Study on geometric Jensen-Shannon divergence for Gaussian measures in Hilbert space.
problem Computing divergence between Gaussian measures in infinite-dimensional Hilbert space.
method Closed form expression and regularization for divergence calculation.
result Closed form expression and regularization for Geometric Jensen-Shannon divergence.
Innovative inequalities for divergences with applications in PAC-Bayesian bounds and Monte Carlo.
problem Developing new inequalities for divergences.
method Introducing novel change of measure inequalities for f-divergences and α-divergences. result Applications in PAC-Bayesian bounds and Monte Carlo estimates.
This paper improves active learning by using robust divergences for committee disagreement.
problem Active learning with high measurement costs.
method Query by committee with Bregman divergence (including Kullback-Leibler divergence as a special case).
result The proposed method is more robust and performs as well as or better than conventional methods.
Disagreement between two classifiers regarding the class membership of an observation in pattern recognition can be indicative of an anomaly and its nuance. As in general classifiers base their decision on class aposteriori probabilities, the most natural approach to detecting classifier incongruence is to use divergen…
New dispersion indices based on inaccuracy and divergence introduced for information measures.
problem Measuring variability in uncertainty measures.
method Introducing new dispersion indices based on Kerridge inaccuracy and Kullback-Leibler divergence.
result Properties, bounds, and examples of new dispersion indices presented.
A one-to-one correspondence is drawn between law invariant risk measures and divergences, which we define as functionals of pairs of probability measures on arbitrary standard Borel spaces satisfying a few natural properties. Divergences include many classical information divergence measures, such as relative entropy a…
Study compares statistical properties and power of divergence measures for credit risk monitoring.
problem Detecting distributional shifts in credit risk models.
method Derives statistical properties and chi-square benchmark values for Jensen-Shannon Divergence and Kullback-Leibler Divergence, demonstrating their applicability in credit risk monitoring.
result Jensen-Shannon Divergence and Kullback-Leibler Divergence follow chi-square distributions and reveal practical trade-offs in minimizing false positives vs. detecting changes.
The study defines divergence for multivector fields on infinite-dimensional manifolds.
problem Defining divergence for multivector fields on infinite-dimensional manifolds.
method Definition of divergence consistent with finite-dimensional geometry, properties transferred from finite to infinite dimensions.
result Natural properties of divergence are preserved in infinite dimensions.
New optimal transport divergences derived from scoring functions.
problem Developing new divergences for optimal transport.
method Using scoring functions as cost functions in optimal transport.
result Comonotonic coupling is optimal for many new divergences.
New f-divergence measures improve robustness in noisy label learning.
problem Improving robustness in learning with noisy labels.
method Derived decoupling property of f-divergence measures under label noise. result Properly defined f-divergence measures are robust with label noise. New KL-divergence for Gaussian distributions based on Wasserstein geometry.
problem Computing KL-divergence for Gaussian distributions efficiently.
method Introducing WKL-divergence based on Wasserstein geometry.
result WKL-divergence evaluates to squared distance between points for Dirac measures.
Study convergence and approximations of entropic regularized Wasserstein distances for Gaussian and RKHS measures.
problem Convergence and approximations of entropic regularized Wasserstein distances in Gaussian and RKHS settings.
method Analysis of convergence and finite sample approximations of entropic regularized Wasserstein distances in Gaussian and RKHS settings.
result Strictly weaker convergence in 2-Sinkhorn divergence for Gaussian measures compared to exact 2-Wasserstein distance.
Proposes a new divergence measure for probability distributions.
problem Challenges in estimating divergences from empirical samples.
method Embeds data into RKHS, computes Jensen-Shannon divergence between covariance operators.
result Establishes RJSD as a lower bound on Jensen-Shannon divergence, enabling variational estimation.
Regularizes f-divergences with MMD to analyze Wasserstein flows.
problem Limitations of f-divergences in measures' support. method Rewriting MMD regularization as Moreau envelope in RKHS, analyzing gradients.
result Analysis of Wasserstein flows of MMD-regularized f-divergences. This paper introduces a new method to train normalizing flows using precision-recall divergences.
problem Training generative models with mode dropping and low-quality samples.
method Introduces PR-divergences and proposes a novel generative model to minimize precision-recall trade-offs.
result Normalizing flows can be trained to achieve specific precision-recall trade-offs using PR-divergences.
