Related papers: Unbiased Bregman-Risk Estimators: Application to R…
Linear inverse problems are ubiquitous. Often the measurements do not follow a Gaussian distribution. Additionally, a model matrix with a large condition number can complicate the problem further by making it ill-posed. In this case, the…
Model estimates obtained from traditional subspace identification methods may be subject to significant variance. This elevated variance is aggravated in the cases of large models or of a limited sample size. Common solutions to reduce the…
We study the variational inference problem of minimizing a regularized R\'enyi divergence over an exponential family. We propose to solve this problem with a Bregman proximal gradient algorithm. We propose a sampling-based algorithm to…
This paper is concerned with general nonlinear regression models where the predictor variables are subject to Berkson-type measurement errors. The measurement errors are assumed to have a general parametric distribution, which is not…
Shrinkage estimation usually reduces variance at the cost of bias. But when we care only about some parameters of a model, I show that we can reduce variance without incurring bias if we have additional information about the distribution of…
In this work we consider the unbiased estimation of expectations w.r.t.~probability measures that have non-negative Lebesgue density, and which are known point-wise up-to a normalizing constant. We focus upon developing an unbiased method…
Many common estimators in machine learning and causal inference are linear smoothers, where the prediction is a weighted average of the training outcomes. Some estimators, such as ordinary least squares and kernel ridge regression, allow…
The purpose of this article is to develop a general parametric estimation theory that allows the derivation of the limit distribution of estimators in non-regular models where the true parameter value may lie on the boundary of the…
This paper discusses basic results and recent developments on variational regularization methods, as developed for inverse problems. In a typical setup we review basic properties needed to obtain a convergent regularization scheme and…
We consider a model selection estimator of the covariance of a random process. Using the Unbiased Risk Estimation (URE) method, we build an estimator of the risk which allows to select an estimator in a collection of model. Then, we present…
We propose a general framework for regularization in M-estimation problems under time dependent (absolutely regular-mixing) data which encompasses many of the existing estimators. We derive non-asymptotic concentration bounds for the…
Several problems in statistics involve the combination of high-variance unbiased estimators with low-variance estimators that are only unbiased under strong assumptions. A notable example is the estimation of causal effects while combining…
In an increasing number of applications, it is of interest to recover an approximately low-rank data matrix from noisy observations. This paper develops an unbiased risk estimate---holding in a Gaussian model---for any spectral estimator…
The maximum likelihood principle is widely used in statistics, and the associated estimators often display good properties. indeed maximum likelihood estimators are guaranteed to be asymptotically efficient under mild conditions. However in…
Sparse model selection is ubiquitous from linear regression to graphical models where regularization paths, as a family of estimators upon the regularization parameter varying, are computed when the regularization parameter is unknown or…
Re-randomization has gained popularity as a tool for experiment-based causal inference due to its superior covariate balance and statistical efficiency compared to classic randomized experiments. However, the basic re-randomization method,…
This paper focuses on the Bregman divergence defined by the reciprocal function, called the inverse divergence. For the loss function defined by the monotonically increasing function $f$ and inverse divergence, the conditions for the…
Regularization method and Bayesian inverse method are two dominating ways for solving inverse problems generated from various fields, e.g., seismic exploration and medical imaging. The two methods are related with each other by the MAP…
Motivated by the proliferation of observational datasets and the need to integrate non-randomized evidence with randomized controlled trials, causal inference researchers have recently proposed several new methodologies for combining biased…
Calibration weighting is a fundamental technique in survey sampling and data integration for incorporating auxiliary information and improving efficiency of estimators. Classical calibration methods are typically formulated through distance…