相关论文: Revisiting the Misspecified Cram\'er-Rao Bound

This is a tutorial aimed at illustrating some recent developments in quantum parameter estimation beyond the Cram\`er-Rao bound, as well as their applications in quantum metrology. Our starting point is the observation that there are…

Seeking the available precision limit of unknown parameters is a significant task in quantum parameter estimation. One often resorts to the widely utilized quantum Cramer-Rao bound (QCRB) based on unbiased estimators to finish this task.…

Although neural networks are powerful function approximators, the underlying modelling assumptions ultimately define the likelihood and thus the hypothesis class they are parameterizing. In classification, these assumptions are minimal as…

We study the asymptotic theory of misspecified models for diffusion processes with noisy nonsynchronous observations. Unlike with correctly specified models, the original maximum-likelihood-type estimator has an asymptotic bias under the…

Model-based reinforcement learning (MBRL) has been shown to be a powerful framework for data-efficiently learning control of continuous tasks. Recent work in MBRL has mostly focused on using more advanced function approximators and planning…

Empirical research in many social disciplines involves constructs that are not directly observable, such as behaviors. To model them, constructs must be operationalized using their relations with indicators. Structural equation modeling…

We propose an adversarial evaluation framework for sensitive feature inference based on minimum mean-squared error (MMSE) estimation with a finite sample size and linear predictive models. Our approach establishes theoretical lower bounds…

With model trustworthiness being crucial for sensitive real-world applications, practitioners are putting more and more focus on improving the uncertainty calibration of deep neural networks. Calibration errors are designed to quantify the…

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…

The theoretical foundation of quantum sensing is rooted in the Cram\'er-Rao formalism, which establishes quantitative precision bounds for a given quantum probe. In many practical scenarios, where more than one parameter is unknown, the…

We consider distributed estimation of a Gaussian source in a heterogenous bandwidth constrained sensor network, where the source is corrupted by independent multiplicative and additive observation noises, with incomplete statistical…

Nested error regression models are commonly used to incorporate observational unit specific auxiliary variables to improve small area estimates. When the mean structure of this model is misspecified, there is generally an increase in the…

We study the estimation error of constrained M-estimators, and derive explicit upper bounds on the expected estimation error determined by the Gaussian width of the constraint set. Both of the cases where the true parameter is on the…

In this paper, we derive for the first time the exact Cramer-Rao bounds (CRBs) on semi-blind channel estimation for amplify-and-forward two-way relay networks. The bounds cover a wide range of modulation schemes that satisfy a certain…

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…

This paper focusses on the sparse estimation in the situation where both the the sensing matrix and the measurement vector are corrupted by additive Gaussian noises. The performance bound of sparse estimation is analyzed and discussed in…

Artificial neural networks have become important tools to harness the complexity of disordered or random photonic systems. Recent applications include the recovery of information from light that has been scrambled during propagation through…

We study behavior of the restricted maximum likelihood (REML) estimator under a misspecified linear mixed model (LMM) that has received much attention in recent gnome-wide association studies. The asymptotic analysis establishes consistency…

We study the problem of the identification of m arms with largest means under a fixed error rate $\delta$ (fixed-confidence Top-m identification), for misspecified linear bandit models. This problem is motivated by practical applications,…

Machine learning (ML) models are typically optimized for their accuracy on a given dataset. However, this predictive criterion rarely captures all desirable properties of a model, in particular how well it matches a domain expert's…