Related papers: The radius of statistical efficiency
A statistical characterization of the fundamental performance bounds of an intelligent reflective surface (IRS) intended for aiding wireless communications is presented. To this end, the outage probability, average symbol error probability,…
Recommender Systems (RS) shape the filtering and curation of online content, yet we have limited understanding of how predictable their recommendation outputs are. We propose data-driven metrics that quantify the predictability of…
Sparse regression is frequently employed in diverse scientific settings as a feature selection method. A pervasive aspect of scientific data that hampers both feature selection and estimation is the presence of strong correlations between…
The Robust Effect Size Index (RESI) is a recently proposed standardized effect size to quantify association strength across models. However, its confidence interval construction has relied on computationally intensive bootstrap procedures.…
Traditional Relative Efficiency (RE), based solely on variance, has limitations in evaluating estimator performance, particularly in planned missing data designs. We introduce Bhirkuti's Relative Efficiency (BRE), a novel metric that…
The recently developed matrix based Renyi's entropy enables measurement of information in data simply using the eigenspectrum of symmetric positive semi definite (PSD) matrices in reproducing kernel Hilbert space, without estimation of the…
We provide a novel -- and to the best of our knowledge, the first -- algorithm for high dimensional sparse regression with constant fraction of corruptions in explanatory and/or response variables. Our algorithm recovers the true sparse…
There are many practical applications based on the Least Square Error (LSE) approximation. It is based on a square error minimization 'on a vertical' axis. The LSE method is simple and easy also for analytical purposes. However, if data…
Rotation averaging (RA) is a fundamental problem in robotics and computer vision. In RA, the goal is to estimate a set of $N$ unknown orientations $R_{1}, ..., R_{N} \in SO(3)$, given noisy measurements $R_{ij} \sim R^{-1}_{i} R_{j}$ of a…
To address the challenges of reliable statistical inference in high-dimensional models, we introduce the Synthetic-data Regularized Estimator (SRE). Unlike traditional regularization methods, the SRE regularizes the complex target model via…
Super-resolution estimation is the problem of recovering a stream of spikes (point sources) from the noisy observation of a few numbers of its first trigonometric moments. The performance of super-resolution is recognized to be intimately…
This special volume of Statistical Sciences presents some innovative, if not provocative, ideas in the area of reliability, or perhaps more appropriately named, integrated system assessment. In this age of exponential growth in science,…
Regular variation provides a convenient theoretical framework to study large events. In the multivariate setting, the dependence structure of the positive extremes is characterized by a measure - the spectral measure - defined on the…
Adversarial robustness has become a topic of growing interest in machine learning since it was observed that neural networks tend to be brittle. We propose an information-geometric formulation of adversarial defense and introduce FIRE, a…
Inspired by the recent work [28] on the statistical robustness of empirical risks in reproducing kernel Hilbert space (RKHS) where the training data are potentially perturbed or even corrupted, we take a step further in this paper to…
In recent years, sparse principal component analysis has emerged as an extremely popular dimension reduction technique for high-dimensional data. The theoretical challenge, in the simplest case, is to estimate the leading eigenvector of a…
Density ratio estimation (DRE) is a useful tool for quantifying discrepancies between probability distributions, but existing approaches often involve a trade-off between estimation quality and computational efficiency. Classical direct DRE…
We consider distributed statistical optimization in one-shot setting, where there are $m$ machines each observing $n$ i.i.d. samples. Based on its observed samples, each machine sends a $B$-bit-long message to a server. The server then…
Training machine learning and statistical models often involves optimizing a data-driven risk criterion. The risk is usually computed with respect to the empirical data distribution, but this may result in poor and unstable out-of-sample…
The wave speed of a stochastic wave equation driven by Riesz noise on the unbounded multidimensional spatial domain is estimated based on discrete measurements. Central limit theorems for second-order variations of the observations in…