Related papers: The ubiquitous problem of learning system paramete…
Hierarchical Bayesian models are increasingly used in large, inhomogeneous complex network dynamical systems by modeling parameters as draws from a hyperparameter-governed distribution. However, theoretical guarantees for these estimates as…
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".…
We propose an efficient family of algorithms to learn the parameters of a Bayesian network from incomplete data. In contrast to textbook approaches such as EM and the gradient method, our approach is non-iterative, yields closed form…
Backpropagation with gradient descent is a common optimization strategy employed by most neural network architectures in machine learning. However, finding optimal hyperparameters to guide training has proven challenging. While it is widely…
In this work, we will investigate a Bayesian approach to estimating the parameters of long memory models. Long memory, characterized by the phenomenon of hyperbolic autocorrelation decay in time series, has garnered significant attention.…
Spatial regression of random fields based on potentially biased sensing information is proposed in this paper. One major concern in such applications is that since it is not known a-priori what the accuracy of the collected data from each…
Before autonomous systems can be deployed in safety-critical applications, we must be able to understand and verify the safety of these systems. For cases where the risk or cost of real-world testing is prohibitive, we propose a…
Various schemes have been proposed to overcome the drawback of the decoherence on quantum-enhanced parameter estimation. Here we suggest an alternative method, quantum feedback, to enhance the parameter precision of optimal quantum…
We present an empirical strategy to determine the Hamiltonian dynamics of a two-qubit system using only initialization and measurement in a single fixed basis. Signal parameters are estimated from measurement data using Bayesian methods…
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…
In high-dimensional Bayesian statistics, various methods have been developed, including prior distributions that induce parameter sparsity to handle many parameters. Yet, these approaches often overlook the rich spectral structure of the…
Frequentist and Bayesian phase estimation strategies lead to conceptually different results on the state of knowledge about the true value of the phase shift. We compare the two frameworks and their sensitivity bounds to the estimation of…
The paper investigates the techniques of quantum computation in metrological predictions, with a particular emphasis on enhancing prediction potential through variational parameter estimation. The applicability of quantum simulations and…
We consider the problem of estimating a variable number of parameters with a dynamic nature. A familiar example is finding the position of moving targets using sensor array observations. The problem is challenging in cases where either the…
It is often of interest to combine available estimates of a similar quantity from multiple data sources. When the corresponding variances of each estimate are also available, a model should take into account the uncertainty of the estimates…
Almost all fields of science rely upon statistical inference to estimate unknown parameters in theoretical and computational models. While the performance of modern computer hardware continues to grow, the computational requirements for the…
Gaussian processes allow for flexible specification of prior assumptions of unknown dynamics in state space models. We present a procedure for efficient Bayesian learning in Gaussian process state space models, where the representation is…
The phase estimation algorithm is a powerful quantum algorithm with applications in cryptography, number theory, and simulation of quantum systems. We use this algorithm to simulate the time evolution of a system of two spin-1/2 particles…
Parameter identification and comparison of dynamical systems is a challenging task in many fields. Bayesian approaches based on Gaussian process regression over time-series data have been successfully applied to infer the parameters of a…
A common approach to modelling extreme values is to consider the excesses above a high threshold as realisations of a non-homogeneous Poisson process. While this method offers the advantage of modelling using threshold-invariant extreme…