# Identifying General Mechanism Shifts in Linear Causal Representations

arXiv: https://arxiv.org/abs/2410.24059 · HTML: https://mlsanity.com/paper/2410.24059/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 50 references that are in the map.
- First posted on arXiv 31 Oct 2024.

## Builds on (most cited first, 21 of 21)

- [Domain Generalization via Invariant Feature Representation](https://mlsanity.com/paper/1301.2115/) (2013)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [Understanding disentangling in β-VAE](https://mlsanity.com/paper/1804.03599/) (2018)
- [Domain Adaptation by Using Causal Inference to Predict Invariant Conditional Distributions](https://mlsanity.com/paper/1707.06422/) (2017)
- [Nonparametric Identifiability of Causal Representations from Unknown Interventions](https://mlsanity.com/paper/2306.00542/) (2023)
- [Linear Causal Disentanglement via Interventions](https://mlsanity.com/paper/2211.16467/) (2022)
- [Desiderata for Representation Learning: A Causal Perspective](https://mlsanity.com/paper/2109.03795/) (2021)
- [Causal Discovery with General Non-Linear Relationships Using Non-Linear ICA](https://mlsanity.com/paper/1904.09096/) (2019)
- [Score-based Causal Representation Learning with Interventions](https://mlsanity.com/paper/2301.08230/) (2023)
- [Causal Discovery with Score Matching on Additive Models with Arbitrary Noise](https://mlsanity.com/paper/2304.03265/) (2023)
- [Why did the distribution change?](https://mlsanity.com/paper/2102.13384/) (2021)
- [Learning nonparametric latent causal graphs with unknown interventions](https://mlsanity.com/paper/2306.02899/) (2023)
- [General Identifiability and Achievability for Causal Representation Learning](https://mlsanity.com/paper/2310.15450/) (2023)
- [Unpaired Multi-Domain Causal Representation Learning](https://mlsanity.com/paper/2302.00993/) (2023)
- [Feature Shift Detection: Localizing Which Features Have Shifted via Conditional Distribution Tests](https://mlsanity.com/paper/2107.06929/) (2021)
- [Causal Mosaic: Cause-Effect Inference via Nonlinear ICA and Ensemble Method](https://mlsanity.com/paper/2001.01894/) (2020)
- [Learning Causal Representations from General Environments: Identifiability and Intrinsic Ambiguity](https://mlsanity.com/paper/2311.12267/) (2023)
- [Direct Estimation of Differences in Causal Graphs](https://mlsanity.com/paper/1802.05631/) (2018)
- [Large Dimensional Independent Component Analysis: Statistical Optimality and Computational Tractability](https://mlsanity.com/paper/2303.18156/) (2023)
- [Learning DAGs from Data with Few Root Causes](https://mlsanity.com/paper/2305.15936/) (2023)
- [Direct Learning with Guarantees of the Difference DAG Between Structural Equation Models](https://mlsanity.com/paper/1906.12024/) (2019)

## Built on by (most cited first, 4 of 4)

- [Towards Interpretable Deep Generative Models via Causal Representation Learning](https://mlsanity.com/paper/2504.11609/) (2025)
- [Sanity Checking Causal Representation Learning on a Simple Real-World System](https://mlsanity.com/paper/2502.20099/) (2025)
- [Detecting Changes in Causal Dependence with Kernels and Copulas](https://mlsanity.com/paper/2605.05809/) (2026)
- [Concept Drift from a Causal Perspective](https://mlsanity.com/paper/2609.25340/) (2026)

## Abstract (arXiv)

We consider the linear causal representation learning setting where we observe a linear mixing of d unknown latent factors, which follow a linear structural causal model. Recent work has shown that it is possible to recover the latent factors as well as the underlying structural causal model over them, up to permutation and scaling, provided that we have at least d environments, each of which corresponds to perfect interventions on a single latent node (factor). After this powerful result, a key open problem faced by the community has been to relax these conditions: allow for coarser than perfect single-node interventions, and allow for fewer than d of them, since the number of latent factors d could be very large. In this work, we consider precisely such a setting, where we allow a smaller than d number of environments, and also allow for very coarse interventions that can very coarsely textitchange the entire causal graph over the latent factors. On the flip side, we relax what we wish to extract to simply the textitlist of nodes that have shifted between one or more environments. We provide a surprising identifiability result that it is indeed possible, under some very mild standard assumptions, to identify the set of shifted nodes. Our identifiability proof moreover is a constructive one: we explicitly provide necessary and sufficient conditions for a node to be a shifted node, and show that we can check these conditions given observed data. Our algorithm lends itself very naturally to the sample setting where instead of just interventional distributions, we are provided datasets of samples from each of these distributions. We corroborate our results on both synthetic experiments as well as an interesting psychometric dataset. The code can be found at https://github.com/TianyuCodings/iLCS.