Related papers: Optimal parameter estimation with a fixed rate of …
Quantum metrology is a general term for methods to precisely estimate the value of an unknown parameter by actively using quantum resources. In particular, some classes of entangled states can be used to significantly suppress the…
Bayesian optimisation has gained great popularity as a tool for optimising the parameters of machine learning algorithms and models. Somewhat ironically, setting up the hyper-parameters of Bayesian optimisation methods is notoriously hard.…
In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a…
We consider the problem of designing an optimal quantum detector to minimize the probability of a detection error when distinguishing between a collection of quantum states, represented by a set of density operators. We show that the design…
We study the problem of parameter-free stochastic optimization, inquiring whether, and under what conditions, do fully parameter-free methods exist: these are methods that achieve convergence rates competitive with optimally tuned methods,…
The ultimate bound to the accuracy of phase estimates is often assumed to be given by the Heisenberg limit. Recent work seemed to indicate that this bound can be violated, yielding measurements with much higher accuracy than was previously…
In most machine learning applications, classification accuracy is not the primary metric of interest. Binary classifiers which face class imbalance are often evaluated by the $F_\beta$ score, area under the precision-recall curve, Precision…
Analyses of accelerated (momentum-based) gradient descent usually assume bounded condition number to obtain exponential convergence rates. However, in many real problems, e.g., kernel methods or deep neural networks, the condition number,…
We consider finite element approximations of ill-posed elliptic problems with conditional stability. The notion of {\emph{optimal error estimates}} is defined including both convergence with respect to mesh parameter and perturbations in…
This paper considers mathematical programs, whose constraints are expressed by a parameterized vector equilibrium problem. The latter is a well recognized framework, which is able to cover multicriteria optimization, vector variational…
Multiparameter quantum estimation is made difficult by the following three obstacles. First, incompatibility among different physical quantities poses a limit on the attainable precision. Second, the ultimate precision is not saturated…
We present an algorithm to approximate the solutions to variational problems where set of admissible functions consists of convex functions. The main motivator behind this numerical method is estimating solutions to Adverse Selection…
Phase estimation protocols provide a fundamental benchmark for the field of quantum metrology. The latter represents one of the most relevant applications of quantum theory, potentially enabling the capability of measuring unknown physical…
We consider a popular family of constrained optimization problems arising in machine learning that involve optimizing a non-decomposable evaluation metric with a certain thresholded form, while constraining another metric of interest.…
We present a quantum algorithm to estimate parameters at the quantum metrology limit using deterministic quantum computation with one bit. When the interactions occurring in a quantum system are described by a Hamiltonian $H= \theta H_0$,…
We consider the problem of chance constrained optimization where it is sought to optimize a function and satisfy constraints, both of which are affected by uncertainties. The real world declinations of this problem are particularly…
Bayesian methods have been very successful in quantifying uncertainty in physics-based problems in parameter estimation and prediction. In these cases, physical measurements y are modeled as the best fit of a physics-based model…
We address the common problem of calculating intervals in the presence of systematic uncertainties. We aim to investigate several approaches, but here describe just a Bayesian technique for setting upper limits. The particular example we…
We propose a general framework for studying optimal impulse control problem in the presence of uncertainty on the parameters. Given a prior on the distribution of the unknown parameters, we explain how it should evolve according to the…
An unconventional approach for optimal stopping under model ambiguity is introduced. Besides ambiguity itself, we take into account how ambiguity-averse an agent is. This inclusion of ambiguity attitude, via an $\alpha$-maxmin nonlinear…