18 research outputs found
Causal Inference by Identification of Vector Autoregressive Processes with Hidden Components
A widely applied approach to causal inference from a non-experimental time
series , often referred to as "(linear) Granger causal analysis", is to
regress present on past and interpret the regression matrix causally.
However, if there is an unmeasured time series that influences , then
this approach can lead to wrong causal conclusions, i.e., distinct from those
one would draw if one had additional information such as . In this paper we
take a different approach: We assume that together with some hidden
forms a first order vector autoregressive (VAR) process with transition matrix
, and argue why it is more valid to interpret causally instead of
. Then we examine under which conditions the most important parts of
are identifiable or almost identifiable from only . Essentially,
sufficient conditions are (1) non-Gaussian, independent noise or (2) no
influence from to . We present two estimation algorithms that are
tailored towards conditions (1) and (2), respectively, and evaluate them on
synthetic and real-world data. We discuss how to check the model using
Identifying Nonlinear 1-Step Causal Influences in Presence of Latent Variables
We propose an approach for learning the causal structure in stochastic
dynamical systems with a -step functional dependency in the presence of
latent variables. We propose an information-theoretic approach that allows us
to recover the causal relations among the observed variables as long as the
latent variables evolve without exogenous noise. We further propose an
efficient learning method based on linear regression for the special sub-case
when the dynamics are restricted to be linear. We validate the performance of
our approach via numerical simulations
Learning Temporal Dependence from Time-Series Data with Latent Variables
We consider the setting where a collection of time series, modeled as random
processes, evolve in a causal manner, and one is interested in learning the
graph governing the relationships of these processes. A special case of wide
interest and applicability is the setting where the noise is Gaussian and
relationships are Markov and linear. We study this setting with two additional
features: firstly, each random process has a hidden (latent) state, which we
use to model the internal memory possessed by the variables (similar to hidden
Markov models). Secondly, each variable can depend on its latent memory state
through a random lag (rather than a fixed lag), thus modeling memory recall
with differing lags at distinct times. Under this setting, we develop an
estimator and prove that under a genericity assumption, the parameters of the
model can be learned consistently. We also propose a practical adaption of this
estimator, which demonstrates significant performance gains in both synthetic
and real-world datasets
Online Joint Topology Identification and Signal Estimation with Inexact Proximal Online Gradient Descent
Identifying the topology that underlies a set of time series is useful for
tasks such as prediction, denoising, and data completion. Vector autoregressive
(VAR) model based topologies capture dependencies among time series, and are
often inferred from observed spatio-temporal data. When the data are affected
by noise and/or missing samples, the tasks of topology identification and
signal recovery (reconstruction) have to be performed jointly. Additional
challenges arise when i) the underlying topology is time-varying, ii) data
become available sequentially, and iii) no delay is tolerated. To overcome
these challenges, this paper proposes two online algorithms to estimate the VAR
model-based topologies. The proposed algorithms have constant complexity per
iteration, which makes them interesting for big data scenarios. They also enjoy
complementary merits in terms of complexity and performance. A performance
guarantee is derived for one of the algorithms in the form of a dynamic regret
bound. Numerical tests are also presented, showcasing the ability of the
proposed algorithms to track the time-varying topologies with missing data in
an online fashion.Comment: 14 pages including supplementary material, 2 figures, submitted to
IEEE Transactions on Signal Processin