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Abstract Many real-world decision-making tasks require learning causal relationships between a set of variables. Traditional causal discovery methods, however, require that all variables are observed, which is often not feasible in practical scenarios. Without additional assumptions about the unobserved variables, it is not possible to recover any causal relationships from observational data. Fortunately, in many applied settings, additional structure among the confounders can be expected. In particular, pervasive confounding is commonly encountered and has been utilised for consistent causal estimation in linear causal models. In this article, we present a provably consistent method to estimate causal relationships in the nonlinear, pervasive confounding setting. The core of our procedure relies on the ability to estimate the confounding variation through a simple spectral decomposition of the observed data matrix. We derive a DAG score function based on this insight, prove its consistency in recovering a correct ordering of the DAG, and empirically compare it to previous approaches. We demonstrate improved performance on both simulated and real datasets by explicitly accounting for both confounders and nonlinear effects.
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Heating and cooling in self-consistent many-body simulations
We present a temperature-extrapolation technique for self-consistent many-body methods, which provides a causal starting point for converging to a solution at a target temperature. The technique employs the Carathéodory formalism for interpolating causal matrix-valued functions and is applicable to various many-body methods, including dynamical mean-field theory, its cluster extensions, and self-consistent perturbative methods such as the self-consistent GW approximation. We show results that demonstrate that this technique can efficiently simulate heating and cooling hysteresis at a first-order phase transition, as well as accelerate convergence.
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- Award ID(s):
- 2001465
- PAR ID:
- 10552764
- Publisher / Repository:
- American Physical Society
- Date Published:
- Journal Name:
- Physical Review B
- Volume:
- 108
- Issue:
- 15
- ISSN:
- 2469-9950
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1103/PhysRevB.108.155116
