Fisher loss improves deep domain adaptation by learning discriminative within-class compact and between-class separable representations.
problem Improving deep domain adaptation performance by learning discriminative representations.
method Proposes a Fisher loss to learn discriminative representations that are within-class compact and between-class separable.
result Noticeable improvements in deep domain adaptation performance, e.g., 6.67% absolute improvement in mean accuracy on the Office-Home dataset.
The paper solves optimal bounds for separating data points in high dimensions.
problem Correcting AI errors and analyzing vulnerabilities in high-dimensional data.
method General stochastic separation theorems with optimal probability estimates.
result Explicit and optimal estimates of separation probabilities for important classes of distributions.
Estimates intrinsic dimensionality of biological datasets using Fisher separability.
problem High-dimensional biological datasets with complex structures.
method Fisher separability analysis to estimate intrinsic dimensionality.
result The method performs competitively with state-of-the-art measures and is robust to noise.
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.
We identify spectral conditions for reliable neural probe interpretation.
problem Unreliable performance of linear probes in interpreting neural representations.
method Formalized Spectral Identifiability Principle (SIP) based on eigengap and Fisher error.
result Reliability of neural probes depends on the eigengap relative to Fisher estimation error.
We consider composite loss functions for multiclass prediction comprising a proper (i.e., Fisher-consistent) loss over probability distributions and an inverse link function. We establish conditions for their (strong) convexity and explore the implications. We also show how the separation of concerns afforded by using …
This work proposes external correctors for quick AI error corrections without system modification.
problem Quick corrections of AI errors without modifying legacy systems.
method Special `external` devices with classifiers for high-dimensional data.
result Simple classifiers can correct small errors in high-dimensional data.
Paper estimates GMMs with unknown covariances using sparse regularization.
problem Estimating GMMs with unknown diagonal covariances from samples.
method Employed Beurling-LASSO (BLASSO) for sparse estimation of component means, covariances, and weights.
result Established non-asymptotic recovery guarantees with nearly parametric convergence rates.
New budget quantifies drift in closed-loop learning, improving reproducibility.
problem Characterizing statistical learning under distributional drift in closed-loop settings.
method Introduces an intrinsic drift budget CT quantifying cumulative information-geometric motion of the data distribution. result Proves a drift-feedback bound of order T−1/2+CT/T for prequential reproducibility, up to controlled second-order remainder terms. Batch Normalization (BN) is essential to effectively train state-of-the-art deep Convolutional Neural Networks (CNN). It normalizes inputs to the layers during training using the statistics of each mini-batch. In this work, we study BN from the viewpoint of Fisher kernels. We show that assuming samples within a mini-ba…
Hypothesis testing in singular models is fundamentally about identifiable vs. non-identifiable parameters.
problem Testing in singular models is inherently problematic due to non-identifiability and degeneracy of Fisher information.
method Formalized the overlap obstruction and showed that hypotheses over non-identifiable parameters are untestable, while those over identifiable parameters reduce to classical testing.
result Hypotheses over non-identifiable parameters are untestable, while those over identifiable parameters reduce to classical testing.
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.
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.
Recently, digital music libraries have been developed and can be plainly accessed. Latest research showed that current organization and retrieval of music tracks based on album information are inefficient. Moreover, they demonstrated that people use emotion tags for music tracks in order to search and retrieve them. In…
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…
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…
A new geometric concept, the dead direction, bridges singular learning theory and information geometry.
problem The gap between singular learning theory and information geometry.
method Introducing the dead direction, a unit vector along degenerating Fisher metric, and showing its KL order can be recovered.
result The KL order of the dead direction can be recovered as the decay rate of the directional Fisher curvature, providing a handle on singular geometry.
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.
Researchers find a class/cross-class structure in deep learning spectra.
problem Understanding the structure of deep learning classifiers.
method Empirical spectral analysis of deepnet classifiers.
result The cross-class structure explains various features in deepnet spectra.
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 …
Adversarial robustness of amortized Bayesian inference is studied, showing it can be improved.
problem Adversarial robustness of amortized Bayesian inference.
method Simulation-based estimation, regularization scheme based on Fisher information.
result Adversarial robustness can be improved with a regularization scheme.
A new distance metric for vMF distributions simplifies spherical data analysis.
problem Intractability of normalization constants and lack of suitable geometric metrics for comparing vMF distributions.
method Proposes a Wasserstein-like distance that decomposes vMF distribution discrepancies into angular and concentration components.
result The proposed distance metric induces a latent geometric structure on the space of non-degenerate vMF distributions.
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…
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.
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.
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.
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 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.
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.
Artificial Intelligence (AI) systems sometimes make errors and will make errors in the future, from time to time. These errors are usually unexpected, and can lead to dramatic consequences. Intensive development of AI and its practical applications makes the problem of errors more important. Total re-engineering of the…