Related papers: Adaptive Designs for Optimal Observed Fisher Infor…
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…
Projective measurements in quantum theory have a very simple algebraic definition, but their information theoretic significance is quite elusive. Here we introduce a simple order relation based on the concentration of Fisher information,…
The ability to design effective experiments is crucial for obtaining data that can substantially reduce the uncertainty in the predictions made using computational models. An optimal experimental design (OED) refers to the choice of a…
The dynamic environment in the real world calls for the adaptive techniques for information filtering, namely to provide real-time responses to the changes of system data. Where many incremental algorithms are designed for this purpose,…
Background: Adaptive interventions provide a guide for using ongoing information about individuals to decide whether and how to modify the type, amount, delivery modality, or timing of treatment, to improve intervention effectiveness while…
Learning for control in repeated tasks allows for well-designed experiments to gather the most useful data. We consider the setting in which we use a data-driven controller that does not have access to the true system dynamics. Rather, the…
Dynamical systems are frequently used to model biological systems. When these models are fit to data it is necessary to ascertain the uncertainty in the model fit. Here we present prediction deviation, a new metric of uncertainty that…
The Fisher information of a quantum observable is shown to be proportional to both (i) the difference of a quantum and a classical variance, thus providing a measure of nonclassicality; and (ii) the rate of entropy increase under Gaussian…
The minimum achievable statistical uncertainty in the estimation of physical parameters is determined by the quantum Fisher information. Its computation for noisy systems is still a challenging problem. Using a variational approach, we…
Variance and Fisher information are ingredients of the Cramer-Rao inequality. We regard Fisher information as a Riemannian metric on a quantum statistical manifold and choose monotonicity under coarse graining as the fundamental property of…
A common approach to analyzing categorical correlated time series data is to fit a generalized linear model (GLM) with past data as covariate inputs. There remain challenges to conducting inference for short time series length. By treating…
This paper deals with the question of how to most effectively conduct experiments in Partially Observed Markov Decision Processes so as to provide data that is most informative about a parameter of interest. Methods from Markov decision…
Bayesian optimal experimental design is a principled framework for conducting experiments that leverages Bayesian inference to quantify how much information one can expect to gain from selecting a certain design. However, accurate Bayesian…
Observations on the past provide some hints about what will happen in the future, and this can be quantified using information theory. The ``predictive information'' defined in this way has connections to measures of complexity that have…
We derive general upper bounds to pointwise mutual information in terms of stochastic Fisher information and show these bounds average to known results in the literature for bounds to mutual information in terms of Fisher information. These…
Bayesian experimental design involves the optimal allocation of resources in an experiment, with the aim of optimising cost and performance. For implicit models, where the likelihood is intractable but sampling from the model is possible,…
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…
When training data are fragmented across batches or federated-learned across different geographic locations, trained models manifest performance degradation. That degradation partly owes to covariate shift induced by data having been…
Bayesian optimal experimental design (OED) provides a principled framework for selecting observations or experiments. We introduce new Bayesian design criteria based on the expected Wasserstein-$p$ distance between the prior and posterior…
In this paper optimal experimental designs for inverse quadratic regression models are determined. We consider two different parameterizations of the model and investigate local optimal designs with respect to the $c$-, $D$- and…