Related papers: Filtering Additive Measurement Noise with Maximum …
Using a Bayesian methodology, we introduce the maximum a posteriori~(MAP) estimator for quantum state and process tomography. The maximum likelihood, hedged maximum likelihood, maximum likelihood-maximum entropy estimator, and estimators of…
Real-world applications such as magnetic resonance imaging with multiple coils, multi-user communication, and diffuse optical tomography often assume a linear model where several sparse signals sharing common sparse supports are acquired by…
We present a general framework to study the simultaneous estimation of multiple phases in the presence of noise as a discretized model for phase imaging. This approach can lead to nontrivial bounds of the precision for multiphase…
Kernel embeddings of distributions and the Maximum Mean Discrepancy (MMD), the resulting distance between distributions, are useful tools for fully nonparametric two-sample testing and learning on distributions. However, it is rarely that…
Several researchers have proposed minimisation of maximum mean discrepancy (MMD) as a method to quantise probability measures, i.e., to approximate a target distribution by a representative point set. We consider sequential algorithms that…
Semi-continuous data comes from a distribution that is a mixture of the point mass at zero and a continuous distribution with support on the positive real line. A clear example is the daily rainfall data. In this paper, we present a novel…
The Expectation Maximization (EM) algorithm is widely used as an iterative modification to maximum likelihood estimation when the data is incomplete. We focus on a semi-supervised case to learn the model from labeled and unlabeled samples.…
Understanding the limitations imposed by noise on current and next-generation quantum devices is a crucial step towards demonstrating practical quantum advantage. In this work, we investigate the accumulation of entropy density as a…
We make remarks on the Maximum Entropy Method (MEM) for studies of the spectral function of hadronic correlators in finite temperature lattice QCD. We discuss the virtues and subtlety of MEM in the cases that one does not have enough number…
Message importance measure (MIM) is applicable to characterize the importance of information in the scenario of big data, similar to entropy in information theory. In fact, MIM with a variable parameter can make an effect on the…
We consider the minimum error entropy (MEE) criterion and an empirical risk minimization learning algorithm in a regression setting. A learning theory approach is presented for this MEE algorithm and explicit error bounds are provided in…
We consider the problem of mean estimation assuming only finite variance. We study a new class of mean estimators constructed by integrating over random noise applied to a soft-truncated empirical mean estimator. For appropriate choices of…
This paper studies the problem of estimation from relative measurements in a graph, in which a vector indexed over the nodes has to be reconstructed from pairwise measurements of differences between its components associated to nodes…
This paper offers a qualitative insight into the convergence of Bayesian parameter inference in a setup which mimics the modeling of the spread of a disease with associated disease measurements. Specifically, we are interested in the…
Parametric amplification is an interesting way of artificially increasing a MEMS Quality factor and could be helpful in many kinds of applications. This paper presents a theoretical study of this principle, based on Matlab/Simulink…
Envelope method was recently proposed as a method to reduce the dimension of responses in multivariate regressions. However, when there exists missing data, the envelope method using the complete case observations may lead to biased and…
The sample mean is often used to aggregate different unbiased estimates of a parameter, producing a final estimate that is unbiased but possibly high-variance. This paper introduces the Bayesian median of means, an aggregation rule that…
We develop a computational procedure to estimate the covariance hyperparameters for semiparametric Gaussian process regression models with additive noise. Namely, the presented method can be used to efficiently estimate the variance of the…
We provide a general theory of the expectation-maximization (EM) algorithm for inferring high dimensional latent variable models. In particular, we make two contributions: (i) For parameter estimation, we propose a novel high dimensional EM…
This paper deals with the parametric inference for integrated signals embedded in an additive Gaussian noise and observed at deterministic discrete instants which are not necessarily equidistant. The unknown parameter is multidimensional…