New f-Betas for portfolio optimization using f-divergence risk measures.
problem Optimizing portfolio performance under varying market conditions.
method Derive f-Betas and Hellinger-Betas, using f-divergence risk measures.
result Demonstrated new Beta metrics provide better performance under stress.
f-divergences are a general class of divergences between probability measures which include as special cases many commonly used divergences in probability, mathematical statistics and information theory such as Kullback-Leibler divergence, chi-squared divergence, squared Hellinger distance, total variation distance e…
New measures generalize existing ones, linking information and risk.
problem Linking information measures and risk in statistical decision problems.
method Introducing new families of divergence measures and deriving an information processing equality.
result Extension of variational φ-divergence representation to multiple distributions. Divergence functions play a key role as to measure the discrepancy between two points in the field of machine learning, statistics and signal processing. Well-known divergences are the Bregman divergences, the Jensen divergences and the f-divergences. In this paper, we show that the symmetric Bregman divergence can be …
Automated feature selection is important for text categorization to reduce the feature size and to speed up the learning process of classifiers. In this paper, we present a novel and efficient feature selection framework based on the Information Theory, which aims to rank the features with their discriminative capacity…
The paper proposes a new method to measure risk with fine-grained tail sensitivity.
problem Risk measures that do not account for tail sensitivity are insufficient for machine learning systems.
method The approach involves specifying a reference distribution with desired tail behavior and constructing risk measures compatible with this upper probability.
result Risk measures with fine-grained tail sensitivity can replace the expectation operator in machine learning systems.
Paper calculates KL divergence for isotropic Gaussian-Markov fields.
problem Measuring divergence between isotropic Gaussian-Markov fields.
method Derives closed-form KL divergence expressions.
result Develops new similarity measures in image processing.
The paper develops divergences for Gaussian processes and RKHS settings.
problem Estimating divergences in infinite-dimensional spaces.
method Formulations of Alpha Log-Det divergences, continuity in norm, laws of large numbers, consistent estimation from finite samples.
result Infinite-dimensional divergences can be estimated from finite-dimensional versions with dimension-independent sample complexities.
New divergence measures improve KL approximation.
problem Improving KL divergence approximation without AC condition.
method Introduced α-geodesical skew divergence. result Properties of α-geodesical skew divergence studied. There has been a growing interest in mutual information measures due to their wide range of applications in Machine Learning and Computer Vision. In this paper, we present a generalized structured regression framework based on Shama-Mittal divergence, a relative entropy measure, which is introduced to the Machine Learn…
Two entropy measures quantify suboptimal portfolio performance.
problem Measuring suboptimality in investment portfolios.
method Relative entropy (KL divergence) calculations.
result Suboptimal portfolios appear better than Kelly portfolios under certain measures.
The paper explores statistical and topological properties of sliced probability divergences.
problem Understanding the topological, statistical, and computational consequences of slicing divergences.
method Deriving theoretical properties of sliced probability divergences, including metric axioms preservation and weak continuity.
result Sliced divergences share similar topological properties and have stable sample complexity.
New insights into Markov chain geometry via positive transition measures.
problem Lack of statistical meaning in the space of transition probabilities.
method Constructing an extension of the space of transition probabilities using Amari's theory of positive measures.
result Introduction of a new dually flat structure for the space of positive transition measures.
We propose to interpret distribution model risk as sensitivity of expected loss to changes in the risk factor distribution, and to measure the distribution model risk of a portfolio by the maximum expected loss over a set of plausible distributions defined in terms of some divergence from an estimated distribution. The…
Risk measures for multivariate financial positions are studied in a utility-based framework. Under a certain incomplete preference relation, shortfall and divergence risk measures are defined as the optimal values of specific set minimization problems. The dual relationship between these two classes of multivariate ris…
In the existing financial literature, entropy based ideas have been proposed in portfolio optimization, in model calibration for options pricing as well as in ascertaining a pricing measure in incomplete markets. The abstracted problem corresponds to finding a probability measure that minimizes the relative entropy (al…
New PAC-Bayes bounds derived using Legendre transform and f-divergences.
problem Deriving PAC-Bayes bounds under various assumptions.
method Combining Legendre transform and Fenchel--Young inequality to derive change-of-measure inequalities.
result Extended PAC-Bayesian guarantees under tailored assumptions.
