sensing we aim to recover a low-rank matrix from few of its element-wise linear projections. In this contribution we analyze the asymptotic performance of a Bayes-optimal inference procedure for a model…