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.
This note improves correlation stress tests using geodesic distance.
problem Improving financial risk management through better covariance stress tests.
method Proposes a new geometrically invariant definition of correlation stress tests.
result Demonstrates a submanifold approach to stress testing covariance matrices.
To answer the existence of optimal swimmer learning/teaching strategies, this work introduces a two-level clustering in order to analyze temporal dynamics of motor learning in breaststroke swimming. Each level have been performed through Sparse Fisher-EM, a unsupervised framework which can be applied efficiently on lar…
A new way to describe correlation matrices makes modeling easier.
problem Describing correlation matrices in a flexible and positive-definite way.
method Introduces a novel parametrization that allows unrestricted vectors for correlation matrices.
result The new parametrization ensures positive definiteness without additional constraints.
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…
Study on collaboration vs. independent data collection in sensor networks.
problem Impact of sensor correlation on data collection strategies.
method Analysis of Fisher information and Cramer-Rao bound.
result Optimal strategy involves transferring non-immediate information for improved estimation.
Kernel methods linked to feature subspaces and maximal correlation kernels.
problem Understanding kernel methods and their relationship to feature extraction.
method Established a correspondence between feature subspaces and kernels, introduced maximal correlation kernels, and demonstrated their optimality.
result Kernel SVM on maximal correlation kernel achieves minimum prediction error.
FisherNet extends Autoencoder using Fisher information for better data reconstruction.
problem Data reconstruction accuracy and model scalability in high-dimensional latent spaces.
method Introduces FisherNet architecture that uses Fisher information to quantify and account for latent space uncertainty.
result FisherNet produces more accurate reconstructions and scales better with latent space dimensions compared to VAE.
We introduce a mean-reverting SDE whose solution is naturally defined on the space of correlation matrices. This SDE can be seen as an extension of the well-known Wright-Fisher diffusion. We provide conditions that ensure weak and strong uniqueness of the SDE, and describe its ergodic limit. We also shed light on a use…
Combining insights from machine learning and quantum Monte Carlo, the stochastic reconfiguration method with neural network Ansatz states is a promising new direction for high-precision ground state estimation of quantum many-body problems. Even though this method works well in practice, little is known about the learn…
Optimizes resource allocation for distributed parameter estimation in sensor networks.
problem Maximizing accuracy in parameter estimation with limited resources.
method Formulates a data collection and collaboration policy design problem as a Fisher information maximization problem. Proposes multi-armed bandit algorithms for learning the optimal policy.
result Identifies optimal data collection and collaboration policies that balance resource use and estimation accuracy.
Paper forecasts stock correlations using a hybrid model combining graph neural networks and transformers.
problem Improving stock correlation forecasts for better portfolio management.
method Hybrid model combining Transformer and graph attention networks for forecasting residual deviations from historical data.
result The hybrid model reduces correlation forecasting error compared to rolling-window estimates.
This work improves OOD detection using deep generative models by approximating Fisher information metrics.
problem Deep generative models often incorrectly infer higher likelihoods for out-of-distribution data.
method Approximating Fisher information metrics using gradient norms of data points.
result The method outperforms existing OOD detection techniques.
New method speeds up solving orthogonality constrained problems.
problem Solving orthogonality constrained problems efficiently.
method Riemannian optimization and Riemannian preconditioning.
result Preconditioning improves computational costs and convergence.
A new algorithm infers causal networks from data using topological thresholds.
problem Inferring causal networks from data.
method Two methods for determining topological thresholds: one to leave no disconnected nodes, the other to find a causal large connected component.
result The novel algorithm is faster and more accurate than the PC algorithm.
It is well known that in a supervised classification setting when the number of features is smaller than the number of observations, Fisher's linear discriminant rule is asymptotically Bayes. However, there are numerous modern applications where classification is needed in the high-dimensional setting. Naive implementa…
While enormous progress has been made to Variational Autoencoder (VAE) in recent years, similar to other deep networks, VAE with deep networks suffers from the problem of degeneration, which seriously weakens the correlation between the input and the corresponding latent codes, deviating from the goal of the representa…
Fisher auto-encoders use Fisher divergence for more robust generative modeling.
problem Model uncertainty in generative models.
method Minimizing Fisher divergence between true and modeled joint distributions.
result Fisher auto-encoders can more accurately quantify model uncertainty.
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…
Paper defines Fisher co-metric on cotangent bundle and clarifies its relation to variance.
problem Defines Fisher co-metric on cotangent bundle and clarifies its relation to variance.
method Defines Fisher co-metric directly from Fisher metric without going through tangent bundle, using a natural correspondence between cotangent vectors and random variables.
result Clarifies the relation between Fisher co-metric and variance/covariance, trivializing the Cramér-Rao inequality.
