Related papers: Classes of lower bounds on outage error probabilit…

We address the problem of classification when data are collected from two samples with measurement errors. This problem turns to be an inverse problem and requires a specific treatment. In this context, we investigate the minimax rates of…

Recent developments on deep learning established some theoretical properties of deep neural networks estimators. However, most of the existing works on this topic are restricted to bounded loss functions or (sub)-Gaussian or bounded input.…

In parametric Bayesian learning, a prior is assumed on the parameter $W$ which determines the distribution of samples. In this setting, Minimum Excess Risk (MER) is defined as the difference between the minimum expected loss achievable when…

Bayesian approach for quantum parameter estimation has gained a renewed interest from practical applications of quantum estimation theory. Recently, a lower bound, called the Bayesian Nagaoka-Hayashi bound for the Bayes risk in quantum…

The existing upper and lower bounds between entropy and error are mostly derived through an inequality means without linking to joint distributions. In fact, from either theoretical or application viewpoint, there exists a need to achieve a…

This paper focuses on boosting the performance of small cell networks (SCNs) by integrating multiple-input multiple-output (MIMO) and non-orthogonal multiple access (NOMA) in consideration of imperfect channel-state information (CSI). The…

Among the many ways to model signals, a recent approach that draws considerable attention is sparse representation modeling. In this model, the signal is assumed to be generated as a random linear combination of a few atoms from a…

As the complexity of control systems increases, the need for systematic methods to guarantee their efficacy grows as well. However, direct testing of these systems is oftentimes costly, difficult, or impractical. As a result, the test and…

In this work we investigate to which extent one can recover class probabilities within the empirical risk minimization (ERM) paradigm. The main aim of our paper is to extend existing results and emphasize the tight relations between…

This paper considers the quantification of the prediction performance in Gaussian process regression. The standard approach is to base the prediction error bars on the theoretical predictive variance, which is a lower bound on the mean…

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…

We consider statistical learning question for $\psi$-weakly dependent processes, that unifies a large class of weak dependence conditions such as mixing, association,$\cdots$ The consistency of the empirical risk minimization algorithm is…

A fairly general class of Bayesian "large-error" lower bounds of the Weiss-Weinstein family, essentially free from regularity conditions on the probability density functions support, and for which a limiting form yields a generalized…

We address the problem of learning to benchmark the best achievable classifier performance. In this problem the objective is to establish statistically consistent estimates of the Bayes misclassification error rate without having to learn a…

Exact lower and upper bounds on the best possible misclassification probability for a finite number of classes are obtained in terms of the total variation norms of the differences between the sub-distributions over the classes. These…

We consider least squares estimation in a general nonparametric regression model. The rate of convergence of the least squares estimator (LSE) for the unknown regression function is well studied when the errors are sub-Gaussian. We find…

For a coherent, binary system made up of binary elements, the exact failure probability requires knowledge of statistical dependence of all orders among the minimal cut sets. Since dependence among the cut sets beyond the second order is…

The present manuscript is concerned with component-wise estimation of the positive power of ordered restricted standard deviation of two normal populations with certain restrictions on the means. We propose several improved estimators under…

In parameter estimation, assumptions about the model are typically considered which allow us to build optimal estimation methods under many statistical senses. However, it is usually the case where such models are inaccurately known or not…

In the context of supervised learning, meta learning uses features, metadata and other information to learn about the difficulty, behavior, or composition of the problem. Using this knowledge can be useful to contextualize classifier…