Shape restrictions such as monotonicity on functions often arise naturally in statistical modeling. We consider a Bayesian approach to the estimation of monotone regression function and testing for monotonicity. construct prior distribution using piecewise constant functions. For estimation, imposing heights these steps is sensible, but resulting posterior harder analyze theoretically. “project...

We construct a regular random projection of metric space onto closed doubling subset and use it to linearly extend Lipschitz C1 functions. This way we prove more directly result by Lee Naor [5] generalize the extension theorem Whitney [8] Banach spaces.

In this article we study some geometric properties of proximally smooth sets. First, introduce a modification the metric projection and prove its existence. Then provide an algorithm for constructing rectifiable curve between two sufficiently close points set in uniformly convex Banach space, with moduli smoothness convexity power type. Our returns reasonably short set, is iterative uses our pr...

The present note deals with the dynamics of metric connections with vectorial torsion, as already described by E. Cartan in 1925. We show that the geodesics of metric connections with vectorial torsion defined by gradient vector fields coincide with the Levi-Civita geodesics of a conformally equivalent metric. By pullback, this yields a systematic way of constructing invariants of motion for su...

We consider the problem of learning a distance metric from a limited amount of pairwise information as effectively as possible. The proposed SERAPH (SEmi-supervised metRic leArning Paradigm with Hyper sparsity) is a direct and substantially more natural approach for semi-supervised metric learning, since the supervised and unsupervised parts are based on a unified information theoretic framewor...

This paper introduces a semi-supervised distance metric learning algorithm which uses pairwise equivalence (similarity and dissimilarity) constraints to discover the desired groups within high-dimensional data. In contrast to the traditional full rank distance metric learning algorithms, the proposed method can learn nonsquare projection matrices that yield low rank distance metrics. This bring...

This paper describes a semi-supervised distance metric learning algorithm which uses pairwise equivalence (similarity and dissimilarity) constraints to discover the desired groups within high-dimensional data. As opposed to the traditional full rank distance metric learning algorithms, the proposed method can learn nonsquare projection matrices that yield low rank distance metrics. This brings ...

Suppose M a compact manifold which admits an Einstein metric g which is Kähler with respect to some complex structure J . Is every other Einstein metric h on M also Kähler-Einstein? If the complex dimension of (M,J) is ≥ 3, the answer is generally no; for example, CP3 admits both the FubiniStudy metric, which is Kähler-Einstein, and a non-Kähler Einstein metric [2] obtained by appropriately squ...