Technical report on f-divergences and f-GAN training properties.
problem Understanding and optimizing f-divergences for GAN training.
method Elementary derivation and detailed expressions of f-divergences and their variational lower bounds.
result Informative properties of f-divergences and f-GAN training, including gradient matching and stability improvements.
Risk measures linked to information divergences via a one-to-one correspondence.
problem Linking risk measures to information divergences for analysis.
method Defining and analyzing divergences as functionals of probability measures, linking their properties to risk measure properties.
result Relative entropy is the only divergence satisfying the chain rule for law invariant risk 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.
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.
A new divergence measure detects classifier incongruence more effectively.
problem Detecting incongruence between classifiers in pattern recognition.
method Proposes Delta divergence, a decision-aware measure.
result Delta divergence outperforms existing measures in detecting incongruence.
Discusses a new divergence function in information geometry.
problem Symmetry properties of divergence functions in information geometry.
method Analyzes a recently introduced canonical divergence function.
result Outlines open problems regarding symmetry properties.
Paper proposes f-EBM for training deep EBMs using various f-divergences.
problem Training deep EBMs with intractable partition functions.
method Introduces f-EBM framework and optimization algorithm for any f-divergence.
result f-EBM outperforms contrastive divergence and other f-divergences.
New divergences extend Bregman and skew Jensen, including f-divergences.
problem Developing new divergences to include f-divergences.
method Introducing g-Bregman and skew g-Jensen divergences, showing they include f-divergences.
result g-divergences generalize existing divergences and inequalities.
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 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. New proof finds three divergence-free vector fields for any 3D manifold.
problem Proving the existence of divergence-free vector fields on 3D manifolds.
method Using geometric properties of eigenspinors in three dimensions.
result Found three divergence-free vector fields that are orthogonal and have the same length at every point.
Paper studies regularized KKL divergence for distributions with disjoint supports.
problem Inability of original KKL divergence to handle distributions with disjoint supports.
method Proposes a regularized variant of KKL divergence, derives bounds, and provides closed-form expression.
result Regularized KKL divergence is well-defined for all distributions and has finite-sample bounds.
New divergences introduced in dually flat spaces with properties.
problem Measuring discrepancy between probability distributions in dually flat spaces.
method Introducing two types of divergences based on affine coordinates and potentials, and deriving relational equations.
result Generalization of the law of cosines and new inequalities between divergences.
Parametric divergences are effective for generative modeling despite being non-optimal.
problem Training high-dimensional distributions with GANs.
method Generalization of GAN losses to parametric divergences, focusing on sensitivity to specific distribution moments.
result Parametric divergences are more suitable for learning high-dimensional distributions due to their sensitivity to specific aspects of the distribution.
Proposes tail-adaptive f-divergences for better inference.
problem Inference difficulties with heavy-tailed importance weights.
method Tail-adaptive f-divergences that change convex function with importance weights tail.
result Significant advantages over classical KL and α-divergences.
This paper re-examines Bregman functions and their divergences, introducing new properties and functions.
problem Exploring properties and applications of Bregman functions and divergences.
method Re-examination of existing Bregman functions and introduction of new ones, providing sufficient conditions for construction.
result Several known Bregman functions are reclassified, and new Bregman functions are introduced.
Unified representation of density-power-based divergences simplifies estimation to M-estimation.
problem Outliers in density estimation.
method Define a norm-based Bregman density power divergence (NB-DPD) that reduces to M-estimation.
result NB-DPD connects and generalizes existing divergences, highlighting robustness properties.
This work improves convergence guarantees for unadjusted HMC in KL and Rényi divergences.
problem Understanding convergence properties of unadjusted HMC in divergences like KL and Rényi.
method One-shot couplings to establish regularization and lift convergence bounds.
result Quantitative control of relative density mismatch and warm-start requirements.
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…
New entropies and divergences defined using group theory.
problem Defining new entropies and divergences with group-theoretical properties.
method Formal group theory and information geometry to construct new entropies and divergences.
result A method for constructing new entropies and divergences from known ones.
This work investigates the properties of Gaussian-smoothed sliced divergences for comparing distributions.
problem Comparing probability distributions while preserving privacy.
method Investigates the theoretical properties of Gaussian-smoothed sliced Wasserstein distance and generalized versions.
result Gaussian smoothed sliced Wasserstein distance converges with a rate of \(O(n^{-1/2})\).
A new approach to MI learning using bag-to-class divergence.
problem Sparse MI training sets and difficulty in classifying bags.
method Introducing bag-to-class divergence to MI learning, emphasizing hierarchical random vectors.
result Bag-to-class divergence is a more effective classifier for MI learning.
The paper analyzes the statistical properties of GANs using f-divergence.
problem Understanding the statistical behavior of GANs and comparing different f-divergences. method Asymptotic analysis of f-divergence GANs, including Kullback-Leibler divergence. result Asymptotically equivalent GANs with the same discriminator classes for correctly specified models.
Rényi divergence is related to Rényi entropy much like Kullback-Leibler divergence is related to Shannon's entropy, and comes up in many settings. It was introduced by Rényi as a measure of information that satisfies almost the same axioms as Kullback-Leibler divergence, and depends on a parameter that is called its or…
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.
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.
