Related papers: Generalized Bhattacharyya and Chernoff upper bound…

Chernoff coefficient is an upper bound of Bayes error probability in classification problem. In this paper, we will develop sharp Chernoff type bound on Bayes error probability. The new bound is not only an upper bound but also a lower…

Chernoff information upper bounds the probability of error of the optimal Bayesian decision rule for $2$-class classification problems. However, it turns out that in practice the Chernoff bound is hard to calculate or even approximate. In…

This paper provides a general technique for lower bounding the Bayes risk of statistical estimation, applicable to arbitrary loss functions and arbitrary prior distributions. A lower bound on the Bayes risk not only serves as a lower bound…

We consider the problem of estimating the probability of error in multi-hypothesis testing when MAP criterion is used. This probability, which is also known as the Bayes risk is an important measure in many communication and information…

Empirically, the PAC-Bayesian analysis is known to produce tight risk bounds for practical machine learning algorithms. However, in its naive form, it can only deal with stochastic predictors while such predictors are rarely used and…

Bayesian inference typically requires the computation of an approximation to the posterior distribution. An important requirement for an approximate Bayesian inference algorithm is to output high-accuracy posterior mean and uncertainty…

PAC generalization bounds on the risk, when expressed in terms of the expected loss, are often insufficient to capture imbalances between subgroups in the data. To overcome this limitation, we introduce a new family of risk measures, called…

We show how to compute lower bounds for the supremum Bayes error if the class-conditional distributions must satisfy moment constraints, where the supremum is with respect to the unknown class-conditional distributions. Our approach makes…

We identify the critical deviation scale governing Bayesian evidence accumulation in regular parametric testing. Under integrated Bayes risk with zero-one loss, the risk-optimal rejection boundary lies in a moderate deviation regime, with a…

We give some results relating asymptotic characterisations of maximum entropy probability measures to characterisations of Bayes optimal classifiers. Our main theorems show that maximum entropy is a universally Bayes optimal decision rule…

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…

The Bayesian posterior minimizes the "inferential risk" which itself bounds the "predictive risk". This bound is tight when the likelihood and prior are well-specified. However since misspecification induces a gap, the Bayesian posterior…

We develop a unified framework for goodness-of-fit (GOF) testing through the lens of Bayes risk. Classical GOF procedures are commonly calibrated either at fixed significance level (CLT scale) or through exponential error exponents (LDP…

This work discusses how to derive upper bounds for the expected generalisation error of supervised learning algorithms by means of the chaining technique. By developing a general theoretical framework, we establish a duality between…

This paper generalizes an important result from the PAC-Bayesian literature for binary classification to the case of ensemble methods for structured outputs. We prove a generic version of the \Cbound, an upper bound over the risk of models…

We introduce a modified version of the excess risk, which can be used to obtain tighter, fast-rate PAC-Bayesian generalisation bounds. This modified excess risk leverages information about the relative hardness of data examples to reduce…

Adversarial examples pose a security threat to many critical systems built on neural networks. Given that deterministic robustness often comes with significantly reduced accuracy, probabilistic robustness (i.e., the probability of having…

The vast majority of statistical theory on binary classification characterizes performance in terms of accuracy. However, accuracy is known in many cases to poorly reflect the practical consequences of classification error, most famously in…

In this work, we propose a PAC-Bayes bound for the generalization risk of the Gibbs classifier in the multi-class classification framework. The novelty of our work is the critical use of the confusion matrix of a classifier as an error…

This paper focuses on parameter estimation and introduces a new method for lower bounding the Bayesian risk. The method allows for the use of virtually \emph{any} information measure, including R\'enyi's $\alpha$, $\varphi$-Divergences, and…