Related papers: A Cram\'er-Rao Type Bound for Bayesian Risk with B…

Frequentist and Bayesian phase estimation strategies lead to conceptually different results on the state of knowledge about the true value of the phase shift. We compare the two frameworks and their sensitivity bounds to the estimation of…

We establish a nonasymptotic lower bound on the $L_2$ minimax risk for a class of generalized linear models. It is further shown that the minimax risk for the canonical linear model matches this lower bound up to a universal constant.…

We establish a Cram\'er-type moderate deviation theorem for double-index permutation statistics (DIPS). To the best of our knowledge, previous results only provided Berry-Esseen type bounds for DIPS, which cannot yield moderate deviation…

In this paper, we extend the transfer learning classification framework from regression function-based methods to decision rules. We propose a novel methodology for modeling posterior drift through Bayes decision rules. By exploiting the…

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,…

Recently, a Wasserstein analogue of the Cramer--Rao inequality has been developed using the Wasserstein information matrix (Otto metric). This inequality provides a lower bound on the Wasserstein variance of an estimator, which quantifies…

We give improved constants for data dependent and variance sensitive confidence bounds, called empirical Bernstein bounds, and extend these inequalities to hold uniformly over classes of functionswhose growth function is polynomial in the…

Existing guarantees in terms of rigorous upper bounds on the generalization error for the original random forest algorithm, one of the most frequently used machine learning methods, are unsatisfying. We discuss and evaluate various…

Unbiased estimators are introduced for averaged Bregman divergences which generalize Stein's Unbiased (Predictive) Risk Estimator, and the minimization of these estimators is proposed as a regularization parameter selection method for…

We propose a unified framework for global-local regularization that bridges the gap between classical techniques -- such as ridge regression and the nonnegative garotte -- and modern Bayesian hierarchical modeling. By estimating local…

Current approaches in approximate inference for Bayesian neural networks minimise the Kullback-Leibler divergence to approximate the true posterior over the weights. However, this approximation is without knowledge of the final application,…

Prediction error is critical to assessing the performance of statistical methods and selecting statistical models. We propose the cross-validation and approximated cross-validation methods for estimating prediction error under a broad…

In this paper, we derive a PAC-Bayes bound on the generalisation gap, in a supervised time-series setting for a special class of discrete-time non-linear dynamical systems. This class includes stable recurrent neural networks (RNN), and the…

We introduce a novel family of distances, called the chord gap divergences, that generalizes the Jensen divergences (also called the Burbea-Rao distances), and study its properties. It follows a generalization of the celebrated statistical…

Classical PAC generalization bounds on the prediction risk of a classifier are insufficient to provide theoretical guarantees on fairness when the goal is to learn models balancing predictive risk and fairness constraints. We propose a…

Estimation under model misspecification arises in many signal processing problems, where the assumed observation model deviates from the true data-generating mechanism due to errors or simplifications. The misspecified Cram\'er-Rao bound…

A Cramer-Rao bound (CRB) for semi-blind channel estimators in redundant block transmission systems is derived. The derived CRB is valid for any system adopting a full-rank linear redundant precoder, including the popular cyclic-prefixed…

One of the tasks of the Bayesian inverse problem is to find a good estimate based on the posterior probability density. The most common point estimators are the conditional mean (CM) and maximum a posteriori (MAP) estimates, which…

Robust Bayesian analysis has been mainly devoted to detecting and measuring robustness w.r.t. the prior distribution. Many contributions in the literature aim to define suitable classes of priors which allow the computation of variations of…

ReRecent studies in machine learning are based on models in which parameters or state variables are bounded restricted. These restrictions are from prior information to ensure the validity of scientific theories or structural consistency…