相关论文: AIMS:Average Information Matrix Splitting
Missing data are a common problem for both the construction and implementation of a prediction algorithm. Pattern mixture kernel submodels (PMKS) - a series of submodels for every missing data pattern that are fit using only data from that…
We derive an information criterion to select a parametric model of complete-data distribution when only incomplete or partially observed data is available. Compared with AIC, our new criterion has an additional penalty term for missing…
The expectation-maximization (EM) algorithm is an iterative computational method to calculate the maximum likelihood estimators (MLEs) from the sample data. It converts a complicated one-time calculation for the MLE of the incomplete data…
We analyse the matrix factorization problem. Given a noisy measurement of a product of two matrices, the problem is to estimate back the original matrices. It arises in many applications such as dictionary learning, blind matrix…
In this paper we study covariance estimation with missing data. We consider missing data mechanisms that can be independent of the data, or have a time varying dependency. Additionally, observed variables may have arbitrary (non uniform)…
One of the main notions of information theory is the notion of mutual information in two messages (two random variables in Shannon information theory or two binary strings in algorithmic information theory). The mutual information in $x$…
Fragmentary data is becoming more and more popular in many areas which brings big challenges to researchers and data analysts. Most existing methods dealing with fragmentary data consider a continuous response while in many applications the…
The quality of numerical reconstructions for unknown parameters in inverse problems depends fundamentally on the selection of experimental data. To ensure a robust reconstruction, it is crucial to select data that are sensitive to the…
The Fisher-matrix formalism is used routinely in the literature on gravitational-wave detection to characterize the parameter-estimation performance of gravitational-wave measurements, given parametrized models of the waveforms, and…
Mimicking the maximum likelihood estimator, we construct first order Cramer-Rao efficient and explicitly computable estimators for the scale parameter $\sigma^2$ in the model $Z_{i,n}=\sigma n^{-\beta}X_i+Y_i,i=1,\ldots,n,\beta>0$ with…
A deep neural network is a hierarchical nonlinear model transforming input signals to output signals. Its input-output relation is considered to be stochastic, being described for a given input by a parameterized conditional probability…
Finite mixtures of matrix normal distributions are a powerful tool for classifying three-way data in unsupervised problems. The distribution of each component is assumed to be a matrix variate normal density. The mixture model can be…
The article develops a hybrid Variational Bayes algorithm that combines the mean-field and fixed-form Variational Bayes methods. The new estimation algorithm can be used to approximate any posterior without relying on conjugate priors. We…
We derive a general upper bound to mutual information in terms of the Fisher information. The bound may be further used to derive a lower bound for the Bayesian quadratic cost. These two provide alternatives to other inequalities in the…
The quantum Fisher information (QFI) is a fundamental quantity of interest in many areas from quantum metrology to quantum information theory. It can in particular be used as a witness to establish the degree of multi-particle entanglement…
In this brief note we compute the Fisher information of a family of generalized normal distributions. Fisher information is usually defined for regular distributions, i.e. continuously differentiable (log) density functions whose support…
A quantum measurement is Fisher symmetric if it provides uniform and maximal information on all parameters that characterize the quantum state of interest. Using (complex projective) 2-designs, we construct measurements on a pair of…
Statistical tasks such as density estimation and approximate Bayesian inference often involve densities with unknown normalising constants. Score-based methods, including score matching, are popular techniques as they are free of…
In distributed systems, communication is a major concern due to issues such as its vulnerability or efficiency. In this paper, we are interested in estimating sparse inverse covariance matrices when samples are distributed into different…
We introduce a novel Mutual Information (MI) estimator that fundamentally reframes the discriminative approach. Instead of training a classifier to discriminate between joint and marginal distributions, we learn a normalizing flow that…