For high-dimensional classification, it is well known that naively performing the Fisher discriminant rule leads to poor results due to diverging spectra and noise accumulation. Therefore, researchers proposed independence rules to circumvent the diverse spectra, and sparse independence rules to mitigate the issue of n…
Although stochastic gradient descent (SGD) is a driving force behind the recent success of deep learning, our understanding of its dynamics in a high-dimensional parameter space is limited. In recent years, some researchers have used the stochasticity of minibatch gradients, or the signal-to-noise ratio, to better char…
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.
Generative Adversarial Networks (GANs) are powerful models for learning complex distributions. Stable training of GANs has been addressed in many recent works which explore different metrics between distributions. In this paper we introduce Fisher GAN which fits within the Integral Probability Metrics (IPM) framework f…
The study examines Fisher-Riemann geodesics for nonparametric probability densities.
problem Understanding nonparametric probability densities using Fisher-Riemann geometry.
method Obtaining Fisher-Riemann geodesics as a limit of parametric cases with increasing parameters.
result The weak limit approach for nonparametric probability densities.
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.
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
The paper studies metrics on Lie groups SO(2) and SO(3) and their integrability.
problem Integrability of gradient systems on Lie groups via Fisher metrics.
method Analysis of Souriau-Fisher metrics and 2-cocycles on Lie groups SO(2) and SO(3).
result Cocycles can locally modify Fisher metrics on Lie group orbits.
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.
Proofs Fisher-Rao distance on Gaussian covariance manifold.
problem Proving Fisher-Rao distance on Gaussian covariance manifold.
method Basic Riemannian geometry.
result Proof of Fisher-Rao distance on covariance cone.
Survey on closed-form Fisher-Rao distance expressions.
problem Finding closed-form expressions for Fisher-Rao distance.
method Collect and present examples of closed-form expressions for Fisher-Rao distance of discrete and continuous distributions.
result Presentation of closed-form expressions for Fisher-Rao distance of various distributions.
New statistics are introduced that maintain the Fisher metric structure closely, akin to sufficient statistics.
problem Maintaining the Fisher metric structure in statistical models.
method Characterizing statistics that maintain the Fisher metric structure bi-Lipschitz equivalently.
result Characterized statistics that preserve the Fisher metric structure closely.
We consider three different approaches to define natural Riemannian metrics on polytopes of stochastic matrices. First, we define a natural class of stochastic maps between these polytopes and give a metric characterization of Chentsov type in terms of invariance with respect to these maps. Second, we consider the Fish…
Fisher score is one of the most widely used supervised feature selection methods. However, it selects each feature independently according to their scores under the Fisher criterion, which leads to a suboptimal subset of features. In this paper, we present a generalized Fisher score to jointly select features. It aims …
We introduce Fisher consistency in the sense of unbiasedness as a desirable property for estimators of class prior probabilities. Lack of Fisher consistency could be used as a criterion to dismiss estimators that are unlikely to deliver precise estimates in test datasets under prior probability and more general dataset…
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…
Study on geometry of Dirichlet distributions using Fisher-Rao metric.
problem Understanding the geometry of Dirichlet distributions.
method Analysis of Fisher-Rao metric on Dirichlet distribution parameter space.
result Geodesic completeness and negative sectional curvature of the space.
Paper formulates particle flow using variational inference and Fisher-Rao gradient flow.
problem Estimating posterior densities in probabilistic models.
method Variational formulation of particle flow, Fisher-Rao gradient flow, Gaussian and Gaussian mixture approximations.
result Gaussian and Gaussian mixture approximations of Fisher-Rao particle flow reduce to Exact Daum and Huang particle flow under linear Gaussian assumptions.
This paper analyzes Barlow Twins' representation efficiency using information-geometric methods.
problem Understanding and comparing the efficiency of self-supervised learning methods.
method Introduces an information-geometric framework to quantify representation efficiency and applies it to Barlow Twins.
result Proves that Barlow Twins achieves optimal representation efficiency (η=1).
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.
New framework assesses neural sensitivity to small perturbations.
problem Comparing neural representations' sensitivity to small changes.
method Local decodable information, Fisher information, and projected pullback/Fisher metric.
result Reveals differences in neural sensitivity not captured by activation alignment.
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.
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.
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.
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 for natural policy gradients converges linearly.
problem Improving natural policy gradient methods for better convergence.
method Fisher-Rao gradient flow applied to state-action distributions.
result Linear convergence rate with geometry-dependent factor.