Related papers: Efficient Unbiased Sparsification
In many semiparametric models that are parameterized by two types of parameters---a Euclidean parameter of interest and an infinite-dimensional nuisance parameter---the two parameters are bundled together, that is, the nuisance parameter is…
Linear regression is a popular machine learning approach to learn and predict real valued outputs or dependent variables from independent variables or features. In many real world problems, its beneficial to perform sparse linear regression…
Standard practice obtains an unbiased variance estimator by dividing by $N-1$ rather than $N$. Yet if only half the data are used to compute the mean, dividing by $N$ can still yield an unbiased estimator. We show that an alternative mean…
For nonparametric regression with one-sided errors and a boundary curve model for Poisson point processes we consider the problem of efficient estimation for linear functionals. The minimax optimal rate is obtained by an unbiased estimation…
We propose a novel sparse sliced inverse regression method based on random projections in a large $p$ small $n$ setting. Embedded in a generalized eigenvalue framework, the proposed approach finally reduces to parallel execution of…
Unsupervised feature selection has been always attracting research attention in the communities of machine learning and data mining for decades. In this paper, we propose an unsupervised feature selection method seeking a feature…
Asymptotic lower bounds for estimation play a fundamental role in assessing the quality of statistical procedures. In this paper we propose a framework for obtaining semi-parametric efficiency bounds for sparse high-dimensional models,…
Regularization is a common tool in variational inverse problems to impose assumptions on the parameters of the problem. One such assumption is sparsity, which is commonly promoted using lasso and total variation-like regularization.…
Consider a Gaussian memoryless multiple source with $m$ components with joint probability distribution known only to lie in a given class of distributions. A subset of $k \leq m$ components are sampled and compressed with the objective of…
Dataset bias is a critical challenge in machine learning since it often leads to a negative impact on a model due to the unintended decision rules captured by spurious correlations. Although existing works often handle this issue based on…
In semi-supervised learning, the prevailing understanding suggests that observing additional unlabeled samples improves estimation accuracy for linear parameters only in the case of model misspecification. In this work, we challenge such a…
The estimation of a sparse vector in the linear model is a fundamental problem in signal processing, statistics, and compressive sensing. This paper establishes a lower bound on the mean-squared error, which holds regardless of the…
Given an n x n matrix A, we present a simple, element-wise sparsification algorithm that zeroes out all sufficiently small elements of A and then retains some of the remaining elements with probabilities proportional to the square of their…
We present an in-depth analysis of the sources of variance in state-of-the-art unbiased volumetric transmittance estimators, and propose several new methods for improving their efficiency. These combine to produce a single estimator that is…
Unitary errors, such as those arising from fault-tolerant compilation of quantum algorithms, systematically bias observable estimates. Correcting this bias typically requires additional resources, such as an increased number of non-Clifford…
We study a simple model of unsupervised learning where the single symmetry breaking vector has binary components $\pm 1$. We calculate exactly the Bayes-optimal performance of an estimator which is required to lie in the same discrete…
In this paper we study von Neumann un-biasing normalisation for ideal and real quantum random number generators, operating on finite strings or infinite bit sequences. In the ideal cases one can obtain the desired un-biasing. This relies…
We propose a novel modular debiasing technique applicable to any discrete random source, addressing the fundamental challenge of reliably extracting high-quality randomness from inherently imperfect physical processes. The method involves…
We consider statistical inference under a semi-supervised setting where we have access to both a labeled dataset consisting of pairs $\{X_i, Y_i \}_{i=1}^n$ and an unlabeled dataset $\{ X_i \}_{i=n+1}^{n+N}$. We ask the question: under what…
Given a set of vectors (the data) in a Hilbert space H, we prove the existence of an optimal collection of subspaces minimizing the sum of the square of the distances between each vector and its closest subspace in the collection. This…