Software for computing eigenvalues and invariant subspaces of general matrix products is proposed. The implemented algorithms are based on orthogonal transformations of the original data and thus attain numerical backward stability, which enables good accuracy even for small eigenvalues. The prospective toolbox combines the efficiency and robustness of library-style Fortran subroutines based on...

We introduce a new notion of algorithmic stability, which we call training stability. We show that training stability is sufficient for good bounds on generalization error. These bounds hold even when the learner has infinite VC dimension. In the PAC setting, training stability gives necessary and sufficient conditions for exponential convergence, and thus serves as a distribution-dependent ana...

This paper presents a theoretical analysis of sample selection bias correction. The sample bias correction technique commonly used in machine learning consists of reweighting the cost of an error on each training point of a biased sample to more closely reflect the unbiased distribution. This relies on weights derived by various estimation techniques based on finite samples. We analyze the effe...

This paper is about omitting types in logic of metric structures introduced by Ben Yaacov, Berenstein, Henson and Usvyatsov. While a complete type is omissible in some model of a countable complete theory if and only if it is not principal, this is not true for the incomplete types by a result of Ben Yaacov. We prove that there is no simple test for determining whether a type is omissible in a ...

We study the singularity formation of smooth solutions of the relativistic Euler equations in (3 + 1)-dimensional spacetime for both finite initial energy and infinite initial energy. For the finite initial energy case, we prove that any smooth solution, with compactly supported non-trivial initial data, blows up in finite time. For the case of infinite initial energy, we first prove the existe...

The Wisdom of Crowds, an innovative theory described in social science, claims that the aggregate decisions made by a group will often be better than those of its individual members if the four fundamental criteria of this theory are satisfied. This theory used for in clustering problems. Previous researches showed that this theory can significantly increase the stability and performance of...

EEcient, large-scale estimation methods such as nested dissection or multiscale estimation rely on a divide-and-conquer strategy, in which a statistical problem is conditionally broken into smaller pieces. This conditional decorrelation is not possible for arbitrarily large problems due to issues of computational complexity and numerical stability. Given the growing interest in global-scale rem...

In any two-sided matching market, a stable matching can be found by a central agency using the deferred acceptance procedure of Gale and Shapley. But if the market is decentralized and information is incomplete then stability of the ensuing matching is not to be expected. Despite the prevalence of such matching situations, and the importance of stability, little theory exists concerning instabi...

This paper uses the notion of algorithmic stability to derive novel generalization bounds for several families of transductive regression algorithms, both by using convexity and closed-form solutions. Our analysis helps compare the stability of these algorithms. It also shows that a number of widely used transductive regression algorithms are in fact unstable. Finally, it reports the results of...