3,856 research outputs found
Global and Local Two-Sample Tests via Regression
Two-sample testing is a fundamental problem in statistics. Despite its long
history, there has been renewed interest in this problem with the advent of
high-dimensional and complex data. Specifically, in the machine learning
literature, there have been recent methodological developments such as
classification accuracy tests. The goal of this work is to present a regression
approach to comparing multivariate distributions of complex data. Depending on
the chosen regression model, our framework can efficiently handle different
types of variables and various structures in the data, with competitive power
under many practical scenarios. Whereas previous work has been largely limited
to global tests which conceal much of the local information, our approach
naturally leads to a local two-sample testing framework in which we identify
local differences between multivariate distributions with statistical
confidence. We demonstrate the efficacy of our approach both theoretically and
empirically, under some well-known parametric and nonparametric regression
methods. Our proposed methods are applied to simulated data as well as a
challenging astronomy data set to assess their practical usefulness
On the nonlinear statistics of range image patches
In [A. B. Lee, K. S. Pedersen, and D. Mumford, Int. J. Comput. Vis., 54 (2003), pp. 83–103], the authors study the distributions of 3 × 3 patches from optical images and from range images. In [G. Carlsson, T. Ishkanov, V. de Silva, and A. Zomorodian, Int. J. Comput. Vis., 76 (2008), pp.
1–12], the authors apply computational topological tools to the data set of optical patches studied by Lee, Pedersen, and Mumford and find geometric structures for high density subsets. One high density subset is called the primary circle and essentially consists of patches with a line separating a light and a dark region. In this paper, we apply the techniques of Carlsson et al. to range patches.
By enlarging to 5×5 and 7×7 patches, we find core subsets that have the topology of the primary circle, suggesting a stronger connection between optical patches and range patches than was found by Lee, Pedersen, and Mumford
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