New α-divergence loss function improves neural density ratio estimation.
problem Optimization challenges in existing DRE methods, especially overfitting and high sample requirements.
method Derived α-divergence loss function (α-Div) for neural density ratio estimation. result The α-divergence loss function (α-Div) offers stable and effective optimization for DRE. 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.
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.
The paper improves semi-supervised learning using f-divergences and α-Rényi divergences.
problem Improving semi-supervised learning with noisy pseudo-labels.
method Inspired by f-divergences and α-Rényi divergences, the paper develops new empirical risk functions and regularization techniques. result The new methods show better performance than traditional self-training methods, especially in noisy pseudo-label scenarios.
Classifies divergence and thickness in right-angled Coxeter groups.
problem Characterizing the divergence and thickness of right-angled Coxeter groups.
method Completely classifies divergence functions and proves conditions for thickness using the hypergraph index.
result Exact divergence functions of RACGs can be computed from their defining graphs.
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. Study explores relationship between Hölder and FDPD divergences.
problem Understanding the relationship between Hölder and FDPD divergences.
method Intersection and generalization of divergence families, proving nonnegativity, deriving inequalities.
result Established ξ-Hölder divergence and derived inequalities. In the field of statistics, many kind of divergence functions have been studied as an amount which measures the discrepancy between two probability distributions. In the differential geometrical approach in statistics (information geometry), dually flat spaces play a key role. In a dually flat space, there exist dual a…
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.
A recently introduced canonical divergence D for a dual structure (g,∇,∇∗) is discussed in connection to other divergence functions. Finally, open problems concerning symmetry properties are outlined.
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 …
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…
Unified deep metric learning approach using neural networks.
problem Learning embeddings of data and extending Euclidean distances.
method Deep Bregman divergences based on neural networks.
result Superior performance on benchmark datasets compared to existing methods.
The paper explores how information geometry impacts classical CR inequalities.
problem Deriving and generalizing CR inequalities using information geometry.
method Examining Eguchi's theory and applying Amari-Nagoaka's theory to KL-divergence, and then extending to other divergences.
result Generalized CR inequalities derived from various divergences.
Upper bound found for divergence-free Killing 2-tensors on manifolds.
problem Bounding the space of divergence-free symmetric Killing 2-tensors.
method Witten deformation and Morse function analysis.
result Explicit calculation of dimension for p=2. Generative adversarial networks (GANs) can be interpreted as an adversarial game between two players, a discriminator D and a generator G, in which D learns to classify real from fake data and G learns to generate realistic data by "fooling" D into thinking that fake data is actually real data. Currently, a dominating …
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. 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.
In high-dimensional data, many sparse regression methods have been proposed. However, they may not be robust against outliers. Recently, the use of density power weight has been studied for robust parameter estimation and the corresponding divergences have been discussed. One of such divergences is the γ-divergence a…
AES uses α-divergence to select informative points for BO, improving optimization performance.
problem Optimizing complex functions with limited evaluations.
method AES uses α-divergence to select points based on dependency with global maximum.
result AES outperforms other information-based acquisition functions in various experiments.
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.
New analysis of annealing paths in sampling and estimation.
problem Sampling from complex distributions and estimating normalization constants.
method Extending known results on Bregman divergence to quasi-arithmetic means under monotonic embedding.
result Analogous result for quasi-arithmetic means, highlighting the interplay between means, parametric families, and divergence functionals.
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 paper develops inequalities for log-concave functions and related surface areas.
problem Understanding log-concave functions and their inequalities.
method Establishing new inequalities through f-divergences and functional affine surface areas.
result New inequalities on functional affine surface area and bounds for Kullback-Leibler divergence.
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. We describe the underlying probabilistic interpretation of alpha and beta divergences. We first show that beta divergences are inherently tied to Tweedie distributions, a particular type of exponential family, known as exponential dispersion models. Starting from the variance function of a Tweedie model, we outline how…
Study compares chi-squared divergence and KL-divergence posteriors for PAC-Bayesian bounds.
problem Investigates optimal posteriors for PAC-Bayesian bounds using chi-squared divergence.
method Analyzes bounds for three distance functions, derives FP equations for computation.
result Chi-squared divergence based posteriors have weaker bounds and worse test errors.
We introduce a new approximation of f-divergences for machine learning.
problem Variational representations of f-divergences for machine learning. method Definition and analysis of Moreau-Yosida approximation of f-divergences with the Wasserstein-1 metric. result Generalization and relaxation of hard Lipschitz constraints in f-divergences. Optimal transport with f-divergence regularization using generalized Sinkhorn algorithm.
problem Optimal transport with f-divergence regularization. method Generalized Sinkhorn algorithm for solving optimal transport problems with various f-divergences. result Strong duality holds, optimums are attained, and convergence to an optimal solution is guaranteed under certain conditions.
