Nonparanormal Structural VAR for Non-Gaussian Data

Dallakyan, Aramayis

doi:10.1007/s10614-020-10009-1

Cited by 1 publication

(4 citation statements)

References 28 publications

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“…The knowledge of the ordering among contemporaneous error terms is used for the estimation of the impulse response functions (for details, see [4,Section 2]). [46], [47] exploit PC algorithm for Gaussian data and [4], [5], [48] propose methods for non-Gaussian data to learn the contemporaneous ordering. [49], [50] propose methods for settings with unmeasured confounding.…”

Section: Macro-economic Applicationmentioning

confidence: 99%

“…[49], [50] propose methods for settings with unmeasured confounding. Algorithm 1 in [5] summarizes steps on the use of DAGs for the SVAR estimation. We iterate it in Algorithm 6 by incorporating the RRCF step in line 7 to recover the ordering of error terms.…”

Section: Macro-economic Applicationmentioning

confidence: 99%

“…It is a puzzle since an increase in the federal funds is expected to be followed by a decrease in the price level rather than an increase (See Figure 4a). [5] showed that utilization of the recent DAG techniques to recover the ordering of error terms in VAR mitigates the price puzzle problem. Here, we show that using the sparse VAR approach and RRCF algorithm to recover the DAG structure of error terms leads to the complete disappearance of the price puzzle (See Figure 4b).…”

Section: Macro-economic Applicationmentioning

confidence: 99%

“…B AYESIAN Networks (BNs) are a popular class of graphical models whose structure is represented by a DAG G. BNs have been used in many applications such as economics, finance, biology, etc [1]- [5]. In recent years the following two approaches have been evolved to learn the structure of the underlying DAG from data: Independencebased (also called constraint-based) methods [6], [7] and score-based methods [8]- [11].…”

Section: Introductionmentioning

confidence: 99%

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Learning Bayesian Networks through Birkhoff Polytope: A Relaxation Method

Dallakyan¹,

Pourahmadi²

2021

Preprint

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We establish a novel framework for learning a directed acyclic graph (DAG) when data are generated from a Gaussian, linear structural equation model. It consists of two parts: (1) introduce a permutation matrix as a new parameter within a regularized Gaussian log-likelihood to represent variable ordering; and (2) given the ordering, estimate the DAG structure through sparse Cholesky factor of the inverse covariance matrix. For permutation matrix estimation, we propose a relaxation technique that avoids the NP-hard combinatorial problem of order estimation. Given an ordering, a sparse Cholesky factor is estimated using a cyclic coordinatewise descent algorithm which decouples row-wise. Our framework recovers DAGs without the need for an expensive verification of the acyclicity constraint or enumeration of possible parent sets. We establish numerical convergence of the algorithm, and consistency of the Cholesky factor estimator when the order of variables is known. Through several simulated and macro-economic datasets, we study the scope and performance of the proposed methodology.

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