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.

First principles interatomic potential for tungsten based on Gaussian process regression

An accurate description of atomic interactions, such as that provided by first principles quantum mechanics, is fundamental to realistic prediction of the properties that govern plasticity, fracture or crack propagation in metals. However, the computational complexity associated with modern schemes explicitly based on quantum mechanics limits their applications to systems of a few hundreds of atoms at most. This thesis investigates the application of the Gaussian Approximation Potential (GAP) scheme to atomistic modelling of tungsten - a bcc transition metal which exhibits a brittle-to-ductile transition and whose plasticity behaviour is controlled by the properties of $\frac{1}{2} \langle 111 \rangle$ screw dislocations. We apply Gaussian process regression to interpolate the quantum-mechanical (QM) potential energy surface from a set of points in atomic configuration space. Our training data is based on QM information that is computed directly using density functional theory (DFT). To perform the fitting, we represent atomic environments using a set of rotationally, permutationally and reflection invariant parameters which act as the independent variables in our equations of non-parametric, non-linear regression. We develop a protocol for generating GAP models capable of describing lattice defects in metals by building a series of interatomic potentials for tungsten. We then demonstrate that a GAP potential based on a Smooth Overlap of Atomic Positions (SOAP) covariance function provides a description of the $\frac{1}{2} \langle 111 \rangle$ screw dislocation that is in agreement with the DFT model. We use this potential to simulate the mobility of $\frac{1}{2} \langle 111 \rangle$ screw dislocations by computing the Peierls barrier and model dislocation-vacancy interactions to QM accuracy in a system containing more than 100,000 atoms.

MoT - Mixture of trees probabilistic graphical model for video segmentation

We present a novel mixture of trees (MoT) graphical model for video segmentation. Each component in this mixture represents a tree structured temporal linkage between super-pixels from the first to the last frame of a video sequence. Our time-series model explicitly captures the uncertainty in temporal linkage between adjacent frames which improves segmentation accuracy. We provide a variational inference scheme for this model to estimate super-pixel labels and their confidences in nearly realtime. The efficacy of our approach is demonstrated via quantitative comparisons on the challenging SegTrack joint segmentation and tracking dataset [23].

The mean value concept in mono-linear regression of multi-variables and its application to trace studies in geosciences

IEECAS SKLLQG

黄土丘陵沟壑区林地水文生态效应

根据安塞水土保持试验站1993～2002年林地径流小区的降雨产流产沙的定位观测资料及2002年土壤含水量资料,分析了不同树种对坡面尺度降雨产流产沙及土壤水分的影响。结果表明:场降雨径流小区的产流量、产沙量与降雨量具有较好的相关性;多元回归分析表明,场降雨产流量和产沙量与降雨量和最大30min雨强的乘积呈正相关,与植被覆盖度呈负相关,场降雨产沙量回归方程复相关系数为0.253,各处理场降雨产流量回归方程复相关系数的变化范围为0.465～0.723,均达到了极显著的水平(P<0.01)。同时,各树种均具有良好的减流减沙功能,与农地相比,年均产流量和产沙量分别减少4.8%～52.9%和26.8%～86.0%;沙棘纯林及其混交林的减流减沙效益优于油松纯林。同时,沙棘纯林及其各混交林在造林初期就表现出良好的减流减沙效益,随着树龄的增长,其作用更加明显;而油松纯林在造林初期作用不明显,甚至出现产流量和产沙量大于农地的现象,但随着树龄的增长,减流减沙作用逐渐呈现并增大。沙棘纯林及其混交林30cm以下土壤含水量在整个生长季中均呈递减趋势,生长季初(4月份)土壤含水量最高,而生长季末(10月份)降到最低值。2002年沙棘纯林的...

CO2 Flux Estimation by Different Regression Methods from an Alpine Meadow on the Qinghai-Tibetan Plateau

National Key Research and Development Program [2010CB833500]; National Natural Science Foundation of China [30590381]; Chinese Academy of Sciences [KZCX2-YW-432]