English
Related papers

Related papers: Bayesian Logarithmic Derivative Type Lower Bounds …

200 papers

Bayesian error analysis paves the way to the construction of credible and plausible error regions for a point estimator obtained from a given dataset. We introduce the concept of region accuracy for error regions (a generalization of the…

Quantum Physics · Physics 2019-07-15 Changhun Oh , Yong Siah Teo , Hyunseok Jeong

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…

Statistics Theory · Mathematics 2026-03-23 Jyotishka Datta , Nicholas G. Polson , Vadim Sokolov , Daniel Zantedeschi

We propose a lower bound on the log marginal likelihood of Gaussian process regression models that can be computed without matrix factorisation of the full kernel matrix. We show that approximate maximum likelihood learning of model…

Machine Learning · Statistics 2021-02-17 Artem Artemev , David R. Burt , Mark van der Wilk

This paper studies the limitations of the generic approaches to solving cryptographic problems in classical and quantum settings in various models. - In the classical generic group model (GGM), we find simple alternative proofs for the…

Quantum Physics · Physics 2024-02-20 Minki Hhan

Compared with the quantum trajectory equation, the quantum Bayesian approach has the advantage of being more efficient to infer quantum state under monitoring, based on the integrated output of measurement. For weak measurement of qubits in…

Quantum Physics · Physics 2015-02-13 Peiyue Wang , Lupei Qin , Xin-Qi Li

Quantum resources, such as entanglement, can decrease the uncertainty of a parameter-estimation procedure beyond what is classically possible. This phenomenon is well described for noiseless systems with asymptotically many measurement…

Quantum Physics · Physics 2021-08-09 Jason Saunders , Jean-Francois Van Huele

With a Bayesian approach, the linear optics correction algorithm for storage rings is revisited. Starting from the Bayes' theorem, a complete linear optics model is simplified as "likelihood functions" and "prior probability distributions".…

Accelerator Physics · Physics 2019-04-18 Yongjun Li , Robert Rainer , Weixing Cheng

Quantum tomography involves obtaining a full classical description of a prepared quantum state from experimental results. We propose a Langevin sampler for quantum tomography, that relies on a new formulation of Bayesian quantum tomography…

We derive a finite-sample probabilistic bound on the parameter estimation error of a system identification algorithm for Linear Switched Systems. The algorithm estimates Markov parameters from a single trajectory and applies a variant of…

Machine Learning · Computer Science 2025-05-19 Daniel Racz , Mihaly Petreczky , Balint Daroczy

We propose two families of asymptotically local minimax lower bounds on parameter estimation performance. The first family of bounds applies to any convex, symmetric loss function that depends solely on the difference between the estimate…

Statistics Theory · Mathematics 2024-09-20 Neri Merhav

Bayesian inference is a widely used technique for real-time characterization of quantum systems. It excels in experimental characterization in the low data regime, and when the measurements have degrees of freedom. A decisive factor for its…

Quantum Physics · Physics 2025-07-10 Alexandra Ramôa , Raffaele Santagati , Nathan Wiebe

Identifying optimal values for a high-dimensional set of hyperparameters is a problem that has received growing attention given its importance to large-scale machine learning applications such as neural architecture search. Recently…

Quantum metrology promises unprecedented measurement precision but suffers in practice from the limited availability of resources such as the number of probes, their coherence time, or non-classical quantum states. The adaptive Bayesian…

Quantum Physics · Physics 2021-04-09 Lukas J. Fiderer , Jonas Schuff , Daniel Braun

The Holevo bound is a keystone in many applications of quantum information theory. We propose "weak maximal Holevo quantity" with weak measurements as the generalization of the standard Holevo quantity which is defined as the optimal…

Quantum Physics · Physics 2015-06-23 Yao-Kun Wang , Shao-Ming Fei , Zhi-Xi Wang , Jun-Peng Cao , Heng Fan

Realisation of experiments even on small and medium-scale quantum computers requires an optimisation of several parameters to achieve high-fidelity operations. As the size of the quantum register increases, the characterisation of quantum…

Quantum Physics · Physics 2020-08-11 F. Martínez-García , D. Vodola , M. Müller

Adiabatic quantum computing is a universal model for quantum computing whose implementation using a gate-based quantum computer requires depths that are unreachable in the early fault-tolerant era. To mitigate the limitations of near-term…

Quantum Physics · Physics 2024-10-18 Ioannis Kolotouros , Ioannis Petrongonas , Miloš Prokop , Petros Wallden

In [2] we introduced a method combining together an observability inequality and a spectral decomposition to get a logarithmic stability estimate for the inverse problem of determining both the potential and the damping coefficient in a…

Analysis of PDEs · Mathematics 2015-05-28 Kais Ammari , Mourad Choulli

Identifying the Hamiltonian of a quantum system from experimental data is considered. General limits on the identifiability of model parameters with limited experimental resources are investigated, and a specific Bayesian estimation…

Quantum Physics · Physics 2019-10-15 S. G. Schirmer , F. C. Langbein

The Bayesian Cram\'er-Rao bound (CRB) provides a lower bound on the mean square error of any Bayesian estimator under mild regularity conditions. It can be used to benchmark the performance of statistical estimators, and provides a…

Machine Learning · Statistics 2024-09-09 Evan Scope Crafts , Xianyang Zhang , Bo Zhao

To avoid poor empirical performance in Metropolis-Hastings and other accept-reject-based algorithms practitioners often tune them by trial and error. Lower bounds on the convergence rate are developed in both total variation and Wasserstein…

Statistics Theory · Mathematics 2024-07-04 Austin Brown , Galin L. Jones