Related papers: Fisher-type information involving higher order der…
Fisher's likelihood is widely used for statistical inference for fixed unknowns. This paper aims to extend two important likelihood-based methods, namely the maximum likelihood procedure for point estimation and the confidence procedure for…
The Fisher information matrix (FIM) has long been of interest in statistics and other areas. It is widely used to measure the amount of information and calculate the lower bound for the variance for maximum likelihood estimation (MLE). In…
Quantum Fisher information is the principal tool used to give the ultimate precision bound on the estimation of parameters for quantum channels. In this work, we present analytical expressions for the quantum Fisher information with three…
The Fisher information $F$ gives a limit to the ultimate precision achievable in a phase estimation protocol. It has been shown recently that the Fisher information for a linear two-mode interferometer cannot exceed the number of particles…
Learning an encoding of feature vectors in terms of an over-complete dictionary or a information geometric (Fisher vectors) construct is wide-spread in statistical signal processing and computer vision. In content based information…
In proofs of L_2-differentiability, Lebesgue densities of a central distribution are often assumed right from the beginning. Generalizing Theorem 4.2 of Huber[81], we show that in the class of smooth parametric group models these densities…
This paper proposes a unifying variational approach for proving and extending some fundamental information theoretic inequalities. Fundamental information theory results such as maximization of differential entropy, minimization of Fisher…
The logarithmic derivative (or, quantum score) of a positive definite density matrix appearing in the quantum Fisher information is discussed, and its exact expression is presented. Then, the problem of estimating the parameters in a class…
We introduce a pair of transformations, which are mutually inverse, acting on rather general classes of probability densities in R. These transformations have the property of interchanging the main informational measures such as p-moments,…
Relative Fisher information (IR), which is a measure of correlative fluctuation between two probability densities, has been pursued for a number of quantum systems, such as, 1D quantum harmonic oscillator (QHO) and a few central potentials…
Two classically equivalent expressions of mutual information of probability distributions (classical bipartite states) diverge when extended to quantum systems, and this difference has been employed to define quantum discord, a quantifier…
Privacy-preserving instance encoding aims to encode raw data as feature vectors without revealing their privacy-sensitive information. When designed properly, these encodings can be used for downstream ML applications such as training and…
Wave packet revivals and fractional revivals are studied by means of a measure of nonclassicality based on the Fisher information. In particular, we show that the spreading and the regeneration of initially Gaussian wave packets in a…
Quantum Fisher information characterizes the phase sensitivity of qubits in the spin-boson model with a finite bandwidth spectrum. In contrast with Markovian reservoirs, the quantum Fisher information will flow from the environments to…
We study a simple model of the stochastic information filtering, in a randomly organized information system. For simplest versions of the model it appears to be possible to describe the filtering dynamics in terms of the master equations.…
We study the problem of identifying viewers of arbitrary images based on their eye gaze. Psychological research has derived generative stochastic models of eye movements. In order to exploit this background knowledge within a…
Training-free conditional diffusion models have received great attention in conditional image generation tasks. However, they require a computationally expensive conditional score estimator to let the intermediate results of each step in…
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…
We consider a general class of empirical-type likelihoods and develop higher order asymptotics with a view to characterizing members thereof that allow the existence of possibly data-dependent probability matching priors ensuring…
Fisher Information (FI) is a quantity ubiquitously measured in such varied areas like metrology, machine learning, and biological complexity. Mathematically, it represents a lower bound in the variance of unknown parameters that are related…