相关论文: MaxEnt assisted MaxLik tomography

We show that the method of maximum-likelihood estimation, recently introduced in the context of quantum process tomography, can be applied to the determination of Mueller matrices characterizing the polarization properties of classical…

In this tutorial we review the essential arguments behing entropic inference. We focus on the epistemological notion of information and its relation to the Bayesian beliefs of rational agents. The problem of updating from a prior to a…

We deal with a generalized statistical description of nonequilibrium complex systems based on least biased distributions given some prior information. A maximum entropy principle is introduced that allows for the determination of the…

In exploratory factor analysis, model parameters are usually estimated by maximum likelihood method. The maximum likelihood estimate is obtained by solving a complicated multivariate algebraic equation. Since the solution to the equation is…

Optimisation problems in science and engineering typically involve finding the ground state (i.e. the minimum energy configuration) of a cost function with respect to many variables. If the variables are corrupted by noise then this…

The maximum likelihood amplitude estimation algorithm (MLAE) is a practical solution to the quantum amplitude estimation problem with Heisenberg limit error convergence. We improve MLAE by using random depths to avoid the so-called critical…

Maximum Likelihood Estimation of continuous variable models can be very challenging in high dimensions, due to potentially complex probability distributions. The existence of multiple interdependencies among variables can make it very…

In Bayesian optimization, accounting for the importance of the output relative to the input is a crucial yet challenging exercise, as it can considerably improve the final result but often involves inaccurate and cumbersome entropy…

The set of solutions inferred by the generic maximum entropy (MaxEnt) or maximum relative entropy (MaxREnt) principles of Jaynes - considered as a function of the moment constraints or their conjugate Lagrangian multipliers - is endowed…

We present a detailed account of quantum state estimation by joint maximization of the likelihood and the entropy. After establishing the algorithms for both perfect and imperfect measurements, we apply the procedure to data from simulated…

The traditional maximum likelihood estimator (MLE) is often of limited use in complex high-dimensional data due to the intractability of the underlying likelihood function. Maximum composite likelihood estimation (McLE) avoids full…

Let $x_{i,j}$, $1 \le i \le m$, $1 \le j \le n_i$, be observations from a doubly-indexed sequence $\{X_{i,j}\}$ of independent random variables (all of them discrete, or all of them absolutely continuous). Suppose that each $X_{i,j}$ has…

The maximum entropy principle is a powerful tool for solving underdetermined inverse problems. This paper considers the problem of discretizing a continuous distribution, which arises in various applied fields. We obtain the approximating…

One-shot information theory entertains a plethora of entropic quantities, such as the smooth max-divergence, hypothesis testing divergence and information spectrum divergence, that characterize various operational tasks and are used to…

We consider the problem of estimating rare event probabilities, focusing on systems whose evolution is governed by differential equations with uncertain input parameters. If the system dynamics is expensive to compute, standard sampling…

We discuss how maximum entropy methods may be applied to the reconstruction of Markov processes underlying empirical time series and compare this approach to usual frequency sampling. It is shown that, at least in low dimension, there…

We consider the problem of optimal processing of quantum information at incomplete experimental data characterizing the quantum source. In particular, we then prove that for one-qubit quantum source the Jaynes principle offers a simple…

The diversity of a community that cannot be fully counted must be inferred. The two preeminent inference methods are the MaxEnt method, which uses information in the form of constraints and Bayes' rule which uses information in the form of…

Quantum machine learning is an emerging field at the intersection of machine learning and quantum computing. Classical cross entropy plays a central role in machine learning. We define its quantum generalization, the quantum cross entropy,…

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…