Improved mean estimation for symmetric distributions with finite-sample guarantees.
problem Estimating the mean of a symmetric distribution from samples.
method Using Fisher information rate for finite-sample guarantees.
result Finite-sample convergence close to subgaussian with variance 1/(n * I_r), where I_r is r-smoothed Fisher information.
Paper discusses the Fisher metric and differentiability in statistical models.
problem Understanding the relationship between Fisher metric and differentiability in statistical models.
method Comparison of different concepts and models in Information Geometry, mathematical statistics, and measure theory.
result Discussion of various models and their differentiability properties.
We improve maximum likelihood for location estimation in finite samples.
problem Estimating a parameter from samples with unknown or varying distribution.
method Use smoothed Fisher information for finite sample size and varying distributions.
result Recover optimal estimation theory for finite n and arbitrary f. Study improves sampling from non-log-concave distributions using Fisher information.
problem Sampling from non-log-concave distributions with high Fisher information guarantees.
method Proximal sampler with RGO implementation, leveraging log-concave sampling results.
result Improved complexity guarantee in relative Fisher information for non-log-concave sampling.
Improved location estimation for high-dimensional data with finite sample size.
problem Estimating the shift in high-dimensional data with limited samples.
method Smoothed estimators and bounds on subgamma vectors.
result Convergence to Cramér-Rao bound for finite sample sizes.
In this communication, we describe some interrelations between generalized q-entropies and a generalized version of Fisher information. In information theory, the de Bruijn identity links the Fisher information and the derivative of the entropy. We show that this identity can be extended to generalized versions of en…
Market strategies minimize Fisher information to minimize risk.
problem Applying minimum Fisher information principle to market dynamics.
method Analytical extension to quantum harmonic oscillator eigenstates and Gibbs distribution.
result Minimizing Fisher information reduces information and risk.
We propose a modified χβ-divergence, give some of its properties, and show that this leads to the definition of a generalized Fisher information. We give generalized Cramér-Rao inequalities, involving this Fisher information, an extension of the Fisher information matrix, and arbitrary norms and power of the estimat…
Blog post discusses various implementations of Fisher Information for EWC in continual learning.
problem Improving Elastic Weight Consolidation (EWC) results by optimizing Fisher Information computation.
method Empirically compares different implementations of Fisher Information for EWC.
result Many reported EWC results can be improved by changing Fisher Information computation methods.
This paper shows any Kähler metric can be a Fisher information metric.
problem Establishing a new characterization of Kähler and coKähler manifolds.
method Statistical approach using Fisher information and exponential families.
result Any Kähler metric is a Fisher information metric.
Proposes a novel node embedding framework for graphs using Fisher Information.
problem Lack of theoretical understanding of attention-based GNNs.
method Uses hierarchical kernels and Fisher Information to learn node embeddings.
result Proposed method outperforms existing GNNs on node classification benchmarks.
In information theory, Fisher information and Shannon information (entropy) are respectively used to quantify the uncertainty associated with the distribution modeling and the uncertainty in specifying the outcome of given variables. These two quantities are complementary and are jointly applied to information behavior…
Natural gradient descent, which preconditions a gradient descent update with the Fisher information matrix of the underlying statistical model, is a way to capture partial second-order information. Several highly visible works have advocated an approximation known as the empirical Fisher, drawing connections between ap…
Fisher width is a geometric measure of complexity on statistical manifolds.
problem Complexity measures on statistical manifolds
method Introducing Fisher width as a Fisher-geometric analogue of Gaussian width
result Fisher width retains key structural features of Gaussian width while capturing anisotropic geometric effects
On a closed manifold of dimension greater than one, every smooth weak Riemannian metric on the space of smooth positive probability densities, that is invariant under the action of the diffeomorphism group, is a multiple of the Fisher--Rao metric.
TopoFisher learns topological summaries by maximizing Fisher information, improving parameter efficiency and inference quality.
problem Simulation-based inference misses key information in low-order statistics, especially for non-Gaussian fields.
method TopoFisher uses a differentiable persistent-homology pipeline that learns topological summaries by maximizing local Gaussian Fisher information.
result TopoFisher recovers much of the available information and outperforms fixed topological vectorizations in weak gravitational lensing.
