Related papers: Adaptive Designs for Optimal Observed Fisher Infor…
Hierarchical parametric models consisting of observable and latent variables are widely used for unsupervised learning tasks. For example, a mixture model is a representative hierarchical model for clustering. From the statistical point of…
We address the fundamental limits of learning unknown parameters of any stochastic process from time-series data, and discover exact closed-form expressions for how optimal inference scales with observation length. Given a parametrized…
We show how to verify the metrological usefulness of quantum states based on the expectation values of an arbitrarily chosen set of observables. In particular, we estimate the quantum Fisher information as a figure of merit of metrological…
We present a novel synthesis of Fisher information and asset pricing theory that yields a practical method for reconstructing the probability density implicit in security prices. The Fisher information approach to these inverse problems…
The Fisher information matrix summarizes the amount of information in a set of data relative to the quantities of interest. There are many applications of the information matrix in statistical modeling, system identification and parameter…
In adaptive control, a controller is precisely designed for a certain model of the system, but that model's parameters are updated online by another mechanism called the adaptive update. This allows the controller to aim for the benefits of…
We consider the impact that temporal correlations in the measurement statistics can have on the achievable precision in a sequential metrological protocol. In this setting, and for a single quantum probe, we establish that it is the…
This paper studies the asymptotic behavior of the Fisher information for a Levy process discretely sampled at an increasing frequency. We show that it is possible to distinguish not only the continuous part of the process from its jumps…
Recently new approaches for sensing the frequency of time dependent Hamiltonians have been presented, and it was shown that the optimal Fisher information scales as $T^{4}.$ We present here our interpretation of this new scaling, where the…
Living organisms exhibit remarkable adaptations across all scales, from molecules to ecosystems. We believe that many of these adaptations correspond to optimal solutions driven by evolution, training, and underlying physical and chemical…
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…
The quantum Fisher information of a quantum state with respect to a certain parameter quantifies the sensitivity of the quantum state to changes in that parameter. Maximizing the quantum Fisher information is essential for achieving the…
Information theory provides a useful tool to understand the evolution of complex nonlinear systems and their sustainability. In particular, Fisher Information (FI) has been evoked as a useful measure of sustainability and the variability of…
DeGroot (1962) developed a general framework for constructing Bayesian measures of the expected information that an experiment will provide for estimation. We propose an analogous framework for measures of information for hypothesis…
For biological experiments aiming at calibrating models with unknown parameters, a good experimental design is crucial, especially for those subject to various constraints, such as financial limitations, time consumption and physical…
The Fisher Information Matrix formalism is extended to cases where the data is divided into two parts (X,Y), where the expectation value of Y depends on X according to some theoretical model, and X and Y both have errors with arbitrary…
Inverse optimization has been increasingly used to estimate unknown parameters in an optimization model based on decision data. We show that such a point estimation is insufficient in a prescriptive setting where the estimated parameters…
Variational data assimilation optimizes for an initial state of a dynamical system such that its evolution fits observational data. The physical model can subsequently be evolved into the future to make predictions. This principle is a…
The conventional formulation of quantum sensing is based on the assumption that the probe is reset to its initial state after each measurement. In a very distinct approach, one can also pursue a sequential measurement scheme in which…
Fisher information measures a disorder system, which is specified by a corresponding probability, the likelihood. In this article, we provide a bridge to connect classical and quantum mechanics by using Fisher information. Following the…