In the past decades, intensive efforts have been put to design various loss functions and metric forms for metric learning problem. These improvements have shown promising results when the test data is similar to the training data. However, the trained models often fail to produce reliable distances on the ambiguous test pairs due to the distribution bias between training set and test set. To a...

Fully observable decision-theoretic planning problems are commonly modeled as stochastic shortest path (SSP) problems. For this class of planning problems, heuristic search algorithms (including LAO*, RTDP, and related algorithms), as well as the value iteration algorithm on which they are based, lack an efficient test for convergence to an -optimal policy (except in the special case of discoun...

Annotation learning is an important task for many kinds of text analysis. Statistical machine learning techniques have been developed to learn annotation models over labeled data that are then used to annotate unlabeled data. One of the major bottlenecks of a conventional machine learning approach is getting sufficient pre-labeled training data: annotating text is a time consuming, tedious and ...

The goal of this work is to investigate the relation of the no-response approach to some other non-iterative reconstruction schemes. We will derive several equivalence statements and dependency results. For simplicity we consider the obstacle reconstruction problem from far field data. In particular, we investigate two versions of the no-response test (NRT) for the inverse scattering problem. T...

We study the convergence of GMRES/FOM and QMR/BiCG methods for solving nonsymmetric Ax = b. We prove that given the results of a BiCG computation on Ax = b, we can obtain a matrix B with the same eigenvalues as A and a vector c such that the residual norms generated by a FOM computation on Bx = c are identical to those generated by the BiCG computations. Using a unitary equivalence for each of ...

In this paper the pointwise approximation of the Bézier variant of Chlodowsky operators for bounded variation functions is studied. By means of the analysis techniques and some results of probability theory, we obtain an estimate formula on this type approximation. Our results correct the mistake of Karsli and Ibikli [H. Karsli and E. Ibikli, Convergence rate of a new Bézier variant of Chlodows...

There is now an extensive empirical literature relating to tests for various forms of convergence between the real per capita outputs of different countries. The evidence from these tests is mixed, and depends upon the type of data used, the countries in question, and the sample period in question. However, very little attention has been paid to the possibility of an associated convergence in “...

in this paper‎, ‎following a very recent‎ ‎and new approach‎, ‎we further generalize recently introduced‎ ‎summability methods‎, ‎namely‎, ‎$i$-statistical convergence and‎ ‎$i$-lacunary statistical convergence (which extend the important‎ ‎summability methods‎, ‎statistical convergence and lacunary‎ ‎statistical convergence using ideals of $mathbb{n}$) and‎ ‎introduce the notions of $i$-statis...

We consider the weak convergence of numerical methods for stochastic differential equations (SDEs). Weak convergence is usually expressed in terms of the convergence of expected values of test functions of the trajectories. Here we present an alternative formulation of weak convergence in terms of the well-known Prokhorov metric on spaces of random variables. For a general class of methods, we ...

degenerate kernel approximation method is generalized to solve hammerstein system of fredholm integral equations of the second kind. this method approximates the system of integral equations by constructing degenerate kernel approximations and then the problem is reduced to the solution of a system of algebraic equations. convergence analysis is investigated and on some test problems, the propo...