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 distribution of outputs. The space of parameters consisting of weights and biases i…
Paper identifies key function spaces for ReLU networks based on Fisher information.
problem Understanding the structure of Fisher information matrices in ReLU networks.
method Spectral decomposition of Fisher information matrices, focusing on the first three eigenspaces.
result The first three eigenspaces account for 97.7% of the trace of the Fisher information matrix, corresponding to spherical harmonic functions of order ≤2.
A new measure of model complexity based on Fisher Information.
problem Model complexity measurement in statistical models.
method Effective dimension defined by the number of cubes needed to cover the model space.
result The effective dimension is scale-dependent and measures model complexity.
The study examines Fisher information matrices and neural tangent kernels for simple ReLU networks with random weights.
problem Understanding the relationship between Fisher information matrices and neural tangent kernels for 2-layer ReLU networks.
method Analyzes Fisher information matrices and neural tangent kernels for 2-layer ReLU networks with random hidden weights, focusing on spectral decomposition and eigenfunctions.
result Obtained an approximation formula for functions represented by 2-layer neural networks.
New method approximates diffusion process posteriors using moment functions.
problem Approximating posteriors of stochastic differential equations.
method Constructs variational process as controlled prior, approximates posterior with moment functions, uses natural gradient descent.
result Richer variational approximations for state-dependent diffusion terms.
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 transforms the search for a probability density into the solution of a differential…
Machine learning approximates phase transitions using Fisher information.
problem Understanding phase transitions from data using machine learning.
method Information geometry and Fisher information.
result Machine learning indicators approximate the square root of Fisher information.
Two Fisher information matrix estimators are analyzed for neural networks, focusing on their variances and trade-offs.
problem Estimating the Fisher information matrix in neural networks due to its high computational cost.
method Examined two popular diagonal Fisher information matrix estimators and their variances in neural networks for regression and classification.
result The variances of the estimators depend on the non-linearity with respect to different parameter groups and should not be neglected.
The space of all probability measures having positive density function on a connected compact smooth manifold M, denoted by P(M), carries the Fisher information metric G. We define the geometric mean of probability measures by the aid of which we investigate information geometry of P(M), equ…
We propose a Bayesian framework of Gaussian process in order to extend Fisher's discriminant to classify functional data such as spectra and images. The probability structure for our extended Fisher's discriminant is explicitly formulated, and we utilize the smoothness assumptions of functional data as prior probabilit…
The paper explores geometry of probability measures and barycenter maps.
problem Understanding the space of probability measures and their barycenter.
method Information geometry, Fisher metric, dualistic structures, divergences, geodesics.
result Recent developments in the geometry of probability measures and barycenter.
We show a general relation between the spatially disjoint product of probability density functions and the sum of their Fisher information metric tensors. We then utilise this result to give a method for constructing the probability density functions for an arbitrary Riemannian Fisher information metric tensor. We note…
New tensor framework connects Fisher information, hypergraphs, and multi-observable correlations.
problem Missing structure in pairwise Fisher graphs for multi-observable radiation patterns.
method Higher-order Fisher tensors and natural exponential-family coordinates.
result Exact triality of Fisher tensors, cumulants, and hypergraphs.
The paper refines classical covariance asymptotics using geometric information geometry.
problem Deviation of finite-sample behavior from classical predictions in curved models.
method Develops a curvature-aware refinement by viewing parametric families as Riemannian manifolds with Fisher-Rao metric.
result Derives an \(n^{-2}\) correction to the leading \(n^{-1}I(θ)^{-1}\) covariance term for score-root estimators.
Study on Gaussian-width complexity on statistical manifolds and its applications in learning and recovery.
problem Understanding the geometry of statistical manifolds and its implications for learning and recovery.
method Analysis of Fisher width and inverse-Fisher width, proving their complementary roles and establishing a relation between them.
result Established a sharp relation between Fisher width and inverse-Fisher width, showing they cannot reduce relative to Euclidean scale.
GANs can be used to extract Fisher vectors for unsupervised feature learning.
problem Unsupervised feature extraction for classification and similarity tasks.
method Derive Fisher Information and Fisher Vectors from GANs' density model.
result GAN-induced Fisher Vectors perform competitively in unsupervised feature extraction.
