Related papers: Sharp bounds on aggregate expert error

In this article, a general problem of sequential statistical inference for general discrete-time stochastic processes is considered. The problem is to minimize an average sample number given that Bayesian risk due to incorrect decision does…

The problem of sequential probability forecasting is considered in the most general setting: a model set C is given, and it is required to predict as well as possible if any of the measures (environments) in C is chosen to generate the…

Current PAC-Bayes generalisation bounds are restricted to scalar metrics of performance, such as the loss or error rate. However, one ideally wants more information-rich certificates that control the entire distribution of possible…

Gaussian empirical Bayes methods usually maintain a precision independence assumption: The unknown parameters of interest are independent from the known standard errors of the estimates. This assumption is often theoretically questionable…

Worst-case bounds on the expected shortfall risk given only limited information on the distribution of the random variables has been studied extensively in the literature. In this paper, we develop a new worst-case bound on the expected…

We derive an asymptotic lower bound on the Bayes risk when N identical quantum systems whose state depends on a vector of unknown parameters are jointly measured in an arbitrary way and the parameters of interest estimated on the basis of…

Bounding causal effects analytically, rather than numerically, is appealing for its interpretability and conceptual clarity. Existing sharp methods rely on optimization-based approaches such as the Balke-Pearl framework, whose computational…

In the sparse normal means model, coverage of adaptive Bayesian posterior credible sets associated to spike and slab prior distributions is considered. The key sparsity hyperparameter is calibrated via marginal maximum likelihood empirical…

Selective classification is a powerful tool for automated decision-making in high-risk scenarios, allowing classifiers to act only when confident and abstain when uncertainty is high. Given a target accuracy, our goal is to minimize…

We consider the problem of unambiguous (error-free) discrimination of N linearly independent pure quantum states with prior probabilities, where the goal is to find a measurement that maximizes the average probability of success. We derive…

A new lower bound on the error probability of maximum likelihood decoding of a binary code on a binary symmetric channel was proved in Barg and McGregor (2004, cs.IT/0407011). It was observed in that paper that this bound leads to a new…

Bayesian classification labels observations based on given prior information, namely class-a priori and class-conditional probabilities. Bayes' risk is the minimum expected classification cost that is achieved by the Bayes' test, the…

Likelihood-free approaches are appealing for performing inference on complex dependence models, either because it is not possible to formulate a likelihood function, or its evaluation is very computationally costly. This is the case for…

We present bounds on the maximal gain of adaptive and randomized algorithms over non-adaptive, deterministic ones for approximating linear operators on convex sets. If the sets are additionally symmetric, then our results are optimal. For…

The support recovery problem consists of determining a sparse subset of a set of variables that is relevant in generating a set of observations, and arises in a diverse range of settings such as compressive sensing, and subset selection in…

Let $X_1,X_2,...,X_n$ be a sequence of independent or locally dependent random variables taking values in $\mathbb{Z}_+$. In this paper, we derive sharp bounds, via a new probabilistic method, for the total variation distance between the…

The article addresses a long-standing open problem on the justification of using variational Bayes methods for parameter estimation. We provide general conditions for obtaining optimal risk bounds for point estimates acquired from…

We analyze boundedly rational updating from aggregate statistics in a model with binary actions and binary states. Agents each take an irreversible action in sequence after observing the unordered set of previous actions. Each agent first…

In order to improve forecasts, a decisionmaker often combines probabilities given by various sources, such as human experts and machine learning classifiers. When few training data are available, aggregation can be improved by incorporating…

The Bayesian approach has proved to be a coherent approach to handle ill posed Inverse problems. However, the Bayesian calculations need either an optimization or an integral calculation. The maximum a posteriori (MAP) estimation requires…