Related papers: Fisher information lower bounds for sampling
In this paper, we study the general problem of optimizing a convex function $F(L)$ over the set of $p \times p$ matrices, subject to rank constraints on $L$. However, existing first-order methods for solving such problems either are too…
Resolving frequencies in a time-dependent field is classically limited by the measurement bandwidth. Using tools from quantum metrology and quantum control may overcome this limit, yet the full advantage afforded by entanglement so far…
The optimal phase estimation strategy is derived when partial a priori knowledge on the estimated phase is available. The structure of the optimal measurements, estimators and the optimal probe states is analyzed. The results fill the gap…
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…
We correct claims about lower bounds on mutual information (MI) between real-valued random variables made in A. Kraskov {\it et al.}, Phys. Rev. E {\bf 69}, 066138 (2004). We show that non-trivial lower bounds on MI in terms of linear…
Uncertain input of a mathematical model induces uncertainties in the output and probabilistic sensitivity analysis identifies the influential inputs to guide decision-making. Of practical concern is the probability that the output would, or…
We develop a line-search second-order algorithmic framework for minimizing finite sums. We do not make any convexity assumptions, but require the terms of the sum to be continuously differentiable and have Lipschitz-continuous gradients.…
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 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 investigated quantum critical behaviours in the non-equilibrium steady state of a $XXZ$ spin chain with boundary Markovian noise using the Fisher information. The latter represents the distance between two infinitesimally close states,…
We give conditions for an O(1/n) rate of convergence of Fisher information and relative entropy in the Central Limit Theorem. We use the theory of projections in L2 spaces and Poincare inequalities, to provide a better understanding of the…
Persistence diagrams provide stable, interpretable summaries of geometric and topological structure and are useful for simulation-based inference when low-order statistics miss key information. Yet persistence-based pipelines require…
Quantum Fisher Information (QFI) is a ubiquitous quantity with applications ranging from quantum metrology and resource theories to condensed matter physics. In equilibrium local quantum many-body systems, the QFI of a subsystem with…
This paper provides a general technique for lower bounding the Bayes risk of statistical estimation, applicable to arbitrary loss functions and arbitrary prior distributions. A lower bound on the Bayes risk not only serves as a lower bound…
An Edgeworth-type expansion is established for the relative Fisher information distance to the class of normal distributions of sums of i.i.d. random variables, satisfying moment conditions. The validity of the central limit theorem is…
We study the problem of estimating a continuous ability parameter from sequential binary responses by actively asking questions with varying difficulties, a setting that arises naturally in adaptive testing and online preference learning.…
The quantum Fisher information (QFI), as a function of quantum states, measures the amount of information that a quantum state carries about an unknown parameter. The (entanglement-assisted) QFI of a quantum channel is defined to be the…
Fisher information is a lower bound on the uncertainty in the statistical estimation of classical and quantum mechanical parameters. While some deterministic dynamical systems are not subject to random fluctuations, they do still have a…
We propose a scheme for parameter estimation with the steady states of non-Hermitian spin chains. The parameters to be estimated are encoded in the system via the external magnetic field that imposed on the first site of the chain. We…
Mixture-of-Experts models are commonly used when there exist distinct clusters with different relationships between the independent and dependent variables. Fitting such models for large datasets, however, is computationally virtually…