Related papers: The radius of statistical efficiency
This paper discusses the properties of certain risk estimators recently proposed to choose regularization parameters in ill-posed problems. A simple approach is Stein's unbiased risk estimator (SURE), which estimates the risk in the data…
A fundamental challenge in interactive learning and decision making, ranging from bandit problems to reinforcement learning, is to provide sample-efficient, adaptive learning algorithms that achieve near-optimal regret. This question is…
Understanding when learning is statistically possible yet computationally hard is a central challenge in high-dimensional statistics. In this work, we investigate this question in the context of single- and multi-index models, classes of…
This study modifies the Russell graph measure of efficiency to find the closest target from the assessed decision-making unit to the efficient frontier of an empirical production possibility set using an extended facet approach. The closest…
Prediction models are often employed in estimating parameters of optimization models. Despite the fact that in an end-to-end view, the real goal is to achieve good optimization performance, the prediction performance is measured on its own.…
The expectation-maximization (EM) algorithm is an iterative computational method to calculate the maximum likelihood estimators (MLEs) from the sample data. It converts a complicated one-time calculation for the MLE of the incomplete data…
RIPE is a novel deterministic and easily understandable prediction algorithm developed for continuous and discrete ordered data. It infers a model, from a sample, to predict and to explain a real variable $Y$ given an input variable $X \in…
This paper addresses the issues of conservativeness and computational complexity of probabilistic robustness analysis. We solve both issues by defining a new sampling strategy and robustness measure. The new measure is shown to be much less…
In many instances, the application of approximate Bayesian methods is hampered by two practical features: 1) the requirement to project the data down to low-dimensional summary, including the choice of this projection, which ultimately…
The unavoidable interaction between a quantum system and the external noisy environment can be mimicked by a sequence of stochastic measurements whose outcomes are neglected. Here we investigate how this stochasticity is reflected in the…
Functional data analysis is a fast evolving branch of modern statistics and the functional linear model has become popular in recent years. However, most estimation methods for this model rely on generalized least squares procedures and…
The approximation ratio has become one of the dominant measures in mechanism design problems. In light of analysis of algorithms, we define the \emph{smoothed approximation ratio} to compare the performance of the optimal mechanism and a…
In both observational data and randomized control trials, researchers select statistical models to articulate how the outcome of interest varies with combinations of observable covariates. Choosing a model that is too simple can obfuscate…
Circular variables that represent directions or periodic observations arise in many fields, such as biology and environmental sciences. An important issue when dealing with circular data is how to estimate their dispersion robustly,…
The trade-off between robustness and accuracy has been widely studied in the adversarial literature. Although still controversial, the prevailing view is that this trade-off is inherent, either empirically or theoretically. Thus, we dig for…
We study the problem of parameter estimation in time series stemming from general stochastic processes, where the outcomes may exhibit arbitrary temporal correlations. In particular, we address the question of how much Fisher information is…
In this chapter, using statistical physics methods, asymptotic closed-form expressions for the mean and variance of the mutual information for a multi-antenna transmitter-receiver pair in the presence of multiple Reconfigurable Intelligent…
Variance and Fisher information are ingredients of the Cramer-Rao inequality. We regard Fisher information as a Riemannian metric on a quantum statistical manifold and choose monotonicity under coarse graining as the fundamental property of…
We study a natural extension of classical empirical risk minimization, where the hypothesis space is a random subspace of a given space. In particular, we consider possibly data dependent subspaces spanned by a random subset of the data,…
This paper proposes an estimation framework to assess the performance of sorting over perturbed/noisy data. In particular, the recovering accuracy is measured in terms of Minimum Mean Square Error (MMSE) between the values of the sorting…