Related papers: Binary Discrimination in Quantum Systems via Hypot…
We investigate a state discrimination problem in operationally the most general framework to use a probability, including both classical, quantum theories, and more. In this wide framework, introducing closely related family of ensembles…
This paper extends the work of Clarke [1] on the Bayesian foundations of the biomagnetic inverse problem. It derives expressions for the expectation and variance of the a posteriori source current probability distribution given a prior…
A Bayesian approach is developed to determine quantum mechanical potentials from empirical data. Bayesian methods, combining empirical measurements and "a priori" information, provide flexible tools for such empirical learning problems. The…
Some statistical models are specified via a data generating process for which the likelihood function cannot be computed in closed form. Standard likelihood-based inference is then not feasible but the model parameters can be inferred by…
This paper proposes the use of causal modeling to detect and mitigate algorithmic bias. We provide a brief description of causal modeling and a general overview of our approach. We then use the Adult dataset, which is available for download…
This paper investigates symmetric composite binary quantum hypothesis testing (QHT), where the goal is to determine which of two uncertainty sets contains an unknown quantum state. While asymptotic error exponents for this problem are…
Accurate comparisons between theoretical models and experimental data are critical for scientific progress. However, inferred physical model parameters can vary significantly with the chosen physics model, highlighting the importance of…
Several recent works encourage the use of a Bayesian framework when assessing performance and fairness metrics of a classification algorithm in a supervised setting. We propose the Uncertainty Matters (UM) framework that generalizes a…
Machine learning models are central to people's lives and impact society in ways as fundamental as determining how people access information. The gravity of these models imparts a responsibility to model developers to ensure that they are…
In the task of discriminating between nonorthogonal quantum states from multiple copies, the key parameters are the error probability and the resources (number of copies) used. Previous studies have considered the task of minimizing the…
Bayesian clustering methods have the widely touted advantage of providing a probabilistic characterization of uncertainty in clustering through the posterior distribution. An amazing variety of priors and likelihoods have been proposed for…
Bayesian model comparison (BMC) offers a principled probabilistic approach to study and rank competing models. In standard BMC, we construct a discrete probability distribution over the set of possible models, conditional on the observed…
Precision control of a quantum system requires accurate determination of the effective system Hamiltonian. We develop a method for estimating the Hamiltonian parameters for some unknown two-state system and providing uncertainty bounds on…
In their seminal 1990 paper, Wasserman and Kadane establish an upper bound for the Bayes' posterior probability of a measurable set $A$, when the prior lies in a class of probability measures $\mathcal{P}$ and the likelihood is precise.…
In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper we show that, despite being prescribed by a fundamental…
This paper considers multiple binary hypothesis tests with adaptive allocation of sensing resources from a shared budget over a small number of stages. A Bayesian formulation is provided for the multistage allocation problem of minimizing…
An understanding of quantum theory in terms of new, underlying descriptions capable of explaining the existence of non-classical correlations, non-commutativity of measurements and other unique and counter-intuitive phenomena remains still…
Being able to reliably assess not only the \emph{accuracy} but also the \emph{uncertainty} of models' predictions is an important endeavour in modern machine learning. Even if the model generating the data and labels is known, computing the…
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…
The duality principle, a cornerstone of quantum mechanics, limits the coexistence of wave and particle behaviours of quantum systems. This limitation takes a quantitative form when applied to the visibility $\mathcal V$ and predictability…