Predictability, Stability, and Computability of Locally Learnt SVMs

We will have a look at the principles predictability, stability, and computability in the field of support vector machines. Support vector machines (SVMs), well-known in machine learning, play a successful role in classification and regression in many areas of science. In the past three decades, much research has been conducted on the statistical and computational properties of support vector machines and related kernel methods. On the one hand, consistency (predictability) and robustness (stability) of the method are of interest. On the other hand, from an applied point of view, there is interest in a method that can deal with many observations and many features (computability). Since SVMs require a lot of computing power and storage capacity, various possibilities for processing large data sets have been proposed. One of them is called regionalization. It divides the space of declaring variables into possibly overlapping domains in a data driven way and defines the function to predict the output by the formation of locally learnt support vector machines. Another advantage of regionalization should be mentioned. If the generating distribution in different regions of the input space has different characteristics, learning only one “global” SVM may lead to an imprecise estimate. Locally trained predictors can overcome this problem. It is possible to show that a locally learnt predictor is consistent and robust under assumptions that can be checked by the user of this method

On the Connection between LpL_p and Risk Consistency and its Implications on Regularized Kernel Methods

As a predictor's quality is often assessed by means of its risk, it is natural to regard risk consistency as a desirable property of learning methods, and many such methods have indeed been shown to be risk consistent. The first aim of this paper is to establish the close connection between risk consistency and $L_p$-consistency for a considerably wider class of loss functions than has been done before. The attempt to transfer this connection to shifted loss functions surprisingly reveals that this shift does not reduce the assumptions needed on the underlying probability measure to the same extent as it does for many other results. The results are applied to regularized kernel methods such as support vector machines.Comment: 33 pages, 1 figur

The role of the host in a cooperating mainframe and workstation environment, volumes 1 and 2

In recent years, advancements made in computer systems have prompted a move from centralized computing based on timesharing a large mainframe computer to distributed computing based on a connected set of engineering workstations. A major factor in this advancement is the increased performance and lower cost of engineering workstations. The shift to distributed computing from centralized computing has led to challenges associated with the residency of application programs within the system. In a combined system of multiple engineering workstations attached to a mainframe host, the question arises as to how does a system designer assign applications between the larger mainframe host and the smaller, yet powerful, workstation. The concepts related to real time data processing are analyzed and systems are displayed which use a host mainframe and a number of engineering workstations interconnected by a local area network. In most cases, distributed systems can be classified as having a single function or multiple functions and as executing programs in real time or nonreal time. In a system of multiple computers, the degree of autonomy of the computers is important; a system with one master control computer generally differs in reliability, performance, and complexity from a system in which all computers share the control. This research is concerned with generating general criteria principles for software residency decisions (host or workstation) for a diverse yet coupled group of users (the clustered workstations) which may need the use of a shared resource (the mainframe) to perform their functions