While Bregman divergences [3] have been used for several machine learning problems in recent years, the facts that they are asymmetric and does not satisfy triangle inequality have been a major limitation. In this paper, we investigate the relationship between two families of symmetrized Bregman divergences and metrics, which satisfy the triangle inequality. Further, we investigate kmeans-type ...

In this talk we are first going to state the so-called ’Representation Theorem’ which provides the representation of general f -divergences in terms of the class of elementary divergences. Then we consider the risk set of a (simple versus simple) testing problem and its characterization by the above mentioned class. These ingredients enable us to prove a sharpening of the ’Range of Values Theor...

We unify f -divergences, Bregman divergences, surrogate loss bounds (regret bounds), proper scoring rules, matching losses, cost curves, ROC-curves and information. We do this by systematically studying integral and variational representations of these objects and in so doing identify their primitives which all are related to cost-sensitive binary classification. As well as clarifying relations...

Light front field theories are known to have the usual infra-red divergences of the equal time theories, as well as new ‘spurious’ infra-red divergences. The former kind of IR divergences are usually treated by giving a small mass to the gauge particle. An alternative method to deal with these divergences is to calculate the transition matrix elements in a coherent state basis. In this paper we...

We used correlated divergence analysis to determine which factors have been most closely associated with changes in seed mass during seed plant evolution. We found that divergences in seed mass have been more consistently associated with divergences in growth form than with divergences in any other variable. This finding is consistent with the strong relationship between seed mass and growth fo...

f -divergences form a class of measures of distance between probability distributions; they are widely used in areas such as information theory and signal processing. In this paper, we unveil a new connection between f -divergences and differential privacy, a confidentiality policy that provides strong privacy guarantees for private data-mining; specifically, we observe that the notion of α-dis...

In theories with extra dimensions the Standard Model Higgs field can be identified with the internal components of higher-dimensional gauge fields (Higgs-gauge unification). The higherdimensional gauge symmetry prevents the Higgs mass from quadratic divergences, but at the fixed points of the orbifold this symmetry is broken and divergences can arise if U(1) subgroups are conserved. We show tha...

Evolution of montane species may be strongly influenced by climate oscillations, particularly species distributed in isolated high-elevation areas (sky islands). Chilean topography is exemplified by montane environments including the Andes and Coastal Mountains. To test hypotheses related to genetic divergence associated with sky islands, we explored population genetics and phylogenetic signatu...

In this paper, the Bregman and Burbea-Rao divergences for matrices are investigated. Two mean-value theorems for the divergences induced by C-functions are derived. As application, certain Cauchy type means of the entries of the matrices are constructed. By utilizing three classes of parametrized convex functions, the exponential convexity of the divergences, thought as a function of the parame...

Using set-theoretic considerations, we show that the forest formula for overlapping divergences comes from the Hopf algebra of rooted trees. Motivation and Introduction The process of renormalization is governed by the forest formula, as derived for example in [1]. The underlying combinatorics is directly related to the Hopf algebra structure of rooted trees. This is evident in the case of Feyn...