arXiv research

New tensor framework connects Fisher information, hypergraphs, and multi-observable correlations.

Estimates metric tensor on neuromanifolds using Fisher information and random methods.

We formulate and solve a tensor model using a latent-variable approach.

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…

Learning an encoding of feature vectors in terms of an over-complete dictionary or a information geometric (Fisher vectors) construct is wide-spread in statistical signal processing and computer vision. In content based information retrieval using deep-learning classifiers, such encodings are learnt on the flattened la…

Information geometry provides a geometric approach to families of statistical models. The key geometric structures are the Fisher quadratic form and the Amari-Chentsov tensor. In statistics, the notion of sufficient statistic expresses the criterion for passing from one model to another without loss of information. Thi…

Two methods preserve tensor structure for reduced dimensionality in tensor regression.

New distances for comparing multivariate normal distributions.

A new metric tensor improves Riemann manifold Monte Carlo for Bayesian models.

Fisher width is a geometric measure of complexity on statistical manifolds.

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…

The paper refines classical covariance asymptotics using geometric information geometry.

Anomaly Detection has several important applications. In this paper, our focus is on detecting anomalies in seller-reviewer data using tensor decomposition. While tensor-decomposition is mostly unsupervised, we formulate Bayesian semi-supervised tensor decomposition to take advantage of sparse labeled data. In addition…

A family of probability distributions parametrized by an open domain $Λ$ in $R^n$ defines the Fisher information matrix on this domain which is positive semi-definite. In information geometry the standard assumption has been that the Fisher information matrix tensor is positive definite defining in this way a Riemannia…

The increasing use of multiple sensors, which produce a large amount of multi-dimensional data, requires efficient representation and classification methods. In this paper, we present a new method for multi-dimensional data classification that relies on two premises: 1) multi-dimensional data are usually represented by…

We develope a new and general notion of parametric measure models and statistical models on an arbitrary sample space $Ω$ which does not assume that all measures of the model have the same null sets. This is given by a diffferentiable map from the parameter manifold $M$ into the set of finite measures or probability me…

Introduces new Finsler metrics and connects them to information geometry.

A new probabilistic BTD method for tensor data.

Study on Gaussian-width complexity on statistical manifolds and its applications in learning and recovery.

Fisher auto-encoders use Fisher divergence for more robust generative modeling.

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.

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…

Develops a new geometric framework for quantum metrics.

The Riemannian Bures metric on the space of (normalized) complex positive matrices is used for parameter estimation of mixed quantum states based on repeated measurements just as the Fisher information in classical statistics. It appears also in the concept of purifications of mixed states in quantum physics. Here we d…

Market strategies minimize Fisher information to minimize 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.

We propose a modified $χ^β$-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.

The paper studies metrics on Lie groups SO(2) and SO(3) and their integrability.

The Conant-Ashby theorem is verified for hypergraph observers, leading to unique learning rules.

This paper shows any Kähler metric can be a Fisher information metric.

Proofs Fisher-Rao distance on Gaussian covariance manifold.

Survey on closed-form Fisher-Rao distance expressions.

New statistics are introduced that maintain the Fisher metric structure closely, akin to sufficient statistics.

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…

GANs can be used to extract Fisher vectors for unsupervised feature learning.

We formulate the Riemannian calculus of the probability set embedded with $L^2$-Wasserstein metric. This is an initial work of transport information geometry. Our investigation starts with the probability simplex (probability manifold) supported on vertices of a finite graph. The main idea is to embed the probability m…

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.

Paper formulates particle flow using variational inference and Fisher-Rao gradient flow.

Paper discusses the Fisher metric and differentiability in statistical models.

Develops an analytic theory for quantum imaginary time evolution.

TopoFisher learns topological summaries by maximizing Fisher information, improving parameter efficiency and inference quality.

Paper identifies key function spaces for ReLU networks based on Fisher information.