arXiv research

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…

This work extends alpha-beta divergences to complex data and finds closed-form solutions.

The paper provides estimates for eigenvalues of elliptic differential problems.

New $f$-divergence measures improve robustness in noisy label learning.

This paper proposes the divergence triangle as a framework for joint training of generator model, energy-based model and inference model. The divergence triangle is a compact and symmetric (anti-symmetric) objective function that seamlessly integrates variational learning, adversarial learning, wake-sleep algorithm, an…

Study local invariants of divergence-free webs in geometry.

Global solutions found for a wave-Klein-Gordon system with strong couplings in divergence form.

Information-theoretic measures such as the entropy, cross-entropy and the Kullback-Leibler divergence between two mixture models is a core primitive in many signal processing tasks. Since the Kullback-Leibler divergence of mixtures provably does not admit a closed-form formula, it is in practice either estimated using …

We extend the recently introduced theory of Lovasz-Bregman (LB) divergences (Iyer & Bilmes 2012) in several ways. We show that they represent a distortion between a "score" and an "ordering", thus providing a new view of rank aggregation and order based clustering with interesting connections to web ranking. We show ho…

We extend the recently introduced theory of Lovasz-Bregman (LB) divergences (Iyer & Bilmes, 2012) in several ways. We show that they represent a distortion between a 'score' and an 'ordering', thus providing a new view of rank aggregation and order based clustering with interesting connections to web ranking. We show h…

We establish a method for giving lower bounds for the fundamental tone of elliptic operators in divergence form in terms of the divergence of vector fields. We then apply this method to the $L_{r}$ operator associated to immersed hypersurfaces with locally bounded $(r+1)$-th mean curvature $H_{r+1}$ of the space forms …

We consider the nonlinear Kalman filtering problem using Kullback-Leibler (KL) and $α$-divergence measures as optimization criteria. Unlike linear Kalman filters, nonlinear Kalman filters do not have closed form Gaussian posteriors because of a lack of conjugacy due to the nonlinearity in the likelihood. In this paper …

The paper finds inequalities for eigenvalues of operators on immersed manifolds.

Technical report on f-divergences and f-GAN training properties.

E$^2$M optimizes tensor density estimation by relaxing $α$-divergence to KL-divergence.

Study on geometric Jensen-Shannon divergence for Gaussian measures in Hilbert space.

This work presents a parametrized family of divergences, namely Alpha-Beta Log- Determinant (Log-Det) divergences, between positive definite unitized trace class operators on a Hilbert space. This is a generalization of the Alpha-Beta Log-Determinant divergences between symmetric, positive definite matrices to the infi…

Study finds rigidity of biconservative hypersurfaces in space forms without curvature assumptions.

In this paper, we study eigenvalue of linear fourth order elliptic operators in divergence form with Dirichlet boundary condition on a bounded domain in a compact Riemannian manifolds with boundary (possibly empty) and find a general inequality for them. As an application, by using this inequality, we study eigenvalues…

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…

New proof finds three divergence-free vector fields for any 3D manifold.

We prove the Reilly formula for a class of elliptic divergence differential operator $L_Au=div(A\nabla u)$, where $A$ is a (1,1)-Codazzi tensor field. Then we get some estimates for the first positive eigenvalue of the operator.

New proof of Willmore inequality using geometric divergence inequality.

New bounds for Neyman-Pearson region using $f$-divergences.

Study optimal transport costs with zero MTW tensor, finding new families of costs and divergence functions.

The paper analyzes the bias-variance tradeoff for Bregman divergences.

The t-distributed Stochastic Neighbor Embedding (t-SNE) is a powerful and popular method for visualizing high-dimensional data. It minimizes the Kullback-Leibler (KL) divergence between the original and embedded data distributions. In this work, we propose extending this method to other f-divergences. We analytically a…

Reformulates divergence map for Turaev cobracket in non-commutative geometry.

DAIS minimizes symmetrized KL divergence between initial and target distributions.

New metrics defined on SPD matrices link to divergences and curvature.

The paper analyzes insurance contracts under distributional uncertainty using Bregman-Wasserstein divergence.

The study proves inequalities for complex operators on curved spaces.

Unified view of KL-divergence and IPMs via DRE, with new DRM metrics.

Study introduces a variational approach for efficient KL divergence estimation in Dirichlet mixture models.

Paper proposes f-DPG for aligning language models with preferences.

Paper calculates KL divergence for isotropic Gaussian-Markov fields.

This paper introduces Wasserstein variational inference, a new form of approximate Bayesian inference based on optimal transport theory. Wasserstein variational inference uses a new family of divergences that includes both f-divergences and the Wasserstein distance as special cases. The gradients of the Wasserstein var…

This work studies Gaussian geometry under entropy-regularized 2-Wasserstein distance.

On non-Kähler manifolds the notion of harmonic maps is modified to that of Hermitian harmonic maps in order to be compatible with the complex structure. The resulting semilinear elliptic system is {\it not} in divergence form. The case of noncompact complete preimage and target manifolds is considered. We give conditio…

We introduce the notion of biconservative hypersurfaces, that is hypersurfaces with conservative stress-energy tensor with respect to the bienergy. We give the (local) classification of biconservative surfaces in 3-dimensional space forms.

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…

New Lie-group methods preserve geometric divergence-free features on manifolds.

Efficiently visualizes uncertainty in local divergence of 2D vector fields.

Paper studies regularized KKL divergence for distributions with disjoint supports.

New method minimizes robust density power-based divergences for general parametric densities.

Black box variational inference (BBVI) with reparameterization gradients triggered the exploration of divergence measures other than the Kullback-Leibler (KL) divergence, such as alpha divergences. In this paper, we view BBVI with generalized divergences as a form of estimating the marginal likelihood via biased import…

We succeed in writing 2-dimensional conformally invariant non-linear elliptic PDE (harmonic map equation, prescribed mean curvature equations...etc) in divergence form. This divergence free quantities generalize to target manifolds without symmetries the well known conservation laws for harmonic maps into homogeneous s…

Neural networks estimate statistical divergences with performance guarantees.