Related papers: AIMS:Average Information Matrix Splitting
Maximum likelihood estimates and corresponding confidence regions of the estimates are commonly used in statistical inference. In practice, people often construct approximate confidence regions with the Fisher information at given sample…
Covariance matrix reconstruction is a topic of great significance in the field of one-bit signal processing and has numerous practical applications. Despite its importance, the conventional arcsine law with zero threshold is incapable of…
Parameter inference with an estimated covariance matrix systematically loses information due to the remaining uncertainty of the covariance matrix. Here, we quantify this loss of precision and develop a framework to hypothetically restore…
Machine-learning models contain information about the data they were trained on. This information leaks either through the model itself or through predictions made by the model. Consequently, when the training data contains sensitive…
Recently proposed methods in data subset selection, that is active learning and active sampling, use Fisher information, Hessians, similarity matrices based on gradients, and gradient lengths to estimate how informative data is for a…
We examine the problem of variance components testing in general mixed effects models using the likelihood ratio test. We account for the presence of nuisance parameters, i.e. the fact that some untested variances might also be equal to…
The Fisher information matrix (FIM) is a fundamental quantity to represent the characteristics of a stochastic model, including deep neural networks (DNNs). The present study reveals novel statistics of FIM that are universal among a wide…
Partial information decomposition (PID) of the multivariate mutual information describes the distinct ways in which a set of source variables contains information about a target variable. The groundbreaking work of Williams and Beer has…
Pattern-mixture models provide a transparent approach for handling missing data, where the full-data distribution is factorized in a way that explicitly shows the parts that can be estimated from observed data alone, and the parts that…
When inferring parameters from a Gaussian-distributed data set by computing a likelihood, a covariance matrix is needed that describes the data errors and their correlations. If the covariance matrix is not known a priori, it may be…
Generalization is the ability of machine learning models to make accurate predictions on new data by learning from training data. However, understanding generalization of quantum machine learning models has been a major challenge. Here, we…
Model merging provides a way of cheaply combining individual models to produce a model that inherits each individual's capabilities. While some merging methods can approach the performance of multitask training, they are often heuristically…
We propose confidence regions with asymptotically correct uniform coverage probability of parameters whose Fisher information matrix can be singular at important points of the parameter set. Our work is motivated by the need for reliable…
Quantum Fisher information matrix (QFIM) is a cornerstone of modern quantum metrology and quantum information geometry. Apart from optimal estimation, it finds applications in description of quantum speed limits, quantum criticality,…
Recent work has explored data thinning, a generalization of sample splitting that involves decomposing a (possibly matrix-valued) random variable into independent components. In the special case of a $n \times p$ random matrix with…
We study model selection and model averaging in generalized additive partial linear models (GAPLMs). Polynomial spline is used to approximate nonparametric functions. The corresponding estimators of the linear parameters are shown to be…
We theoretically investigate parameter quantum estimation in quantum chaotic systems. Our analysis is based on an effective description of non-integrable quantum systems in terms of a random matrix Hamiltonian. Based on this approach we…
In some multivariate problems with missing data, pairs of variables exist that are never observed together. For example, some modern biological tools can produce data of this form. As a result of this structure, the covariance matrix is…
The properties of the normal distribution under linear transformation, as well the easy way to compute the covariance matrix of marginals and conditionals, offer a unique opportunity to get an insight about several aspects of uncertainties…
We consider an inference on the eigenvalues of the covariance matrix of a multivariate normal distribution. The family of multivariate normal distributions with a fixed mean is seen as a Riemannian manifold with Fisher information metric.…