16,778 research outputs found
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
Graphical Modeling for Multivariate Hawkes Processes with Nonparametric Link Functions
Hawkes (1971) introduced a powerful multivariate point process model of
mutually exciting processes to explain causal structure in data. In this paper
it is shown that the Granger causality structure of such processes is fully
encoded in the corresponding link functions of the model. A new nonparametric
estimator of the link functions based on a time-discretized version of the
point process is introduced by using an infinite order autoregression.
Consistency of the new estimator is derived. The estimator is applied to
simulated data and to neural spike train data from the spinal dorsal horn of a
rat.Comment: 20 pages, 4 figure
Learning why things change: The Difference-Based Causality Learner
In this paper, we present the Difference-Based Causality Learner (DBCL), an algorithm for learning a class of discrete-time dynamic models that represents all causation across time by means of difference equations driving change in a system. We motivate this representation with real-world mechanical systems and prove DBCL's correctness for learning structure from time series data, an endeavour that is complicated by the existence of latent derivatives that have to be detected. We also prove that, under common assumptions for causal discovery, DBCL will identify the presence or absence of feedback loops, making the model more useful for predicting the effects of manipulating variables when the system is in equilibrium. We argue analytically and show empirically the advantages of DBCL over vector autoregression (VAR) and Granger causality models as well as modified forms of Bayesian and constraintbased structure discovery algorithms. Finally, we show that our algorithm can discover causal directions of alpha rhythms in human brains from EEG data
Learning causal models that make correct manipulation predictions with time series data
One of the fundamental purposes of causal models is using them to predict the effects of manipulating various components of a system. It has been argued by Dash (2005, 2003) that the Do operator will fail when applied to an equilibrium model, unless the underlying dynamic system obeys what he calls Equilibration-Manipulation Commutability. Unfortunately, this fact renders most existing causal discovery algorithms unreliable for reasoning about manipulations. Motivated by this caveat, in this paper we present a novel approach to causal discovery of dynamic models from time series. The approach uses a representation of dynamic causal models motivated by Iwasaki and Simon (1994), which asserts that all ācausation across time" occurs because a variableās derivative has been affected instantaneously. We present an algorithm that exploits this representation within a constraint-based learning framework by numerically calculating derivatives and learning instantaneous relationships. We argue that due to numerical errors in higher order derivatives, care must be taken when learning causal structure, but we show that the Iwasaki-Simon representation reduces the search space considerably, allowing us to forego calculating many high-order derivatives. In order for our algorithm to discover the dynamic model, it is necessary that the time-scale of the data is much finer than any temporal process of the system. Finally, we show that our approach can correctly recover the structure of a fairly complex dynamic system, and can predict the effect of manipulations accurately when a manipulation does not cause an instability. To our knowledge, this is the first causal discovery algorithm that has demonstrated that it can correctly predict the effects of manipulations for a system that does not obey the EMC condition
Causal inference using the algorithmic Markov condition
Inferring the causal structure that links n observables is usually based upon
detecting statistical dependences and choosing simple graphs that make the
joint measure Markovian. Here we argue why causal inference is also possible
when only single observations are present.
We develop a theory how to generate causal graphs explaining similarities
between single objects. To this end, we replace the notion of conditional
stochastic independence in the causal Markov condition with the vanishing of
conditional algorithmic mutual information and describe the corresponding
causal inference rules.
We explain why a consistent reformulation of causal inference in terms of
algorithmic complexity implies a new inference principle that takes into
account also the complexity of conditional probability densities, making it
possible to select among Markov equivalent causal graphs. This insight provides
a theoretical foundation of a heuristic principle proposed in earlier work.
We also discuss how to replace Kolmogorov complexity with decidable
complexity criteria. This can be seen as an algorithmic analog of replacing the
empirically undecidable question of statistical independence with practical
independence tests that are based on implicit or explicit assumptions on the
underlying distribution.Comment: 16 figure
Online Causal Structure Learning in the Presence of Latent Variables
We present two online causal structure learning algorithms which can track
changes in a causal structure and process data in a dynamic real-time manner.
Standard causal structure learning algorithms assume that causal structure does
not change during the data collection process, but in real-world scenarios, it
does often change. Therefore, it is inappropriate to handle such changes with
existing batch-learning approaches, and instead, a structure should be learned
in an online manner. The online causal structure learning algorithms we present
here can revise correlation values without reprocessing the entire dataset and
use an existing model to avoid relearning the causal links in the prior model,
which still fit data. Proposed algorithms are tested on synthetic and
real-world datasets, the latter being a seasonally adjusted commodity price
index dataset for the U.S. The online causal structure learning algorithms
outperformed standard FCI by a large margin in learning the changed causal
structure correctly and efficiently when latent variables were present.Comment: 16 pages, 9 figures, 2 table
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