4 research outputs found
Non-linear Causal Inference using Gaussianity Measures
We provide theoretical and empirical evidence for a type of asymmetry between
causes and effects that is present when these are related via linear models
contaminated with additive non-Gaussian noise. Assuming that the causes and the
effects have the same distribution, we show that the distribution of the
residuals of a linear fit in the anti-causal direction is closer to a Gaussian
than the distribution of the residuals in the causal direction. This
Gaussianization effect is characterized by reduction of the magnitude of the
high-order cumulants and by an increment of the differential entropy of the
residuals. The problem of non-linear causal inference is addressed by
performing an embedding in an expanded feature space, in which the relation
between causes and effects can be assumed to be linear. The effectiveness of a
method to discriminate between causes and effects based on this type of
asymmetry is illustrated in a variety of experiments using different measures
of Gaussianity. The proposed method is shown to be competitive with
state-of-the-art techniques for causal inference.Comment: 35 pages, 9 figure
Directional Dependence in the Analysis of Single Subjects
Many statistical methods applied in person-oriented research make use of theoretical principles originally derived in a variable-oriented context. From this perspective, it naturally follows that advances originated in variable-oriented methodology may potentially contribute to the development of methods suitable for person-oriented perspectives. Direction Dependence Analysis (DDA) constitutes one of these recent advances and provides a framework to statistically evaluate asymmetric properties of observed variable relations. These asymmetric properties enable researchers to make statements whether a model of the form x ! y or a model assuming y ! x is more likely to approximate the underlying data-generating process in non-experimental settings. The present article introduces DDA to the context of person-oriented research and extends the DDA principle to (linear) vector autoregressive models (VAR) which can be used to describe individual development. We show that DDA can be used to empirically evaluate directional theories of (potentially multivariate) intraindividual development (e.g., which of two longitudinally observed variables is more likely to be the explanatory variable and which one is more likely to reflect the outcome). An illustrative example is provided from a study on the development of experienced mood and alcohol consumption behavior. It is demonstrated that VAR-DDA resolves the issue of identifying the direction of contemporaneous effects in longitudinal data. Temporality issues of directional theories used to explain intraindividual development, guidelines to achieve acceptable power, methodological requirements, and potential further extensions of DDA for person-oriented research are discussed
Gaussianity measures for detecting the direction of causal time series
We conjecture that the distribution of the time-reversed residuals of a causal linear process is closer to a Gaussian than the distribution of the noise used to generate the process in the forward direction. This property is demonstrated for causal AR(1) processes assuming that all the cumulants of the distribution of the noise are defined. Based on this observation, it is possible to design a decision rule for detecting the direction of time series that can be described as linear processes: The correct direction (forward in time) is the one in which the residuals from a linear fit to the time series are less Gaussian. A series of experiments with simulated and real-world data illustrate the superior results of the proposed rule when compared with other state-of-the-art methods based on independence tests