Related papers: Quadratic Point Estimate Method for Probabilistic …
We endeavour to estimate numerous multi-dimensional means of various probability distributions on a common space based on independent samples. Our approach involves forming estimators through convex combinations of empirical means derived…
Due to its significance as a subroutine, in this work, we consider the coherent version of the quantum phase estimation problem, where given an arbitrary input state and black-box access to unitaries $U$ and controlled-$U$, the goal is to…
Approximating integrals is a fundamental task in probability theory and statistical inference, and their applied fields of signal processing, and Bayesian learning, as soon as expectations over probability distributions must be computed…
In this letter, an accelerated quadratic programming (QP) algorithm is proposed based on the proximal gradient method. The algorithm can achieve convergence rate $O(1/p^{\alpha})$, where $p$ is the iteration number and $\alpha$ is the given…
Quantization for a probability distribution refers to the idea of estimating a given probability by a discrete probability supported by a finite number of points. In this paper, firstly a general approach to this process is outlined using…
We introduce new rounding methods to improve the accuracy of finite precision quantum arithmetic. These quantum rounding methods are applicable when multiple samples are being taken from a quantum program. We show how to use multiple…
In this paper, we address the risk estimation problem where one aims at estimating the probability of violation of safety constraints for a robot in the presence of bounded uncertainties with arbitrary probability distributions. In this…
This dissertation explores the topics of parameter estimation and model reduction in the context of quantum filtering. Chapters 2 and 3 provide a review of classical and quantum probability theory, stochastic calculus and filtering. Chapter…
The problem of estimating certain distributions over $\{0,1\}^d$ is considered here. The distribution represents a quantum system of $d$ qubits, where there are non-trivial dependencies between the qubits. A maximum entropy approach is…
A new method involving particle diagrams is introduced and developed into a rigorous framework for carrying out embedded random matrix calculations. Using particle diagrams and the attendant methodology including loop counting it becomes…
In this paper, novel closed-form point estimators of the beta distribution are proposed and investigated. The first estimators are a modified version of Pearson's method of moments. The underlying idea is to involve the sufficient…
We develop an efficient quantum implementation of an important signal processing algorithm for line spectral estimation: the matrix pencil method, which determines the frequencies and damping factors of signals consisting of finite sums of…
In this study the determinant of the average quadratic error matrix is used as the measure of state estimation efficiency. This quantity is easily computable in some cases, so it gives us a reasonable tool to find optimal measurement setup…
This paper studies a method, which has been proposed in the Physics literature by [8, 7, 10], for estimating the quasi-stationary distribution. In contrast to existing methods in eigenvector estimation, the method eliminates the need for…
We present quantum algorithms for solving two problems regarding stochastic processes. The first algorithm prepares the thermal Gibbs state of a quantum system and runs in time almost linear in $\sqrt{N \beta/{\cal Z}}$ and polynomial in…
We derive the joint probability distribution of the first two spectral moments for the G$\beta$E random matrix ensembles in N dimensions for any N. This is achieved by making use of two complementary invariants of the domain in…
We develop moment estimators for the parameters of affine stochastic volatility models. We first address the challenge of calculating moments for the models by introducing a recursive equation for deriving closed-form expressions for…
We develop a quantum version of the probability estimation framework [arXiv:1709.06159] for randomness generation with quantum side information. We show that most of the properties of probability estimation hold for quantum probability…
This paper addresses the challenging computational problem of estimating intractable expectations over discrete domains. Existing approaches, including Monte Carlo and Russian Roulette estimators, are consistent but often require a large…
System state estimation constitutes a key problem in several applications involving multi-agent system architectures. This rests upon the estimation of the state of each agent in the group, which is supposed to access only relative…