Related papers: Maximum Fidelity

We consider the problem of estimating the population probability distribution given a finite set of multivariate samples, using the maximum entropy approach. In strict keeping with Jaynes' original definition, our precise formulation of the…

We study the empirical likelihood approach to construct confidence intervals for the optimal value and the optimality gap of a given solution, henceforth quantify the statistical uncertainty of sample average approximation, for optimization…

Prediction, where observed data is used to quantify uncertainty about a future observation, is a fundamental problem in statistics. Prediction sets with coverage probability guarantees are a common solution, but these do not provide…

In system analysis and design optimization, multiple computational models are typically available to represent a given physical system. These models can be broadly classified as high-fidelity models, which provide highly accurate…

This manuscript studies a general approach to construct confidence sets for the solution of stochastic optimization, rendering empirical risk minimization as special cases. Statistical inference for stochastic optimization poses significant…

Estimating the fidelity with a target state is important in quantum information tasks. Many fidelity estimation techniques present a suitable measurement scheme to perform the estimation. In contrast, we present techniques that allow the…

Statistical modeling plays a fundamental role in understanding the underlying mechanism of massive data (statistical inference) and predicting the future (statistical prediction). Although all models are wrong, researchers try their best to…

The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible constrained to match empirical data, for instance, feature expectations. We seek to generalize…

Conformal prediction is a distribution-free uncertainty quantification method that has gained popularity in the machine learning community due to its finite-sample guarantees and ease of use. Its most common variant, dubbed split conformal…

Existing approaches to model uncertainty typically either compare models using a quantitative model selection criterion or evaluate posterior model probabilities having set a prior. In this paper, we propose an alternative strategy which…

In statistical inference, uncertainty is unknown and all models are wrong. That is to say, a person who makes a statistical model and a prior distribution is simultaneously aware that both are fictional candidates. To study such cases,…

A great deal of effort has been devoted to reducing the risk of spurious scientific discoveries, from the use of sophisticated validation techniques, to deep statistical methods for controlling the false discovery rate in multiple…

In many fairness and distribution robustness problems, one has access to labeled data from multiple source distributions yet the test data may come from an arbitrary member or a mixture of them. We study the problem of constructing a…

In the past decades, most work in the area of data analysis and machine learning was focused on optimizing predictive models and getting better results than what was possible with existing models. To what extent the metrics with which such…

Conformal prediction is a framework for providing prediction intervals with distribution-free validity, guaranteeing predictive coverage for data drawn from any distribution. Its two main variants are full conformal prediction and split…

Predictive inference is a fundamental task in statistics, traditionally addressed using parametric assumptions about the data distribution and detailed analyses of how models learn from data. In recent years, conformal prediction has…

Likelihood-free Bayesian inference algorithms are popular methods for calibrating the parameters of complex, stochastic models, required when the likelihood of the observed data is intractable. These algorithms characteristically rely…

Estimations of physical parameters using data usually involve non-uniform experimental efficiencies. In this article, a method of maximum likelihood fit is introduced using the efficiency as a weight, while the probability distribution…

Belief functions are a powerful and popular framework for the mathematical characterisation of uncertainty, in particular in situations in which lack of data renders learning a probability distribution for the problem impractical. The first…

Independence testing is a fundamental problem in statistical inference: given samples from a joint distribution $p$ over multiple random variables, the goal is to determine whether $p$ is a product distribution or is $\epsilon$-far from all…