Recently, several blind signal separation algorithms have been developed which are based on second order statistics. Little has been published however on whether second order statistics are sufficient to obtain a unique solution. Especially for applications that involve convolutive mixing and unmixing of signals that are correlated in time, there is a lack of knowledge on why and in what cases ...

While Kolmogorov complexity is the accepted absolute measure of information content of an individual finite object, a similarly absolute notion is needed for the relation between an individual data sample and an individual model summarizing the information in the data, for example, a finite set (or probability distribution) where the data sample typically came from. The statistical theory based...

Strong laws of large numbers are given for L-statistics (linear com­ binations of order statistics) and for U -statistics (averages of kernels of ran­ dom samples) for ergodic stationary processes, extending classical theorems of Hoeffding and of Helmers for iid sequences. Examples are given to show that strong and even weak convergence may fail if the given sufficient conditions are not satisf...

There are many settings in which we wish to fit a model of the behavior of individuals but where our data consist only of aggregate information (counts or low-dimensional contingency tables). This paper introduces Collective Graphical Models—a framework for modeling and probabilistic inference that operates directly on the sufficient statistics of the individual model. We derive a highlyefficie...

This paper is about the use of metric data structures in high-dimensional or non-Euclidean space to permit cached sufficient statistics accelerations of learning algorithms. It has recently been shown that for less than about 10 dimensions, decorating kd-trees with additional "cached sufficient statistics" such as first and second moments and contingency tables can provide satisfying accelerati...

Information geometry provides a geometric approach to families of statistical models. The key geometric structures are the Fisher quadratic form and the Amari-Chentsov tensor. In statistics, the notion of sufficient statistic expresses the criterion for passing from one model to another without loss of information. This leads to the question how the geometric structures behave under such suffic...

In this paper, we develop a comprehensive framework forre-optimization of a large and useful set of queries, called repetitive queries. Repetitive queries refer tothosequeries that are likely to be used repeatedly or frequently in the future. Theydeserve more optimization efforts than ordinary ad hoc queries. In this research, weidentify statistics, called sufficient statistics,that are suffici...