Automatic construction and natural-language description of nonparametric regression models

Copyright © 2014, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. This paper presents the beginnings of an automatic statistician, focusing on regression problems. Our system explores an open-ended space of statistical models to discover a good explanation of a data set, and then produces a detailed report with figures and natural- language text. Our approach treats unknown regression functions non- parametrically using Gaussian processes, which has two important consequences. First, Gaussian processes can model functions in terms of high-level properties (e.g. smoothness, trends, periodicity, changepoints). Taken together with the compositional structure of our language of models this allows us to automatically describe functions in simple terms. Second, the use of flexible nonparametric models and a rich language for composing them in an open-ended manner also results in state- of-the-art extrapolation performance evaluated over 13 real time series data sets from various domains.

Convex relaxation of mixture regression with efficient algorithms

We develop a convex relaxation of maximum a posteriori estimation of a mixture of regression models. Although our relaxation involves a semidefinite matrix variable, we reformulate the problem to eliminate the need for general semidefinite programming. In particular, we provide two reformulations that admit fast algorithms. The first is a max-min spectral reformulation exploiting quasi-Newton descent. The second is a min-min reformulation consisting of fast alternating steps of closed-form updates. We evaluate the methods against Expectation-Maximization in a real problem of motion segmentation from video data.

Energy use of buildings at urban scale: A case study of london school buildings

The diversity of non-domestic buildings at urban scale poses a number of difficulties to develop building stock models. This research proposes an engineering-based bottom-up stock model in a probabilistic manner to address these issues. School buildings are used for illustrating the application of this probabilistic method. Two sampling-based global sensitivity methods are used to identify key factors affecting building energy performance. The sensitivity analysis methods can also create statistical regression models for inverse analysis, which are used to estimate input information for building stock energy models. The effects of different energy saving measures are analysed by changing these building stock input distributions.