15 research outputs found
Causal discovery with general non-linear relationships using non-linear ICA
We consider the problem of inferring causal relationships between two or more passively observed variables. While the problem of such causal discovery has been extensively studied, especially in the bivariate setting, the majority of current methods assume a linear causal relationship, and the few methods which consider non-linear relations usually make the assumption of additive noise. Here, we propose a framework through which we can perform causal discovery in the presence of general non-linear relationships. The proposed method is based on recent progress in non-linear independent component analysis (ICA) and exploits the non-stationarity of observations in order to recover the underlying sources. We show rigorously that in the case of bivariate causal discovery, such non-linear ICA can be used to infer causal direction via a series of independence tests. We further propose an alternative measure for inferring causal direction based on asymptotic approximations to the likelihood ratio, as well as an extension to multivariate causal discovery. We demonstrate the capabilities of the proposed method via a series of simulation studies and conclude with an application to neuroimaging data
Meta Learning for Causal Direction
The inaccessibility of controlled randomized trials due to inherent
constraints in many fields of science has been a fundamental issue in causal
inference. In this paper, we focus on distinguishing the cause from effect in
the bivariate setting under limited observational data. Based on recent
developments in meta learning as well as in causal inference, we introduce a
novel generative model that allows distinguishing cause and effect in the small
data setting. Using a learnt task variable that contains distributional
information of each dataset, we propose an end-to-end algorithm that makes use
of similar training datasets at test time. We demonstrate our method on various
synthetic as well as real-world data and show that it is able to maintain high
accuracy in detecting directions across varying dataset sizes
Independent Component Analysis for Binary Data
Independent Component Analysis (ICA) aims to separate the observed signals into their underlying independent components responsible for generating the observations. Most research in ICA has focused on continuous signals, while the methodology for binary and discrete signals is less developed. Yet, binary observations are equally present in various fields and applications, such as causal discovery, signal processing, and bioinformatics. In the last decade, Boolean OR and XOR mixtures have been shown to be identifiable by ICA, but such models suffer from limited expressivity, calling for new methods to solve the problem.
In this thesis, "Independent Component Analysis for Binary Data", we estimate the mixing matrix of ICA from binary observations and an additionally observed auxiliary variable by employing a linear model inspired by the Identifiable Variational Autoencoder (iVAE), which exploits the non-stationarity of the data. The model is optimized with a gradient-based algorithm that uses second-order optimization with limited memory, resulting in a training time in the order of seconds for the particular study cases.
We investigate which conditions can lead to the reconstruction of the mixing matrix, concluding that the method is able to identify the mixing matrix when the number of observed variables is greater than the number of sources. In such cases, the linear binary iVAE can reconstruct the mixing matrix up to order and scale indeterminacies, which are considered in the evaluation with the Mean Cosine Similarity Score. Furthermore, the model can reconstruct the mixing matrix even under a limited sample size. Therefore, this work demonstrates the potential for applications in real-world data and also offers a possibility to study and formalize identifiability in future work.
In summary, the most important contributions of this thesis are the empirical study of the conditions that enable the mixing matrix reconstruction using the binary iVAE, and the empirical results on the performance and efficiency of the model. The latter was achieved through a new combination of existing methods, including modifications and simplifications of a linear binary iVAE model and the optimization of such a model under limited computational resources