100,165 research outputs found
High-Dimensional Dependency Structure Learning for Physical Processes
In this paper, we consider the use of structure learning methods for
probabilistic graphical models to identify statistical dependencies in
high-dimensional physical processes. Such processes are often synthetically
characterized using PDEs (partial differential equations) and are observed in a
variety of natural phenomena, including geoscience data capturing atmospheric
and hydrological phenomena. Classical structure learning approaches such as the
PC algorithm and variants are challenging to apply due to their high
computational and sample requirements. Modern approaches, often based on sparse
regression and variants, do come with finite sample guarantees, but are usually
highly sensitive to the choice of hyper-parameters, e.g., parameter
for sparsity inducing constraint or regularization. In this paper, we present
ACLIME-ADMM, an efficient two-step algorithm for adaptive structure learning,
which estimates an edge specific parameter in the first step,
and uses these parameters to learn the structure in the second step. Both steps
of our algorithm use (inexact) ADMM to solve suitable linear programs, and all
iterations can be done in closed form in an efficient block parallel manner. We
compare ACLIME-ADMM with baselines on both synthetic data simulated by partial
differential equations (PDEs) that model advection-diffusion processes, and
real data (50 years) of daily global geopotential heights to study information
flow in the atmosphere. ACLIME-ADMM is shown to be efficient, stable, and
competitive, usually better than the baselines especially on difficult
problems. On real data, ACLIME-ADMM recovers the underlying structure of global
atmospheric circulation, including switches in wind directions at the equator
and tropics entirely from the data.Comment: 21 pages, 8 figures, International Conference on Data Mining 201
Detecting and quantifying causal associations in large nonlinear time series datasets
Identifying causal relationships and quantifying their strength from observational time series data are key problems in disciplines dealing with complex dynamical systems such as the Earth system or the human body. Data-driven causal inference in such systems is challenging since datasets are often high dimensional and nonlinear with limited sample sizes. Here, we introduce a novel method that flexibly combines linear or nonlinear conditional independence tests with a causal discovery algorithm to estimate causal networks from large-scale time series datasets. We validate the method on time series of well-understood physical mechanisms in the climate system and the human heart and using large-scale synthetic datasets mimicking the typical properties of real-world data. The experiments demonstrate that our method outperforms state-of-the-art techniques in detection power, which opens up entirely new possibilities to discover and quantify causal networks from time series across a range of research fields
Linear State-Space Model with Time-Varying Dynamics
This paper introduces a linear state-space model with time-varying dynamics.
The time dependency is obtained by forming the state dynamics matrix as a
time-varying linear combination of a set of matrices. The time dependency of
the weights in the linear combination is modelled by another linear Gaussian
dynamical model allowing the model to learn how the dynamics of the process
changes. Previous approaches have used switching models which have a small set
of possible state dynamics matrices and the model selects one of those matrices
at each time, thus jumping between them. Our model forms the dynamics as a
linear combination and the changes can be smooth and more continuous. The model
is motivated by physical processes which are described by linear partial
differential equations whose parameters vary in time. An example of such a
process could be a temperature field whose evolution is driven by a varying
wind direction. The posterior inference is performed using variational Bayesian
approximation. The experiments on stochastic advection-diffusion processes and
real-world weather processes show that the model with time-varying dynamics can
outperform previously introduced approaches.Comment: The final publication is available at Springer via
http://dx.doi.org/10.1007/978-3-662-44851-9_2
Decomposing feature-level variation with Covariate Gaussian Process Latent Variable Models
The interpretation of complex high-dimensional data typically requires the
use of dimensionality reduction techniques to extract explanatory
low-dimensional representations. However, in many real-world problems these
representations may not be sufficient to aid interpretation on their own, and
it would be desirable to interpret the model in terms of the original features
themselves. Our goal is to characterise how feature-level variation depends on
latent low-dimensional representations, external covariates, and non-linear
interactions between the two. In this paper, we propose to achieve this through
a structured kernel decomposition in a hybrid Gaussian Process model which we
call the Covariate Gaussian Process Latent Variable Model (c-GPLVM). We
demonstrate the utility of our model on simulated examples and applications in
disease progression modelling from high-dimensional gene expression data in the
presence of additional phenotypes. In each setting we show how the c-GPLVM can
extract low-dimensional structures from high-dimensional data sets whilst
allowing a breakdown of feature-level variability that is not present in other
commonly used dimensionality reduction approaches
Optimal Reinforcement Learning for Gaussian Systems
The exploration-exploitation trade-off is among the central challenges of
reinforcement learning. The optimal Bayesian solution is intractable in
general. This paper studies to what extent analytic statements about optimal
learning are possible if all beliefs are Gaussian processes. A first order
approximation of learning of both loss and dynamics, for nonlinear,
time-varying systems in continuous time and space, subject to a relatively weak
restriction on the dynamics, is described by an infinite-dimensional partial
differential equation. An approximate finite-dimensional projection gives an
impression for how this result may be helpful.Comment: final pre-conference version of this NIPS 2011 paper. Once again,
please note some nontrivial changes to exposition and interpretation of the
results, in particular in Equation (9) and Eqs. 11-14. The algorithm and
results have remained the same, but their theoretical interpretation has
change
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