In multi-label classification, where the evaluation of predictions is less straightforward than in single-label various meaningful, though different, loss functions have been proposed. Ideally, learning algorithm should be customizable towards a specific choice performance measure. Modern implementations boosting, most prominently gradient boosted decision trees, appear to appealing from this p...

Abstract: Decomposable graphs are known for their tedious and complicated Markov update steps. Instead of modelling them directly, this work introduces a class of tree-dependent bipartite graphs that span the projective space of decomposable graphs. This is achieved through dimensionality expansion that causes the graph nodes to be conditionally independent given a latent tree. The Markov updat...

The dequantization scheme developed in [1] is modified in the present paper to incorporate the orbital symmetry for a system of two particles. Classical functions on phase space are introduced as expectation values of operators between symmetrized coherent states of the Weyl group. The equations of motion are derived from the timedependent variational principle. An analysis of the classical tra...

Abstract. Given a symmetrized Sobolev inner product of order N , the corresponding sequence of monic orthogonal polynomials {Qn} satisfies Q2n(x) = Pn(x), Q2n+1(x) = xRn(x) for certain sequences of monic polynomials {Pn} and {Rn}. In this paper we consider the particular case when all the measures that define the symmetrized Sobolev inner product are equal, absolutely continuous and semiclassic...

In this paper some types of decomposable signed fuzzy measures have been presented. We discuss properties of 6-and ⊕decomposable signed fuzzy measures. We consider their relationship with bi-capacities.

Throughout this study, the concept of symmetrized harmonically convex stochastic processes will be discussed in further detail. Some certain characterizations for are that use Hermite–Hadamard-type inequalities. A Hyers–Ulam-type stability result is given as well.

In this paper, we study the symmetrized Talagrand inequality that was proved by Fathi and has a connection with Blaschke-Santaló in convex geometry. As corollaries of our results, have several refined functional inequalities under some conditions. We also give an alternative proof Fathi's on real line.