Related papers: Fisher Information and Dynamical Sampling I
In information theory, the link between continuous information and discrete information is established through well-known sampling theorems. Sampling theory explains, for example, how frequency-filtered music signals are reconstructible…
Unsupervised learning plays an important role in many fields, such as artificial intelligence, machine learning, and neuroscience. Compared to static data, methods for extracting low-dimensional structure for dynamic data are lagging. We…
The interest in variable selection for clustering has increased recently due to the growing need in clustering high-dimensional data. Variable selection allows in particular to ease both the clustering and the interpretation of the results.…
The quantum Fisher information, the quantum analogue of the classical Fisher information, is a central quantity in quantum metrology and quantum sensing due to its connection to parameter estimation and fidelity susceptibility. Using…
Modern large-scale datasets are frequently said to be high-dimensional. However, their data point clouds frequently possess structures, significantly decreasing their intrinsic dimensionality (ID) due to the presence of clusters, points…
The Fisher-Rao metric from Information Geometry is related to phase transition phenomena in classical statistical mechanics. Several studies propose to extend the use of Information Geometry to study more general phase transitions in…
Expected Fisher information can be found a priori and as a result its inverse is the primary variance approximation used in the design of experiments. This is in contrast to the common claim that the inverse of observed Fisher information…
The mean of an unknown variance-$\sigma^2$ distribution $f$ can be estimated from $n$ samples with variance $\frac{\sigma^2}{n}$ and nearly corresponding subgaussian rate. When $f$ is known up to translation, this can be improved…
Quantum learning (in metrology and machine learning) involves estimating unknown parameters from measurements of quantum states. The quantum Fisher information matrix can bound the average amount of information learnt about the unknown…
A deep neural network is a hierarchical nonlinear model transforming input signals to output signals. Its input-output relation is considered to be stochastic, being described for a given input by a parameterized conditional probability…
When we extract information from a system by performing a quantum measurement, the state of the system is disturbed due to the backaction of the measurement. Numerous studies have been performed to quantitatively formulate tradeoff…
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…
The Fisher information matrix (FIM) is a key quantity in statistics as it is required for example for evaluating asymptotic precisions of parameter estimates, for computing test statistics or asymptotic distributions in statistical testing,…
Quantum Fisher information is a central quantity in quantum metrology. We discuss an alternative representation of quantum Fisher information for unitary parametrization processes. The highlight of this representation is that all…
The relevance of the concept of Fisher information is increasing in both statistical physics and quantum computing. From a statistical mechanical standpoint, the application of Fisher information in the kinetic theory of gases is…
Metadynamics is an enhanced sampling method of great popularity, based on the on-the-fly construction of a bias potential that is function of a selected number of collective variables. We propose here a change in perspective that shifts the…
The Fisher information matrix (FIM) is a foundational concept in statistical signal processing. The FIM depends on the probability distribution, assumed to belong to a smooth parametric family. Traditional approaches to estimating the FIM…
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…
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…
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.…