Neural networks estimate statistical divergences with performance guarantees.
problem Estimating statistical divergences with theoretical performance guarantees.
method Parametrizing empirical variational form by a neural network and optimizing over parameter space.
result Established non-asymptotic absolute error bounds for neural estimators of four f-divergences. Paper introduces symmetric divergence link models for probability distributions.
problem Symmetric divergence measures for probability distributions.
method Two general classes of link models: one for survival functions and another for cumulative probability distribution functions.
result Advantages of symmetric divergence measures over asymmetric measures for model averaging and feature assessment.
Paper introduces a new method for learning Bregman divergence from data.
problem Suboptimal performance of classic distance metrics in deep metric learning.
method Learning empirical Bregman divergence from data using deep learning.
result Empirical Bregman divergence method outperforms other methods on public datasets.
Proposes a new loss function for learning with noisy labels.
problem Improving model learnability with noisy labels.
method Uses generalized Jensen-Shannon divergence as a noise-robust loss function.
result Shows state-of-the-art results on noisy data.
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.
An optimal feedback controller for a given Markov decision process (MDP) can in principle be synthesized by value or policy iteration. However, if the system dynamics and the reward function are unknown, a learning agent must discover an optimal controller via direct interaction with the environment. Such interactive d…
Dual optimization connects ERM-fDR to normalization function.
problem Empirical risk minimization with f-divergence regularization.
method Dual formulation, Legendre-Fenchel transform, implicit function theorem, nonlinear ODE.
result Computational method to calculate normalization function efficiently.
In this paper we investigate the higher dimensional divergence functions of mapping class groups of surfaces and of CAT(0)--groups. We show that, for mapping class groups of surfaces, these functions exhibit phase transitions at the rank (as measured by thrice the genus plus the number of punctures minus 3). We also pr…
This work develops a unified framework for RLHF with general f-divergence regularization.
problem Theoretical understanding of general f-divergence regularization in RLHF. method Holistic approach across f-divergence class, two algorithms based on distinct sampling principles. result Provably efficient algorithms with O(logT) regret and O(1/T) sub-optimality gap. New bounds for estimating partition functions under bounded f-divergence.
problem Estimating partition functions with limited sample access.
method Information-theoretic characterization using integrated coverage profile and f-divergences. result Sharp phase transitions in sample complexity under f-divergences. To ensure stability of learning, state-of-the-art generalized policy iteration algorithms augment the policy improvement step with a trust region constraint bounding the information loss. The size of the trust region is commonly determined by the Kullback-Leibler (KL) divergence, which not only captures the notion of d…
Optimal payoff choice constrained by Bregman-Wasserstein divergence.
problem Maximizing utility under a deviation constraint from a benchmark.
method Solving the problem using Bregman-Wasserstein divergence with a convex function φ.
result Provided the optimal payoff choice in this setting.
Bregman divergences generalize measures such as the squared Euclidean distance and the KL divergence, and arise throughout many areas of machine learning. In this paper, we focus on the problem of approximating an arbitrary Bregman divergence from supervision, and we provide a well-principled approach to analyzing such…
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.
Proposes practical kernel tests for f-divergences with theoretical guarantees.
problem Two-sample testing and machine unlearning evaluation.
method Regularized f-divergence kernel tests, adaptive to hyperparameters. result Different f-divergences highlight localized differences. Unified technique for sequential estimation of convex divergences.
problem Estimating convex divergences between distributions.
method Martingale methods and maximal inequalities for reverse submartingales.
result Valid time-uniform confidence sequences for arbitrary stopping times.
New algorithm speeds up NMF with β-divergence.
problem Efficiently factorize nonnegative matrices with β-divergence. method Joint majorization-minimization with multiplicative updates.
result Significant reduction in computation time for NMF.
This work explores function-space inference using KL divergence and proposes Bayesian linear regression as a benchmark.
problem Approximating the predictive posterior distribution of Bayesian models without parameter posterior approximation.
method Employing Kullback-Leibler divergence and proposing featurized Bayesian linear regression as a benchmark.
result Minimizing KL divergence leads to an ill-defined objective function, highlighting limitations of this approach.
New method tightens variational representations of divergences for faster learning.
problem Improving tightness of variational representations of divergences for faster statistical estimation.
method Improved objective functionals constructed via an auxiliary optimization problem, leveraging neural network approximation.
result Tighter variational representations can result in significantly faster learning and more accurate estimation of divergences.