We construct an algorithm for estimating the mean of a heavy-tailed random variable when given adversarial corrupted sample N independent observations. The only assumption we make on distribution noncorrupted (or informative) data is existence covariance matrix Σ, unknown to statistician. Our outputs μˆ, which robust presence |O| outliers and satisfies (1)‖μˆ−μ‖2≲ Tr(Σ) N+ ‖Σ‖opK with probabili...

The problem of portfolio choice is an example of sequential decision making under uncertainty. Investors must consider their attitudes towards risk and reward in face of an unknown future, in order to make complex financial choices. Often, mathematical models of investor preferences and asset return dynamics aid in this process, resulting in a wide range of portfolio choice paradigms, one of wh...

In this paper, we prove a generalized integral inequality for submanifolds with parallel mean curvature vector in an arbitrary Riemannian manifold, and from which we obtain a pinching theorem for compact oriented submanifolds with parallel mean curvature vector in a complete simply connected pinched Riemannian manifold, which generalizes the results obtained by Alencar-do Carmo and Hong-Wei Xu.

This paper deals with two subjects. First, we will show how support vector machine (SVM) regression problem can be solved as the maximum a posteriori prediction in the Bayesian framework. The second part describes an approximation technique that is useful in performing calculations for SVMs based on the mean ÿeld algorithm which was originally proposed in Statistical Physics of disordered syste...

In recent years, gradient vector flow (GVF) based algorithms have been successfully used to segment a variety of 2-D and 3-D imagery. However, due to the compromise of internal and external energy forces within the resulting partial differential equations, these methods may lead to biased segmentation results. In this paper, we propose MSGVF, a mean shift based GVF segmentation algorithm that c...

Since Stein’s original proposal in 1962, a series of papers have constructed confidence regions of smaller volume than the standard spheres for the mean vector of a multivariate normal distribution. A general approach to this problem is developed here, and used to calculate a lower bound on the attainable volume. Bayes and fiducial methods are involved in the calculation. Scheffe-type problems ...