Study on convergence rates of degenerate SDEs using Fisher information and generalized Bochner's formula.
problem Analysis of dynamical behaviors of degenerate stochastic differential equations.
method Use of Fisher information as Lyapunov functional, generalized Gamma calculus, and generalized Bochner's formula.
result Derivation of convergence rate conditions and examples in specific sub-Riemannian structures.
Paper improves Fisher information estimation methods.
problem Estimating Fisher information for location parameters.
method Revisits and improves Bhattacharya estimator, introduces clipped estimator.
result Clipped estimator shows superior convergence rates in Gaussian noise.
Paper proposes a method to verify PINN fidelity using Fisher information from dynamical systems.
problem Quantifying PINN fidelity beyond simple trajectory prediction.
method Employing Fisher information for differentiable dynamical systems to compare PINN's learned equations with analytical models.
result PINN fidelity is verified by matching Fisher information landscapes of learned equations and analytical models.
Inequalities linking entropy, Fisher info, Stein discrepancy, and Wasserstein distance on Riemannian manifolds.
problem Linking entropy, Fisher info, Stein discrepancy, and Wasserstein distance on Riemannian manifolds.
method Deriving inequalities linking these measures on Riemannian manifolds.
result Strengthening and extending existing inequalities to Riemannian manifolds.
Directly estimates Fisher score for likelihood maximization.
problem Intractable likelihood functions with model simulations.
method Gradient-based optimization using local score matching and linear parameterization.
result Efficient approximation of Fisher score improves likelihood maximization.
Data processing inequalities link Fisher information to local differential privacy constraints.
problem Understanding how Fisher information scales with local differential privacy constraints.
method Developed data processing inequalities for Fisher information under local differential privacy.
result Implications for private estimation with optimal bounds and error rates.
Cosine schedule is optimal for discrete diffusion models.
problem Choosing the best discretization schedule for diffusion models.
method Optimized using Fisher-Rao geometry.
result Cosine schedule is Fisher-Rao optimal.
We study geodesic equations for a family of right-invariant Riemannian metrics on the group of diffeomorphisms of a compact manifold. The metrics descend to Fisher's information metric on the space of smooth probability densities. The right reduced geodesic equations are higher-dimensional generalisations of the μ--H…
FedFisher improves one-shot FL by using Fisher information.
problem Reducing communication rounds in federated learning.
method Bayesian perspective, Fisher information matrices, diagonal Fisher, K-FAC approximation.
result FedFisher achieves vanishingly small error in two-layer neural networks.
We analyze the variance of Fisher information estimators in deep learning models.
problem Understanding the variance of Fisher information in deep learning models.
method Investigated two unbiased and consistent estimators of Fisher information matrix.
result The variance of estimators is influenced by the model's parametric structure.
The paper sets lower bounds for sampling non-log-concave distributions using Fisher information.
problem Understanding the complexity of sampling non-log-concave distributions.
method Proves two lower bounds using Fisher information in the context of sampling.
result Lower bounds on the complexity of sampling non-log-concave distributions, ruling out high-accuracy algorithms.
New distances for comparing multivariate normal distributions.
problem Comparing multivariate normal distributions efficiently and accurately.
method Approximated Fisher-Rao distance and pullback SPD cone distances.
result Efficient computation of distances between normal distributions.
The probability distribution function (PDF) for prices on financial markets is derived by extremization of Fisher information. It is shown how on that basis the quantum-like description for financial markets arises and different financial market models are mapped by quantum mechanical ones.
Estimates metric tensor on neuromanifolds using Fisher information and random methods.
problem Computing the metric tensor on high-dimensional neuromanifolds efficiently and accurately.
method Deterministic bounds and unbiased random estimators based on Hutchinson's trace method.
result An efficient random estimator with bounded standard deviation.
The Fisher-Rao geometry is applied to elliptical distributions for optimization and classification.
problem Optimizing and classifying covariance matrices using geometric tools.
method Riemannian optimization and intrinsic Cramér-Rao bounds.
result Geometric tools enhance covariance matrix estimation and classification.
SQFA learns features maximizing Fisher-Rao distance for better classification.
problem Improving classification accuracy through feature learning.
method SQFA learns linear features maximizing Fisher-Rao distance between class-conditional distributions.
result SQFA-H features achieve the best classification accuracy.