Paper presents ERM with f-divergence regularization and its properties.
problem Minimizing empirical risk with f-divergence constraints. method Introduces normalization function and solves ERM-fDR via ODE. result Characterizes difference between empirical risks and provides numerical algorithm.
Paper introduces a new variational objective using Alpha-Beta divergence.
problem Improving variational inference methods for complex distributions.
method Direct optimization of the sAB divergence with two control parameters.
result The sAB divergence framework provides a smooth interpolation and trade-offs between distribution properties.
The divergence theorem in its usual form applies only to suitably smooth vector fields. For vector fields which are merely piecewise smooth, as is natural at a boundary between regions with different physical properties, one must patch together the divergence theorem applied separately in each region. We give an elegan…
Develops a new divergence framework that combines f-divergences and IPMs.
problem Comparing distributions that are not absolutely continuous.
method Introduces (f,Γ)-divergences as a two-stage mass-redistribution/mass-transport process. result Improves estimation, learning, and uncertainty quantification in GANs for heavy-tailed distributions.
Improved Bayesian inference using power priors with historical data.
problem Improving Bayesian inference with historical data.
method Generalized power priors that adapt to the α parameter of Amari's α-divergence. result Improved performance through appropriate choices of the α parameter. Unified framework for debiased machine learning using Riesz representer and Bregman divergence.
problem Estimating causal and structural parameters in machine learning.
method Generalized Riesz regression for fitting Riesz representer via Bregman divergence minimization.
result Automatic covariate balancing and Neyman orthogonality properties for debiased estimation.
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. The article recovers tensor fields from partial data using weighted divergent ray transforms.
problem Recovering tensor fields from partial data.
method Weighted divergent ray transforms, unique continuation property of fractional Laplacian, explicit reconstruction formulas.
result Recovery of symmetric m-tensor fields and unique continuation for vector fields and symmetric 2-tensor fields. The paper introduces a new method for estimating optimal policies in dynamic treatment regimes using information geometry.
problem Estimating optimal policies in dynamic treatment regimes.
method Minimum information divergence method based on γ-power divergence. result The γ-power divergence method effectively seeks the optimal policy by vanishing the divergence between policy-equivalent Q-functions. Paper presents efficient feature selection for text categorization.
problem Reducing feature size and speeding up text categorization.
method Develops feature selection methods based on JMH divergence.
result Extensive experiments show the effectiveness of proposed methods.
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. Paper proposes robust and sparse regression using γ-divergence.
problem Sparse regression methods are not robust against outliers.
method Extends γ-divergence to regression problem with sparse regularization and efficient update algorithm.
result The proposed method outperforms past robust and sparse methods in numerical experiments and real data analyses.
A new metric, Cramér distance, solves biased gradients in GANs.
problem Biased gradients in GANs using Wasserstein metric.
method Proposed Cramér distance, which is sum-invariant, scale-sensitive, and unbiased.
result Cramér distance outperforms Wasserstein GAN in practice.
CO2 algorithm creates coresets for generic smooth divergences efficiently.
problem Efficiently creating coresets for generic smooth divergences.
method CO2 algorithm using functional Taylor expansion and maximum mean discrepancy minimization.
result Poly-logarithmically many data points suffice for Sinkhorn divergence approximation.
LDP is equivalent to contraction of E_γ-divergence, impacting privacy and utility.
problem Analyzing trade-offs between privacy and utility in estimation problems.
method Equivalence of LDP constraints to contraction coefficients of E_γ-divergence, using f-divergences and estimation-theoretic tools.
result LDP guarantees can be expressed in terms of contraction coefficients of arbitrary f-divergences.
The paper improves generalization bounds using interpolation between various divergences.
problem Improving generalization bounds in machine learning.
method Derives new PAC-Bayes generalization bounds based on (f,Γ)-divergence and interpolates between various divergences. result Connects derived bounds to earlier statistical learning results and provides practical training objectives.
The problem of f-divergence estimation is important in the fields of machine learning, information theory, and statistics. While several nonparametric divergence estimators exist, relatively few have known convergence properties. In particular, even for those estimators whose MSE convergence rates are known, the asympt…
A new differentiable divergence for time series comparison.
problem Computing discrepancies between time series of varying lengths.
method Proposed a new divergence, soft-DTW divergence, addressing issues of differentiability and positivity.
result Showed that the new divergence is a valid divergence: non-negative and minimized when time series are equal.
New divergences improve estimation and GAN training performance.
problem Improving estimation and training in machine learning models.
method Function-space regularized Rényi divergences.
result New divergences reduce variance and improve training performance.
Diffusion Variational Autoencoders capture topological properties of datasets.
problem Standard VAEs struggle with topological properties of certain datasets.
method Introduces Diffusion VAEs with transition kernels of Brownian motion on arbitrary manifolds.
result Diffusion VAEs can capture topological properties of synthetic datasets.
This work analyzes the statistical properties of adaptive gradient methods.
problem Lack of understanding of the statistical properties of adaptive gradient methods.
method Theoretical analyses and experiments on the variance of update magnitudes.
result The variance of update magnitudes is an increasing and bounded function of time, not diverging.
Boosting framework for vector-valued prediction with geometric stability.
problem Lack of a general theoretical understanding of aggregation for structured prediction.
method Identifies (α,β)-stability property and proposes a boosting framework based on exponential reweighting and geometric-median aggregation. result Obtains exponential decay of empirical divergence error under weak learner condition and (α,β)-stability.