Stochastic partition models divide a multi-dimensional space into a number of rectangular regions, such that the data within each region exhibit certain types of homogeneity. Due to the nature of their partition strategy, existing partition models may create many unnecessary divisions in sparse regions when trying to describe data in dense regions. To avoid this problem we introduce a new parsimonious partition model -- the Rectangular Bounding Process (RBP) -- to efficiently partition multi-dimensional spaces, by employing a bounding strategy to enclose data points within rectangular bounding boxes. Unlike existing approaches, the RBP possesses several attractive theoretical properties that make it a powerful nonparametric partition prior on a hypercube. In particular, the RBP is self-consistent and as such can be directly extended from a finite hypercube to infinite (unbounded) space.
We consider the optimization of an uncertain objective over continuous and multi-dimensional decision spaces in problems in which we are only provided with observational data. We propose a novel algorithmic framework that is tractable, asymptotically consistent, and superior to comparable methods on example problems. Our approach leverages predictive machine learning methods and incorporates information on the uncertainty of the predicted outcomes for the purpose of prescribing decisions. We demonstrate the efficacy of our method on examples involving both synthetic and real data sets. Papers published at the Neural Information Processing Systems Conference.
In simple words, information database or IDB is a collection of records or data that is stored in a computer or information system and is used to create and sustain information. Every business does that – variably or invariably. Multidimensional analysis, on the other hand, is a process to analyze data that groups data into two categories: data dimensions and measurements. It takes into account different relationships – each of which represent a separate dimension. For instance, a retail chain owner wants to understand the relationships among sales by the location of its stores in different regions, quarters, demographic distribution such as income and gender, and by product.
We propose representing high-dimensional data in 2-dimensions using cliques mapped onto several planes. Currently, Multidimensional Scaling (MDS) projects every point onto an R space medium. However, this may not produce the most ideal result as some relations between points may exhibit higher stress than others. We propose utilizing cliques to extract a complete subset of points into separate facets in order to convey the most accurate distance representation as possible, therefore achieveing low stress in each instance.