165,465 research outputs found
Invariant Causal Prediction for Nonlinear Models
An important problem in many domains is to predict how a system will respond
to interventions. This task is inherently linked to estimating the system's
underlying causal structure. To this end, Invariant Causal Prediction (ICP)
(Peters et al., 2016) has been proposed which learns a causal model exploiting
the invariance of causal relations using data from different environments. When
considering linear models, the implementation of ICP is relatively
straightforward. However, the nonlinear case is more challenging due to the
difficulty of performing nonparametric tests for conditional independence. In
this work, we present and evaluate an array of methods for nonlinear and
nonparametric versions of ICP for learning the causal parents of given target
variables. We find that an approach which first fits a nonlinear model with
data pooled over all environments and then tests for differences between the
residual distributions across environments is quite robust across a large
variety of simulation settings. We call this procedure "invariant residual
distribution test". In general, we observe that the performance of all
approaches is critically dependent on the true (unknown) causal structure and
it becomes challenging to achieve high power if the parental set includes more
than two variables. As a real-world example, we consider fertility rate
modelling which is central to world population projections. We explore
predicting the effect of hypothetical interventions using the accepted models
from nonlinear ICP. The results reaffirm the previously observed central causal
role of child mortality rates
Mining Heterogeneous Multivariate Time-Series for Learning Meaningful Patterns: Application to Home Health Telecare
For the last years, time-series mining has become a challenging issue for
researchers. An important application lies in most monitoring purposes, which
require analyzing large sets of time-series for learning usual patterns. Any
deviation from this learned profile is then considered as an unexpected
situation. Moreover, complex applications may involve the temporal study of
several heterogeneous parameters. In that paper, we propose a method for mining
heterogeneous multivariate time-series for learning meaningful patterns. The
proposed approach allows for mixed time-series -- containing both pattern and
non-pattern data -- such as for imprecise matches, outliers, stretching and
global translating of patterns instances in time. We present the early results
of our approach in the context of monitoring the health status of a person at
home. The purpose is to build a behavioral profile of a person by analyzing the
time variations of several quantitative or qualitative parameters recorded
through a provision of sensors installed in the home
Self-Similar Anisotropic Texture Analysis: the Hyperbolic Wavelet Transform Contribution
Textures in images can often be well modeled using self-similar processes
while they may at the same time display anisotropy. The present contribution
thus aims at studying jointly selfsimilarity and anisotropy by focusing on a
specific classical class of Gaussian anisotropic selfsimilar processes. It will
first be shown that accurate joint estimates of the anisotropy and
selfsimilarity parameters are performed by replacing the standard 2D-discrete
wavelet transform by the hyperbolic wavelet transform, which permits the use of
different dilation factors along the horizontal and vertical axis. Defining
anisotropy requires a reference direction that needs not a priori match the
horizontal and vertical axes according to which the images are digitized, this
discrepancy defines a rotation angle. Second, we show that this rotation angle
can be jointly estimated. Third, a non parametric bootstrap based procedure is
described, that provides confidence interval in addition to the estimates
themselves and enables to construct an isotropy test procedure, that can be
applied to a single texture image. Fourth, the robustness and versatility of
the proposed analysis is illustrated by being applied to a large variety of
different isotropic and anisotropic self-similar fields. As an illustration, we
show that a true anisotropy built-in self-similarity can be disentangled from
an isotropic self-similarity to which an anisotropic trend has been
superimposed
Intermittent process analysis with scattering moments
Scattering moments provide nonparametric models of random processes with
stationary increments. They are expected values of random variables computed
with a nonexpansive operator, obtained by iteratively applying wavelet
transforms and modulus nonlinearities, which preserves the variance. First- and
second-order scattering moments are shown to characterize intermittency and
self-similarity properties of multiscale processes. Scattering moments of
Poisson processes, fractional Brownian motions, L\'{e}vy processes and
multifractal random walks are shown to have characteristic decay. The
Generalized Method of Simulated Moments is applied to scattering moments to
estimate data generating models. Numerical applications are shown on financial
time-series and on energy dissipation of turbulent flows.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1276 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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