تقرير
Inference via low-dimensional couplings
| العنوان: | Inference via low-dimensional couplings |
|---|---|
| المؤلفون: | Spantini, Alessio, Bigoni, Daniele, Marzouk, Youssef |
| المصدر: | Journal of Machine Learning Research, volume 19 (66): 1-71, 2018 |
| سنة النشر: | 2017 |
| المجموعة: | Statistics |
| مصطلحات موضوعية: | Statistics - Methodology, Statistics - Computation, Statistics - Machine Learning |
| الوصف: | We investigate the low-dimensional structure of deterministic transformations between random variables, i.e., transport maps between probability measures. In the context of statistics and machine learning, these transformations can be used to couple a tractable "reference" measure (e.g., a standard Gaussian) with a target measure of interest. Direct simulation from the desired measure can then be achieved by pushing forward reference samples through the map. Yet characterizing such a map---e.g., representing and evaluating it---grows challenging in high dimensions. The central contribution of this paper is to establish a link between the Markov properties of the target measure and the existence of low-dimensional couplings, induced by transport maps that are sparse and/or decomposable. Our analysis not only facilitates the construction of transformations in high-dimensional settings, but also suggests new inference methodologies for continuous non-Gaussian graphical models. For instance, in the context of nonlinear state-space models, we describe new variational algorithms for filtering, smoothing, and sequential parameter inference. These algorithms can be understood as the natural generalization---to the non-Gaussian case---of the square-root Rauch-Tung-Striebel Gaussian smoother. Comment: 78 pages, 25 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1703.06131 |
| رقم الأكسشن: | edsarx.1703.06131 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |