Estimation of a Structural Vector Autoregression Model Using Non-Gaussianity

By Aapo Hyvärinen, Kun Zhang, Shohei Shimizu, Patrik O. Hoyer. 2010

466 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Cognitive Neuroscience, Computational Theory and Mathematics

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Citations in the corpus

Causal Discovery from Heterogeneous/Nonstationary Data (2019, background): “In many scenarios, e.g., dynamic systems with insuﬃcient time resolution, there may exist both instantaneous and time-lagged causal relationships over the measured data (Hyv¨arinen et al., 2010; Gong* et al., 2015).”
Specific and Shared Causal Relation Modeling and Mechanism-Based Clustering (2019, methodology): “Next, thanks to the identifiability of independent component analysis-based models [7, 32], we can show that in each group, instantaneous causal relations bij and lagged causal relations aij,p are identifiable [21].”
A Survey of Learning Causality with Data (2018, background): “One step further, Post-nonlinear Models expand the functional space with non-linear relations between the variables and the noise [163].”
Causal Discovery and Forecasting in Nonstationary Environments with State-Space Models (2019, methodology): “…that some causal interactions occur in the same time period, and thus it is important to consider contemporaneous causal relations, especially in time series with low temporal resolutions (Hyvärinen et al., 2010; Gong* et al., 2015), in aggregated data (Gong et al., 2017), or in equilibrium data.”
Identifiability and estimation of structural vector autoregressive models for subsampled and mixed-frequency time series. (2017, methodology): “Assumption A4 is common in SVAR models due to the inherent non-identifiability between scaling the etjs and scaling the columns of C. Assumption A5 is mild, and contains the more restrictive assumptions in non-Gaussian SVAR models (necessary to infer the instantaneous structural DAG [25]), that C ma”
Identification of Time-Dependent Causal Model: A Gaussian Process Treatment (2015, methodology): “For low time resolution data, it is important to consider the instantaneous causal influence, and [Hyvärinen et al., 2010] demonstrated that neglecting it might lead to misleading interpretations of causal relations.”
Causal Discovery from Subsampled Time Series Data by Constraint Optimization (2016, background): “…1980)) or combine a model of measurement timescale transitions with so-called “instantaneous” or “contemporaneous” causal relations that (are supposed to) capture any interactions that are faster than the measurement process (e.g., SVAR) (Lütkepohl, 2005; Hamilton, 1994; Hyvärinen et al., 2010).”
Multi-scale Graphical Models for Spatio-Temporal Processes (2014, background): “These implicitly assume that all dynamics and interactions occur at similar time-scales and are acquired at the same frequency [14], although VAR models for data at different sampling rates have also been proposed [2].”
Granger Causality: A Review and Recent Advances (2021, methodology): “When the errors, e t , are non-Gaussian, both the causal ordering and instantaneous eﬀects C may be inferred directly from the data using techniques from independent component analysis (Hyv¨arinen et al., 2010).”
DYNOTEARS: Structure Learning from Time-Series Data (2020, methodology): “The two hyperparameters of the time-series version of LiNGAM are the weight thresholds τ W and τ A , which we include for comparability with the other algorithms.”
GMM Estimation of Non-Gaussian Structural Vector Autoregression (2019, unknown): “Similar results have been put forth in the related literature by Hyv¨arinen et al. (2010), and Moneta et al. (2013), inter alia, but they all assume ε t to be an independent and identically distributed process (instead of being just serially uncorrelated).”
Bayesian nonparametric vector autoregressive models (2018, unknown): “They are used in regression to estimate the conditional density p(y|x) of a univariate y for all values of a (often, high-dimensional) covariate x, using mixtures where the component weights depend on a x, see Jacobs et al. (1991), Jordan and Jacobs (1994), Geweke and Keane (2007) and Villani et al.”
Causal Inference by Identification of Vector Autoregressive Processes with Hidden Components (2014, background): “Harnessing non-Gaussian noise for causal inference: The paper (Hyvaerinen et al., 2010) uses non-Gaussian noise to infer instantaneous effects.”
A Survey of Learning Causality with Data: Problems and Methods (2018, background): “For example, an auto-regressive LiNGAM is proposed to learn causal relationships [64].”
Pairwise Likelihood Ratios for Estimation of Non-Gaussian Structural Equation Models (2013, background): “The likelihood of the LiNGAM in which x → y was given by Hyvärinen et al. (2010) as log L(x → y) = ∑ t G x (x t ) + G d ( y t − ρx t 1 − ρ 2 ) − T log(1 − ρ 2 ) where G x (u) = log p x (u), and G d is the standardized log-pdf of the residual when regressing y on x.”
DirectLiNGAM: A Direct Method for Learning a Linear Non-Gaussian Structural Equation Model (2011, methodology): “Then we have two options to do further analysis [9]: i) Find significant directed edges or direct causal effects bij and significant total causal effects aij with A=(I−B) ; ii) Estimate redundant directed edges to find the underlying DAG.”