相关论文: A maximum likelihood algorithm for the estimation …
We consider the problem of estimating a probability distribution that maximizes the entropy while satisfying a finite number of moment constraints, possibly corrupted by noise. Based on duality of convex programming, we present a novel…
We outline an efficient method for the reconstruction of a probability density function from the knowledge of its infinite sequence of ordinary moments. The approximate density is obtained resorting to maximum entropy technique, under the…
Maximum likelihood estimation is one of the most used methods in quantum state tomography, where the aim is to reconstruct the density matrix of a physical system from measurement results. One strategy to deal with positivity and unit trace…
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…
This paper concerns the use of the expectation-maximisation (EM) algorithm for inference in partially observed diffusion processes. In this context, a well known problem is that all except a few diffusion processes lack closed-form…
The {\lambda}-exponential family has recently been proposed to generalize the exponential family. While the exponential family is well-understood and widely used, this it not the case of the {\lambda}-exponential family. However, many…
The Expectation-Maximization (EM) algorithm is routinely used for the maximum likelihood estimation in the latent class analysis. However, the EM algorithm comes with no guarantees of reaching the global optimum. We study the geometry of…
A new maximum likelihood method for deconvoluting a continuous density with a positive lower bound on a known compact support in additive measurement error models with known error distribution using the approximate Bernstein type polynomial…
A Monte Carlo Renormalization Group algorithm is used on the Ising model to derive critical exponents and the critical temperature. The algorithm is based on a minimum relative entropy iteration developed previously to derive potentials…
A new parameterization and algorithm are proposed for seeking the primary relative maximum of the likelihood function in the three-parameter lognormal distribution. The parameterization yields the dimension reduction of the three-parameter…
Probability density estimation is a core problem of statistics and signal processing. Moment methods are an important means of density estimation, but they are generally strongly dependent on the choice of feasible functions, which severely…
In this paper we propose a novel method to study critical systems numerically by a combined collective-mode algorithm and Renormalization Group on the lattice. This method is an improved version of MCRG in the sense that it has all the…
Expectation-Maximization (EM) algorithm is a widely used iterative algorithm for computing (local) maximum likelihood estimate (MLE). It can be used in an extensive range of problems, including the clustering of data based on the Gaussian…
Maximum likelihood estimation (MLE) of latent variable models is often recast as the minimization of a free energy functional over an extended space of parameters and probability distributions. This perspective was recently combined with…
This paper presents a detailed theoretical analysis of the three stochastic approximation proximal gradient algorithms proposed in our companion paper [49] to set regularization parameters by marginal maximum likelihood estimation. We prove…
Maximum-likelihood methods are applied to the problem of absorption tomography. The reconstruction is done with the help of an iterative algorithm. We show how the statistics of the illuminating beam can be incorporated into the…
Maximum likelihood iteration is one of the most commonly used reconstruction algorithms in quantum tomography. The main appeal of the method is that it is easy to implement and that it converges reliably to a physically meaningful density…
The $\lambda$-exponential family generalizes the standard exponential family via a generalized convex duality motivated by optimal transport. It is the constant-curvature analogue of the exponential family from the information-geometric…
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…
In this paper, we present a local information theoretic approach to explicitly learn probabilistic clustering of a discrete random variable. Our formulation yields a convex maximization problem for which it is NP-hard to find the global…