Related papers: Quantifying lost information due to covariance mat…
The Matern family of covariance functions is currently the most commonly used for the analysis of geostatistical data due to its ability to describe different smoothness behaviors. Yet, in many applications the smoothness parameter is set…
For sparse high-dimensional regression problems, Cox and Battey [1, 9] emphasised the need for confidence sets of models: an enumeration of those small sets of variables that fit the data equivalently well in a suitable statistical sense.…
The Fisher information matrix can be used to characterize the local geometry of the parameter space of neural networks. It elucidates insightful theories and useful tools to understand and optimize neural networks. Given its high…
An approach based on the Fisher information (FI) is developed to quantify the maximum information gain and optimal experimental design in neutron reflectometry experiments. In these experiments, the FI can be analytically calculated and…
We prove lower bounds on the error of any estimator for the mean of a real probability distribution under the knowledge that the distribution belongs to a given set. We apply these lower bounds both to parametric and nonparametric…
In this work we construct an optimal linear shrinkage estimator for the covariance matrix in high dimensions. The recent results from the random matrix theory allow us to find the asymptotic deterministic equivalents of the optimal…
We explore fairness from a statistical perspective by selectively utilizing either conditional distance covariance or distance covariance statistics as measures to assess the independence between predictions and sensitive attributes. We…
Many imaging systems are used to estimate a vector of parameters associated with the object being imaged. In many cases there are other parameters in the model for the imaging data that are not of interest for the task at hand. We refer to…
In this work we study the problem of measuring the fairness of a machine learning model under noisy information. Focusing on group fairness metrics, we investigate the particular but common situation when the evaluation requires controlling…
We consider regression models involving multilayer perceptrons (MLP) with one hidden layer and a Gaussian noise. The estimation of the parameters of the MLP can be done by maximizing the likelihood of the model. In this framework, it is…
Similarity metrics such as representational similarity analysis (RSA) and centered kernel alignment (CKA) have been used to compare layer-wise representations between neural networks. However, these metrics are confounded by the population…
We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…
We consider the problem of determining the weights of a quantum ensemble. That is to say, given a quantum system that is in a set of possible known states according to an unknown probability law, we give strategies to estimate the…
Upcoming cosmological surveys will achieve increasingly precise constraints in cosmological parameter estimation. To guarantee the robustness of cosmological analyses, it is essential to account for and model systematic effects that can…
In the context of the usual calibration model, we consider the case in which the independent variable is unobservable, but a pre-fixed value on its surrogate is available. Thus, considering controlled variables and assuming that the…
In order to provide a guaranteed precision and a more accurate judgement about the true value of the Cram\'{e}r-Rao bound and its scaling behavior, an upper bound (equivalently a lower bound on the quantum Fisher information) for precision…
We consider the estimation of large covariance and precision matrices from high-dimensional sub-Gaussian or heavier-tailed observations with slowly decaying temporal dependence. The temporal dependence is allowed to be long-range so with…
We consider statistical inference for errors-in-variables regression models with dependent observations under the high dimensionality of the error covariance matrix. It is tempting to prewhiten the model and data that had led to efficient…
When data contains measurement errors, it is necessary to make assumptions relating the observed, erroneous data to the unobserved true phenomena of interest. These assumptions should be justifiable on substantive grounds, but are often…
Recent literature provides many computational and modeling approaches for covariance matrices estimation in a penalized Gaussian graphical models but relatively little study has been carried out on the choice of the tuning parameter. This…