A New Framework for Join Product Skew

Different types of data skew can result in load imbalance in the context of parallel joins under the shared nothing architecture. We study one important type of skew, join product skew (JPS). A static approach based on frequency classes is proposed which takes for granted the data distribution of join attribute values. It comes from the observation that the join selectivity can be expressed as a sum of products of frequencies of the join attribute values. As a consequence, an appropriate assignment of join sub-tasks, that takes into consideration the magnitude of the frequency products can alleviate the join product skew. Motivated by the aforementioned remark, we propose an algorithm, called Handling Join Product Skew (HJPS), to handle join product skew

Unachievable Region in Precision-Recall Space and Its Effect on Empirical Evaluation

Precision-recall (PR) curves and the areas under them are widely used to summarize machine learning results, especially for data sets exhibiting class skew. They are often used analogously to ROC curves and the area under ROC curves. It is known that PR curves vary as class skew changes. What was not recognized before this paper is that there is a region of PR space that is completely unachievable, and the size of this region depends only on the skew. This paper precisely characterizes the size of that region and discusses its implications for empirical evaluation methodology in machine learning.Comment: ICML2012, fixed citations to use correct tech report numbe

Weak topologies for Carath\'eodory differential equations. Continuous dependence, exponential Dichotomy and attractors

We introduce new weak topologies and spaces of Carath\'eodory functions where the solutions of the ordinary differential equations depend continuously on the initial data and vector fields. The induced local skew-product flow is proved to be continuous, and a notion of linearized skew-product flow is provided. Two applications are shown. First, the propagation of the exponential dichotomy over the trajectories of the linearized skew-product flow and the structure of the dichotomy or Sacker-Sell spectrum. Second, how particular bounded absorbing sets for the process defined by a Carath\'eodory vector field $f$ provide bounded pullback attractors for the processes with vector fields in the alpha-limit set, the omega-limit set or the whole hull of $f$. Conditions for the existence of a pullback or a global attractor for the skew-product semiflow, as well as application examples are also given.Comment: 34 page