Unified approach for sample aggregation in transfer learning across various divergence measures.
problem Optimizing sample aggregation from source to target distributions for improved target performance.
method Unified algorithmic approach that adapts to multiple divergence measures via a weak modulus of transfer.
result Unified approach achieves near optimal rates in terms of the unknown strong modulus, applicable in more general settings.
ERM with f-divergence regularization yields unique solution.
problem Optimizing empirical risk with f-divergence. method Mild conditions on f lead to unique optimal measure. result Equivalence of ERM-fDR to different f-divergence regularization. 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.
New model learns better policies from expert demonstrations with higher efficiency.
problem Learning accurate policies from expert demonstrations with high efficiency.
method Generative adversarial imitation learning (GAIL) model that learns f-divergence automatically. result Learns better policies with higher data efficiency in physics-based control tasks.
New tools quantify deep generative models' performance.
problem Measuring the quality-diversity trade-off in deep generative models.
method Established non-asymptotic bounds on sample complexity and introduced frontier integrals.
result Smoothed estimators improve convergence rates of divergence frontiers.
We study exponential Levy models with change-point which is a random variable, independent from initial Levy processes. On canonical space with initially enlarged filtration we describe all equivalent martingale measures for change-point model and we give the conditions for the existence of f-divergence minimal equival…
New methods minimize GFlowNet training divergences for better sampling.
problem Training GFlowNets with KL divergence leads to biased and high-variance estimators.
method Design and implement efficient estimators for four divergence measures.
result Properly minimizing these divergences yields a provably correct and effective training scheme.
New method to measure compositional generalization on realistic data.
problem Limited compositional generalization in machine learning.
method Maximizing compound divergence while ensuring small atom divergence.
result Machine learning architectures fail to generalize compositionally.
The family of f-divergences is ubiquitously applied to generative modeling in order to adapt the distribution of the model to that of the data. Well-definedness of f-divergences, however, requires the distributions of the data and model to overlap completely in every time step of training. As a result, as soon as the s…
This paper generalizes beta divergence beyond its classical form associated with power variance functions of Tweedie models. Generalized form is represented by a compact definite integral as a function of variance function of the exponential dispersion model. This compact integral form simplifies derivations of many pr…
Geodesics in curved spaces spread evenly over time.
problem Equidistribution of geodesics in negatively curved spaces.
method Proving equidistribution of geodesic flow orbits towards measures of maximal entropy and Bowen-Margulis measure.
result Equidistribution of divergent geodesics in negative curvature as their complexity increases.
A new, computationally friendly formula for a class of risk-averse preferences.
problem Characterizing a class of risk-averse preferences called uniformly weighted divergence preferences.
method Introducing a new formula that characterizes UWDP as the translation-invariant hull of state-independent expected utility.
result UWDP are the translation-invariant hull of state-independent expected utility over L0. Introduces a new divergence measure for optimal transport.
problem Optimal transport distances and information divergences.
method Infimal convolution formulation of proximal optimal transport divergence.
result Establishes connections to dynamic formulations and partial differential equations.
New loss functions based on f-divergences improve language model performance.
problem Improving multiclass classification and language modeling performance.
method Constructing new convex loss functions using f-divergences and deriving an operator for computation.
result The α-divergence loss function with α=1.5 performs well across various tasks. Proposes robust ABC method for outlier detection.
problem Outliers sensitivity in ABC methods.
method γ-divergence estimator with redescending property.
result Significantly higher robustness than existing methods.
Information divergence functions play a critical role in statistics and information theory. In this paper we show that a non-parametric f-divergence measure can be used to provide improved bounds on the minimum binary classification probability of error for the case when the training and test data are drawn from the sa…