Adapts Roy's criterion for non-normal returns using Cornish Fisher expansion.
problem Selecting one risky asset from many when returns are non-normal.
method Adapts Roy's criterion via Cornish Fisher expansion for non-normal returns.
result Investment objective consistent with first order stochastic dominance, equal to Sharpe ratio for normal returns.
This paper provides an insight to the time-varying dynamics of the shape of the distribution of financial return series by proposing an exponential weighted moving average model that jointly estimates volatility, skewness and kurtosis over time using a modified form of the Gram-Charlier density in which skewness and ku…
Paper provides Edgeworth expansions for network moments, improving accuracy of sampling distributions.
problem Accurate descriptions of sampling distributions of network moment statistics.
method Edgeworth expansion applied to studentized network moment statistics.
result Higher-order accurate approximation to sampling CDF of network moment statistics.
This thesis builds a real-time VaR calculation workflow for crypto derivatives.
problem Managing risk in volatile cryptocurrency markets.
method Applied EMWA, GARCH, and HAR models to forecast volatility; used delta-gamma-theta approach and Cornish-Fisher expansion.
result Real-time VaR estimates with millisecond calculation latencies.
Study analyzes how COVID-19 impacts crypto and stock market volatility.
problem Impact of COVID-19 on cryptocurrency and stock market volatility.
method Two-stage multivariate EGARCH model with DCC approach, VaR and CFVaR.
result Significant spillover effects and conditional volatility surges after shocks.
This study provides an explicit expansion of KL divergence's gradient flow in Fisher-Rao geometry.
problem Sampling techniques struggle to traverse between modes in non-convex potential functions.
method Explicit expansion of KL divergence's gradient flow in Fisher-Rao geometry.
result The convergence rate to π is independent of the potential function.
This article presents differential equations and solution methods for the functions of the form Q(x)=F−1(G(x)), where F and G are cumulative distribution functions. Such functions allow the direct recycling of Monte Carlo samples from one distribution into samples from another. The method may be developed an…
MULTIFIT tests independence between two random vectors using multiscale Fisher's test.
problem Detecting local dependence between two random vectors.
method MULTIFIT uses a resampling-free approach to test independence.
result MULTIFIT can easily handle large sample sizes and interpret dependency nature.
EigenVI uses orthogonal function expansions for efficient variational inference.
problem Efficiently approximate complex distributions in variational inference.
method EigenVI constructs variational approximations using orthogonal function expansions, minimizing Fisher divergence.
result EigenVI provides more accurate approximations than existing methods for Gaussian BBVI.
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 derives higher-order asymptotic expansions for parametric complexity in statistical models.
problem Improving the accuracy of parametric complexity estimation in statistical models.
method Derives higher-order asymptotic expansions for parametric complexity using cumulants and Amari-Chentsov tensors.
result Higher-order approximations have better finite-sample behavior than Rissanen's approximation.
Develops a real-analytic embedding for diffeomorphisms of the line, linking to Fisher-Rao geometry.
problem Embedding diffeomorphisms of the line in a geometric framework.
method Real-analytic embedding, Lp Fisher-Rao geometry, Schwarzian curvature. result Establishes a connection between diffeomorphisms and Fisher-Rao geometry, providing explicit geodesics and connections.
We derive an equation of motion for interest-rate yield curves by applying a minimum Fisher information variational approach to the implied probability density. By construction, solutions to the equation of motion recover observed bond prices. More significantly, the form of the resulting equation explains the success …
Paper establishes limits for accurately estimating low-rank matrices from noisy, non-linear data.
problem Estimating low-rank matrices from noisy, non-linear observations.
method Proves strong universality result with equivalent Gaussian model and effective prior parameters.
result Signal-to-noise ratio requirement grows as $N^{ rac 12 (1-1/k_F)}$ for accurate reconstruction.
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.
The study limits the number of ribbon concordant fibered knots.
problem Understanding the relationship between ribbon concordance and fibered knots.
method Combining Floer homology results with fixed points of monodromy and volume inequalities.
result There are only finitely many hyperbolic fibered knots ribbon concordant to any given knot.
Disputes the empirical Fisher approximation for natural gradient descent.
problem The empirical Fisher approximation fails to capture second-order information in general.
method Comparison of empirical Fisher and Fisher information matrices.
result The empirical Fisher does not generally approximate the Fisher or Hessian.
The paper proves geometric and spectral alignment for deep neural networks.
problem Understanding the singular spectra of deep neural network layers.
method Proves deterministic quotient-geometric estimates for singular spectra of Frobenius-normalized layer factors.
result Exact power-law spectra form a trace-normalized Cartan orbit under Frobenius normalization.
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.
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.
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.
Fisher GAN improves GAN training stability and efficiency.
problem Stable training of GANs with minimal data constraints.
method Integrates Fisher information into IPM framework for GAN training.
result Fisher GAN achieves stable and efficient training without compromising critic capacity.
Explains Fisher and Kernel Fisher Discriminant Analysis with examples and comparisons.
problem Classifying data with different features and dimensions.
method Projection and reconstruction, scatters analysis, PCA comparison, Fisher forest.
result Equivalence of Fisher and Linear Discriminant Analysis, effectiveness of Fisher forest.
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…
This paper explores VAEs in Fisher-Shannon plane, revealing the relationship between Fisher information and Shannon entropy.
problem Understanding the relationship between Fisher information and Shannon entropy in VAEs.
method Investigation of VAEs in Fisher-Shannon plane, focusing on the trade-off between Fisher information and Shannon entropy.
result VAEs' representation learning and log-likelihood estimation are intrinsically related to Fisher information and Shannon entropy.
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.
Fisher consistency improves class probability estimation under dataset shift.
problem Lack of Fisher consistency can lead to unreliable class probability estimates.
method Introduced Fisher consistency as a desirable property for class prior probability estimators.
result CDE-Iterate is not Fisher consistent and cannot be trusted for reliable estimates.
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…
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.
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.
Financial market PDF derived from Fisher information extremization.
problem Deriving financial market probability distribution.
method Extremization of Fisher information for PDF derivation.
result Quantum-like description of financial markets.
We link probability density functions to Fisher information metrics.
problem Constructing probability density functions from Fisher information metrics.
method Utilizing the spatially disjoint product of probability density functions and their Fisher information metric tensors.
result A method for constructing arbitrary Riemannian Fisher information metric tensors.
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.
The paper simplifies the Fisher information matrix for random deep networks, speeding up learning.
problem Learning deep neural networks efficiently with large parameter spaces.
method Statistical neurodynamical method to reveal Fisher information properties, proving unit-wise block diagonal structure and explicit inverse.
result Explicit natural gradient formula without matrix inversion, speeding up learning.
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 …
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 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.
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.
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.
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.